Class Calib3d

java.lang.Object
org.opencv.calib3d.Calib3d

public class Calib3d
extends Object
  • Field Details

  • Constructor Details

  • Method Details

    • Rodrigues

      public static void Rodrigues​(Mat src, Mat dst, Mat jacobian)
      Converts a rotation matrix to a rotation vector or vice versa.
      Parameters:
      src - Input rotation vector (3x1 or 1x3) or rotation matrix (3x3).
      dst - Output rotation matrix (3x3) or rotation vector (3x1 or 1x3), respectively.
      jacobian - Optional output Jacobian matrix, 3x9 or 9x3, which is a matrix of partial derivatives of the output array components with respect to the input array components. \(\begin{array}{l} \theta \leftarrow norm(r) \\ r \leftarrow r/ \theta \\ R = \cos(\theta) I + (1- \cos{\theta} ) r r^T + \sin(\theta) \vecthreethree{0}{-r_z}{r_y}{r_z}{0}{-r_x}{-r_y}{r_x}{0} \end{array}\) Inverse transformation can be also done easily, since \(\sin ( \theta ) \vecthreethree{0}{-r_z}{r_y}{r_z}{0}{-r_x}{-r_y}{r_x}{0} = \frac{R - R^T}{2}\) A rotation vector is a convenient and most compact representation of a rotation matrix (since any rotation matrix has just 3 degrees of freedom). The representation is used in the global 3D geometry optimization procedures like REF: calibrateCamera, REF: stereoCalibrate, or REF: solvePnP . Note: More information about the computation of the derivative of a 3D rotation matrix with respect to its exponential coordinate can be found in:
      • A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates, Guillermo Gallego, Anthony J. Yezzi CITE: Gallego2014ACF
      Note: Useful information on SE(3) and Lie Groups can be found in:
      • A tutorial on SE(3) transformation parameterizations and on-manifold optimization, Jose-Luis Blanco CITE: blanco2010tutorial
      • Lie Groups for 2D and 3D Transformation, Ethan Eade CITE: Eade17
      • A micro Lie theory for state estimation in robotics, Joan Solà, Jérémie Deray, Dinesh Atchuthan CITE: Sol2018AML
    • Rodrigues

      public static void Rodrigues​(Mat src, Mat dst)
      Converts a rotation matrix to a rotation vector or vice versa.
      Parameters:
      src - Input rotation vector (3x1 or 1x3) or rotation matrix (3x3).
      dst - Output rotation matrix (3x3) or rotation vector (3x1 or 1x3), respectively. derivatives of the output array components with respect to the input array components. \(\begin{array}{l} \theta \leftarrow norm(r) \\ r \leftarrow r/ \theta \\ R = \cos(\theta) I + (1- \cos{\theta} ) r r^T + \sin(\theta) \vecthreethree{0}{-r_z}{r_y}{r_z}{0}{-r_x}{-r_y}{r_x}{0} \end{array}\) Inverse transformation can be also done easily, since \(\sin ( \theta ) \vecthreethree{0}{-r_z}{r_y}{r_z}{0}{-r_x}{-r_y}{r_x}{0} = \frac{R - R^T}{2}\) A rotation vector is a convenient and most compact representation of a rotation matrix (since any rotation matrix has just 3 degrees of freedom). The representation is used in the global 3D geometry optimization procedures like REF: calibrateCamera, REF: stereoCalibrate, or REF: solvePnP . Note: More information about the computation of the derivative of a 3D rotation matrix with respect to its exponential coordinate can be found in:
      • A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates, Guillermo Gallego, Anthony J. Yezzi CITE: Gallego2014ACF
      Note: Useful information on SE(3) and Lie Groups can be found in:
      • A tutorial on SE(3) transformation parameterizations and on-manifold optimization, Jose-Luis Blanco CITE: blanco2010tutorial
      • Lie Groups for 2D and 3D Transformation, Ethan Eade CITE: Eade17
      • A micro Lie theory for state estimation in robotics, Joan Solà, Jérémie Deray, Dinesh Atchuthan CITE: Sol2018AML
    • findHomography

      public static Mat findHomography​(MatOfPoint2f srcPoints, MatOfPoint2f dstPoints, int method, double ransacReprojThreshold, Mat mask, int maxIters, double confidence)
      Finds a perspective transformation between two planes.
      Parameters:
      srcPoints - Coordinates of the points in the original plane, a matrix of the type CV_32FC2 or vector<Point2f> .
      dstPoints - Coordinates of the points in the target plane, a matrix of the type CV_32FC2 or a vector<Point2f> .
      method - Method used to compute a homography matrix. The following methods are possible:
      • 0 - a regular method using all the points, i.e., the least squares method
      • REF: RANSAC - RANSAC-based robust method
      • REF: LMEDS - Least-Median robust method
      • REF: RHO - PROSAC-based robust method
      ransacReprojThreshold - Maximum allowed reprojection error to treat a point pair as an inlier (used in the RANSAC and RHO methods only). That is, if \(\| \texttt{dstPoints} _i - \texttt{convertPointsHomogeneous} ( \texttt{H} \cdot \texttt{srcPoints} _i) \|_2 > \texttt{ransacReprojThreshold}\) then the point \(i\) is considered as an outlier. If srcPoints and dstPoints are measured in pixels, it usually makes sense to set this parameter somewhere in the range of 1 to 10.
      mask - Optional output mask set by a robust method ( RANSAC or LMeDS ). Note that the input mask values are ignored.
      maxIters - The maximum number of RANSAC iterations.
      confidence - Confidence level, between 0 and 1. The function finds and returns the perspective transformation \(H\) between the source and the destination planes: \(s_i \vecthree{x'_i}{y'_i}{1} \sim H \vecthree{x_i}{y_i}{1}\) so that the back-projection error \(\sum _i \left ( x'_i- \frac{h_{11} x_i + h_{12} y_i + h_{13}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2+ \left ( y'_i- \frac{h_{21} x_i + h_{22} y_i + h_{23}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2\) is minimized. If the parameter method is set to the default value 0, the function uses all the point pairs to compute an initial homography estimate with a simple least-squares scheme. However, if not all of the point pairs ( \(srcPoints_i\), \(dstPoints_i\) ) fit the rigid perspective transformation (that is, there are some outliers), this initial estimate will be poor. In this case, you can use one of the three robust methods. The methods RANSAC, LMeDS and RHO try many different random subsets of the corresponding point pairs (of four pairs each, collinear pairs are discarded), estimate the homography matrix using this subset and a simple least-squares algorithm, and then compute the quality/goodness of the computed homography (which is the number of inliers for RANSAC or the least median re-projection error for LMeDS). The best subset is then used to produce the initial estimate of the homography matrix and the mask of inliers/outliers. Regardless of the method, robust or not, the computed homography matrix is refined further (using inliers only in case of a robust method) with the Levenberg-Marquardt method to reduce the re-projection error even more. The methods RANSAC and RHO can handle practically any ratio of outliers but need a threshold to distinguish inliers from outliers. The method LMeDS does not need any threshold but it works correctly only when there are more than 50% of inliers. Finally, if there are no outliers and the noise is rather small, use the default method (method=0). The function is used to find initial intrinsic and extrinsic matrices. Homography matrix is determined up to a scale. Thus, it is normalized so that \(h_{33}=1\). Note that whenever an \(H\) matrix cannot be estimated, an empty one will be returned. SEE: getAffineTransform, estimateAffine2D, estimateAffinePartial2D, getPerspectiveTransform, warpPerspective, perspectiveTransform
      Returns:
      automatically generated
    • findHomography

      public static Mat findHomography​(MatOfPoint2f srcPoints, MatOfPoint2f dstPoints, int method, double ransacReprojThreshold, Mat mask, int maxIters)
      Finds a perspective transformation between two planes.
      Parameters:
      srcPoints - Coordinates of the points in the original plane, a matrix of the type CV_32FC2 or vector<Point2f> .
      dstPoints - Coordinates of the points in the target plane, a matrix of the type CV_32FC2 or a vector<Point2f> .
      method - Method used to compute a homography matrix. The following methods are possible:
      • 0 - a regular method using all the points, i.e., the least squares method
      • REF: RANSAC - RANSAC-based robust method
      • REF: LMEDS - Least-Median robust method
      • REF: RHO - PROSAC-based robust method
      ransacReprojThreshold - Maximum allowed reprojection error to treat a point pair as an inlier (used in the RANSAC and RHO methods only). That is, if \(\| \texttt{dstPoints} _i - \texttt{convertPointsHomogeneous} ( \texttt{H} \cdot \texttt{srcPoints} _i) \|_2 > \texttt{ransacReprojThreshold}\) then the point \(i\) is considered as an outlier. If srcPoints and dstPoints are measured in pixels, it usually makes sense to set this parameter somewhere in the range of 1 to 10.
      mask - Optional output mask set by a robust method ( RANSAC or LMeDS ). Note that the input mask values are ignored.
      maxIters - The maximum number of RANSAC iterations. The function finds and returns the perspective transformation \(H\) between the source and the destination planes: \(s_i \vecthree{x'_i}{y'_i}{1} \sim H \vecthree{x_i}{y_i}{1}\) so that the back-projection error \(\sum _i \left ( x'_i- \frac{h_{11} x_i + h_{12} y_i + h_{13}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2+ \left ( y'_i- \frac{h_{21} x_i + h_{22} y_i + h_{23}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2\) is minimized. If the parameter method is set to the default value 0, the function uses all the point pairs to compute an initial homography estimate with a simple least-squares scheme. However, if not all of the point pairs ( \(srcPoints_i\), \(dstPoints_i\) ) fit the rigid perspective transformation (that is, there are some outliers), this initial estimate will be poor. In this case, you can use one of the three robust methods. The methods RANSAC, LMeDS and RHO try many different random subsets of the corresponding point pairs (of four pairs each, collinear pairs are discarded), estimate the homography matrix using this subset and a simple least-squares algorithm, and then compute the quality/goodness of the computed homography (which is the number of inliers for RANSAC or the least median re-projection error for LMeDS). The best subset is then used to produce the initial estimate of the homography matrix and the mask of inliers/outliers. Regardless of the method, robust or not, the computed homography matrix is refined further (using inliers only in case of a robust method) with the Levenberg-Marquardt method to reduce the re-projection error even more. The methods RANSAC and RHO can handle practically any ratio of outliers but need a threshold to distinguish inliers from outliers. The method LMeDS does not need any threshold but it works correctly only when there are more than 50% of inliers. Finally, if there are no outliers and the noise is rather small, use the default method (method=0). The function is used to find initial intrinsic and extrinsic matrices. Homography matrix is determined up to a scale. Thus, it is normalized so that \(h_{33}=1\). Note that whenever an \(H\) matrix cannot be estimated, an empty one will be returned. SEE: getAffineTransform, estimateAffine2D, estimateAffinePartial2D, getPerspectiveTransform, warpPerspective, perspectiveTransform
      Returns:
      automatically generated
    • findHomography

      public static Mat findHomography​(MatOfPoint2f srcPoints, MatOfPoint2f dstPoints, int method, double ransacReprojThreshold, Mat mask)
      Finds a perspective transformation between two planes.
      Parameters:
      srcPoints - Coordinates of the points in the original plane, a matrix of the type CV_32FC2 or vector<Point2f> .
      dstPoints - Coordinates of the points in the target plane, a matrix of the type CV_32FC2 or a vector<Point2f> .
      method - Method used to compute a homography matrix. The following methods are possible:
      • 0 - a regular method using all the points, i.e., the least squares method
      • REF: RANSAC - RANSAC-based robust method
      • REF: LMEDS - Least-Median robust method
      • REF: RHO - PROSAC-based robust method
      ransacReprojThreshold - Maximum allowed reprojection error to treat a point pair as an inlier (used in the RANSAC and RHO methods only). That is, if \(\| \texttt{dstPoints} _i - \texttt{convertPointsHomogeneous} ( \texttt{H} \cdot \texttt{srcPoints} _i) \|_2 > \texttt{ransacReprojThreshold}\) then the point \(i\) is considered as an outlier. If srcPoints and dstPoints are measured in pixels, it usually makes sense to set this parameter somewhere in the range of 1 to 10.
      mask - Optional output mask set by a robust method ( RANSAC or LMeDS ). Note that the input mask values are ignored. The function finds and returns the perspective transformation \(H\) between the source and the destination planes: \(s_i \vecthree{x'_i}{y'_i}{1} \sim H \vecthree{x_i}{y_i}{1}\) so that the back-projection error \(\sum _i \left ( x'_i- \frac{h_{11} x_i + h_{12} y_i + h_{13}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2+ \left ( y'_i- \frac{h_{21} x_i + h_{22} y_i + h_{23}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2\) is minimized. If the parameter method is set to the default value 0, the function uses all the point pairs to compute an initial homography estimate with a simple least-squares scheme. However, if not all of the point pairs ( \(srcPoints_i\), \(dstPoints_i\) ) fit the rigid perspective transformation (that is, there are some outliers), this initial estimate will be poor. In this case, you can use one of the three robust methods. The methods RANSAC, LMeDS and RHO try many different random subsets of the corresponding point pairs (of four pairs each, collinear pairs are discarded), estimate the homography matrix using this subset and a simple least-squares algorithm, and then compute the quality/goodness of the computed homography (which is the number of inliers for RANSAC or the least median re-projection error for LMeDS). The best subset is then used to produce the initial estimate of the homography matrix and the mask of inliers/outliers. Regardless of the method, robust or not, the computed homography matrix is refined further (using inliers only in case of a robust method) with the Levenberg-Marquardt method to reduce the re-projection error even more. The methods RANSAC and RHO can handle practically any ratio of outliers but need a threshold to distinguish inliers from outliers. The method LMeDS does not need any threshold but it works correctly only when there are more than 50% of inliers. Finally, if there are no outliers and the noise is rather small, use the default method (method=0). The function is used to find initial intrinsic and extrinsic matrices. Homography matrix is determined up to a scale. Thus, it is normalized so that \(h_{33}=1\). Note that whenever an \(H\) matrix cannot be estimated, an empty one will be returned. SEE: getAffineTransform, estimateAffine2D, estimateAffinePartial2D, getPerspectiveTransform, warpPerspective, perspectiveTransform
      Returns:
      automatically generated
    • findHomography

      public static Mat findHomography​(MatOfPoint2f srcPoints, MatOfPoint2f dstPoints, int method, double ransacReprojThreshold)
      Finds a perspective transformation between two planes.
      Parameters:
      srcPoints - Coordinates of the points in the original plane, a matrix of the type CV_32FC2 or vector<Point2f> .
      dstPoints - Coordinates of the points in the target plane, a matrix of the type CV_32FC2 or a vector<Point2f> .
      method - Method used to compute a homography matrix. The following methods are possible:
      • 0 - a regular method using all the points, i.e., the least squares method
      • REF: RANSAC - RANSAC-based robust method
      • REF: LMEDS - Least-Median robust method
      • REF: RHO - PROSAC-based robust method
      ransacReprojThreshold - Maximum allowed reprojection error to treat a point pair as an inlier (used in the RANSAC and RHO methods only). That is, if \(\| \texttt{dstPoints} _i - \texttt{convertPointsHomogeneous} ( \texttt{H} \cdot \texttt{srcPoints} _i) \|_2 > \texttt{ransacReprojThreshold}\) then the point \(i\) is considered as an outlier. If srcPoints and dstPoints are measured in pixels, it usually makes sense to set this parameter somewhere in the range of 1 to 10. mask values are ignored. The function finds and returns the perspective transformation \(H\) between the source and the destination planes: \(s_i \vecthree{x'_i}{y'_i}{1} \sim H \vecthree{x_i}{y_i}{1}\) so that the back-projection error \(\sum _i \left ( x'_i- \frac{h_{11} x_i + h_{12} y_i + h_{13}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2+ \left ( y'_i- \frac{h_{21} x_i + h_{22} y_i + h_{23}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2\) is minimized. If the parameter method is set to the default value 0, the function uses all the point pairs to compute an initial homography estimate with a simple least-squares scheme. However, if not all of the point pairs ( \(srcPoints_i\), \(dstPoints_i\) ) fit the rigid perspective transformation (that is, there are some outliers), this initial estimate will be poor. In this case, you can use one of the three robust methods. The methods RANSAC, LMeDS and RHO try many different random subsets of the corresponding point pairs (of four pairs each, collinear pairs are discarded), estimate the homography matrix using this subset and a simple least-squares algorithm, and then compute the quality/goodness of the computed homography (which is the number of inliers for RANSAC or the least median re-projection error for LMeDS). The best subset is then used to produce the initial estimate of the homography matrix and the mask of inliers/outliers. Regardless of the method, robust or not, the computed homography matrix is refined further (using inliers only in case of a robust method) with the Levenberg-Marquardt method to reduce the re-projection error even more. The methods RANSAC and RHO can handle practically any ratio of outliers but need a threshold to distinguish inliers from outliers. The method LMeDS does not need any threshold but it works correctly only when there are more than 50% of inliers. Finally, if there are no outliers and the noise is rather small, use the default method (method=0). The function is used to find initial intrinsic and extrinsic matrices. Homography matrix is determined up to a scale. Thus, it is normalized so that \(h_{33}=1\). Note that whenever an \(H\) matrix cannot be estimated, an empty one will be returned. SEE: getAffineTransform, estimateAffine2D, estimateAffinePartial2D, getPerspectiveTransform, warpPerspective, perspectiveTransform
      Returns:
      automatically generated
    • findHomography

      public static Mat findHomography​(MatOfPoint2f srcPoints, MatOfPoint2f dstPoints, int method)
      Finds a perspective transformation between two planes.
      Parameters:
      srcPoints - Coordinates of the points in the original plane, a matrix of the type CV_32FC2 or vector<Point2f> .
      dstPoints - Coordinates of the points in the target plane, a matrix of the type CV_32FC2 or a vector<Point2f> .
      method - Method used to compute a homography matrix. The following methods are possible:
      • 0 - a regular method using all the points, i.e., the least squares method
      • REF: RANSAC - RANSAC-based robust method
      • REF: LMEDS - Least-Median robust method
      • REF: RHO - PROSAC-based robust method
      (used in the RANSAC and RHO methods only). That is, if \(\| \texttt{dstPoints} _i - \texttt{convertPointsHomogeneous} ( \texttt{H} \cdot \texttt{srcPoints} _i) \|_2 > \texttt{ransacReprojThreshold}\) then the point \(i\) is considered as an outlier. If srcPoints and dstPoints are measured in pixels, it usually makes sense to set this parameter somewhere in the range of 1 to 10. mask values are ignored. The function finds and returns the perspective transformation \(H\) between the source and the destination planes: \(s_i \vecthree{x'_i}{y'_i}{1} \sim H \vecthree{x_i}{y_i}{1}\) so that the back-projection error \(\sum _i \left ( x'_i- \frac{h_{11} x_i + h_{12} y_i + h_{13}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2+ \left ( y'_i- \frac{h_{21} x_i + h_{22} y_i + h_{23}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2\) is minimized. If the parameter method is set to the default value 0, the function uses all the point pairs to compute an initial homography estimate with a simple least-squares scheme. However, if not all of the point pairs ( \(srcPoints_i\), \(dstPoints_i\) ) fit the rigid perspective transformation (that is, there are some outliers), this initial estimate will be poor. In this case, you can use one of the three robust methods. The methods RANSAC, LMeDS and RHO try many different random subsets of the corresponding point pairs (of four pairs each, collinear pairs are discarded), estimate the homography matrix using this subset and a simple least-squares algorithm, and then compute the quality/goodness of the computed homography (which is the number of inliers for RANSAC or the least median re-projection error for LMeDS). The best subset is then used to produce the initial estimate of the homography matrix and the mask of inliers/outliers. Regardless of the method, robust or not, the computed homography matrix is refined further (using inliers only in case of a robust method) with the Levenberg-Marquardt method to reduce the re-projection error even more. The methods RANSAC and RHO can handle practically any ratio of outliers but need a threshold to distinguish inliers from outliers. The method LMeDS does not need any threshold but it works correctly only when there are more than 50% of inliers. Finally, if there are no outliers and the noise is rather small, use the default method (method=0). The function is used to find initial intrinsic and extrinsic matrices. Homography matrix is determined up to a scale. Thus, it is normalized so that \(h_{33}=1\). Note that whenever an \(H\) matrix cannot be estimated, an empty one will be returned. SEE: getAffineTransform, estimateAffine2D, estimateAffinePartial2D, getPerspectiveTransform, warpPerspective, perspectiveTransform
      Returns:
      automatically generated
    • findHomography

      public static Mat findHomography​(MatOfPoint2f srcPoints, MatOfPoint2f dstPoints)
      Finds a perspective transformation between two planes.
      Parameters:
      srcPoints - Coordinates of the points in the original plane, a matrix of the type CV_32FC2 or vector<Point2f> .
      dstPoints - Coordinates of the points in the target plane, a matrix of the type CV_32FC2 or a vector<Point2f> .
      • 0 - a regular method using all the points, i.e., the least squares method
      • REF: RANSAC - RANSAC-based robust method
      • REF: LMEDS - Least-Median robust method
      • REF: RHO - PROSAC-based robust method
      (used in the RANSAC and RHO methods only). That is, if \(\| \texttt{dstPoints} _i - \texttt{convertPointsHomogeneous} ( \texttt{H} \cdot \texttt{srcPoints} _i) \|_2 > \texttt{ransacReprojThreshold}\) then the point \(i\) is considered as an outlier. If srcPoints and dstPoints are measured in pixels, it usually makes sense to set this parameter somewhere in the range of 1 to 10. mask values are ignored. The function finds and returns the perspective transformation \(H\) between the source and the destination planes: \(s_i \vecthree{x'_i}{y'_i}{1} \sim H \vecthree{x_i}{y_i}{1}\) so that the back-projection error \(\sum _i \left ( x'_i- \frac{h_{11} x_i + h_{12} y_i + h_{13}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2+ \left ( y'_i- \frac{h_{21} x_i + h_{22} y_i + h_{23}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2\) is minimized. If the parameter method is set to the default value 0, the function uses all the point pairs to compute an initial homography estimate with a simple least-squares scheme. However, if not all of the point pairs ( \(srcPoints_i\), \(dstPoints_i\) ) fit the rigid perspective transformation (that is, there are some outliers), this initial estimate will be poor. In this case, you can use one of the three robust methods. The methods RANSAC, LMeDS and RHO try many different random subsets of the corresponding point pairs (of four pairs each, collinear pairs are discarded), estimate the homography matrix using this subset and a simple least-squares algorithm, and then compute the quality/goodness of the computed homography (which is the number of inliers for RANSAC or the least median re-projection error for LMeDS). The best subset is then used to produce the initial estimate of the homography matrix and the mask of inliers/outliers. Regardless of the method, robust or not, the computed homography matrix is refined further (using inliers only in case of a robust method) with the Levenberg-Marquardt method to reduce the re-projection error even more. The methods RANSAC and RHO can handle practically any ratio of outliers but need a threshold to distinguish inliers from outliers. The method LMeDS does not need any threshold but it works correctly only when there are more than 50% of inliers. Finally, if there are no outliers and the noise is rather small, use the default method (method=0). The function is used to find initial intrinsic and extrinsic matrices. Homography matrix is determined up to a scale. Thus, it is normalized so that \(h_{33}=1\). Note that whenever an \(H\) matrix cannot be estimated, an empty one will be returned. SEE: getAffineTransform, estimateAffine2D, estimateAffinePartial2D, getPerspectiveTransform, warpPerspective, perspectiveTransform
      Returns:
      automatically generated
    • findHomography

      public static Mat findHomography​(MatOfPoint2f srcPoints, MatOfPoint2f dstPoints, Mat mask, UsacParams params)
    • RQDecomp3x3

      public static double[] RQDecomp3x3​(Mat src, Mat mtxR, Mat mtxQ, Mat Qx, Mat Qy, Mat Qz)
      Computes an RQ decomposition of 3x3 matrices.
      Parameters:
      src - 3x3 input matrix.
      mtxR - Output 3x3 upper-triangular matrix.
      mtxQ - Output 3x3 orthogonal matrix.
      Qx - Optional output 3x3 rotation matrix around x-axis.
      Qy - Optional output 3x3 rotation matrix around y-axis.
      Qz - Optional output 3x3 rotation matrix around z-axis. The function computes a RQ decomposition using the given rotations. This function is used in #decomposeProjectionMatrix to decompose the left 3x3 submatrix of a projection matrix into a camera and a rotation matrix. It optionally returns three rotation matrices, one for each axis, and the three Euler angles in degrees (as the return value) that could be used in OpenGL. Note, there is always more than one sequence of rotations about the three principal axes that results in the same orientation of an object, e.g. see CITE: Slabaugh . Returned tree rotation matrices and corresponding three Euler angles are only one of the possible solutions.
      Returns:
      automatically generated
    • RQDecomp3x3

      public static double[] RQDecomp3x3​(Mat src, Mat mtxR, Mat mtxQ, Mat Qx, Mat Qy)
      Computes an RQ decomposition of 3x3 matrices.
      Parameters:
      src - 3x3 input matrix.
      mtxR - Output 3x3 upper-triangular matrix.
      mtxQ - Output 3x3 orthogonal matrix.
      Qx - Optional output 3x3 rotation matrix around x-axis.
      Qy - Optional output 3x3 rotation matrix around y-axis. The function computes a RQ decomposition using the given rotations. This function is used in #decomposeProjectionMatrix to decompose the left 3x3 submatrix of a projection matrix into a camera and a rotation matrix. It optionally returns three rotation matrices, one for each axis, and the three Euler angles in degrees (as the return value) that could be used in OpenGL. Note, there is always more than one sequence of rotations about the three principal axes that results in the same orientation of an object, e.g. see CITE: Slabaugh . Returned tree rotation matrices and corresponding three Euler angles are only one of the possible solutions.
      Returns:
      automatically generated
    • RQDecomp3x3

      public static double[] RQDecomp3x3​(Mat src, Mat mtxR, Mat mtxQ, Mat Qx)
      Computes an RQ decomposition of 3x3 matrices.
      Parameters:
      src - 3x3 input matrix.
      mtxR - Output 3x3 upper-triangular matrix.
      mtxQ - Output 3x3 orthogonal matrix.
      Qx - Optional output 3x3 rotation matrix around x-axis. The function computes a RQ decomposition using the given rotations. This function is used in #decomposeProjectionMatrix to decompose the left 3x3 submatrix of a projection matrix into a camera and a rotation matrix. It optionally returns three rotation matrices, one for each axis, and the three Euler angles in degrees (as the return value) that could be used in OpenGL. Note, there is always more than one sequence of rotations about the three principal axes that results in the same orientation of an object, e.g. see CITE: Slabaugh . Returned tree rotation matrices and corresponding three Euler angles are only one of the possible solutions.
      Returns:
      automatically generated
    • RQDecomp3x3

      public static double[] RQDecomp3x3​(Mat src, Mat mtxR, Mat mtxQ)
      Computes an RQ decomposition of 3x3 matrices.
      Parameters:
      src - 3x3 input matrix.
      mtxR - Output 3x3 upper-triangular matrix.
      mtxQ - Output 3x3 orthogonal matrix. The function computes a RQ decomposition using the given rotations. This function is used in #decomposeProjectionMatrix to decompose the left 3x3 submatrix of a projection matrix into a camera and a rotation matrix. It optionally returns three rotation matrices, one for each axis, and the three Euler angles in degrees (as the return value) that could be used in OpenGL. Note, there is always more than one sequence of rotations about the three principal axes that results in the same orientation of an object, e.g. see CITE: Slabaugh . Returned tree rotation matrices and corresponding three Euler angles are only one of the possible solutions.
      Returns:
      automatically generated
    • decomposeProjectionMatrix

      public static void decomposeProjectionMatrix​(Mat projMatrix, Mat cameraMatrix, Mat rotMatrix, Mat transVect, Mat rotMatrixX, Mat rotMatrixY, Mat rotMatrixZ, Mat eulerAngles)
      Decomposes a projection matrix into a rotation matrix and a camera intrinsic matrix.
      Parameters:
      projMatrix - 3x4 input projection matrix P.
      cameraMatrix - Output 3x3 camera intrinsic matrix \(\cameramatrix{A}\).
      rotMatrix - Output 3x3 external rotation matrix R.
      transVect - Output 4x1 translation vector T.
      rotMatrixX - Optional 3x3 rotation matrix around x-axis.
      rotMatrixY - Optional 3x3 rotation matrix around y-axis.
      rotMatrixZ - Optional 3x3 rotation matrix around z-axis.
      eulerAngles - Optional three-element vector containing three Euler angles of rotation in degrees. The function computes a decomposition of a projection matrix into a calibration and a rotation matrix and the position of a camera. It optionally returns three rotation matrices, one for each axis, and three Euler angles that could be used in OpenGL. Note, there is always more than one sequence of rotations about the three principal axes that results in the same orientation of an object, e.g. see CITE: Slabaugh . Returned tree rotation matrices and corresponding three Euler angles are only one of the possible solutions. The function is based on #RQDecomp3x3 .
    • decomposeProjectionMatrix

      public static void decomposeProjectionMatrix​(Mat projMatrix, Mat cameraMatrix, Mat rotMatrix, Mat transVect, Mat rotMatrixX, Mat rotMatrixY, Mat rotMatrixZ)
      Decomposes a projection matrix into a rotation matrix and a camera intrinsic matrix.
      Parameters:
      projMatrix - 3x4 input projection matrix P.
      cameraMatrix - Output 3x3 camera intrinsic matrix \(\cameramatrix{A}\).
      rotMatrix - Output 3x3 external rotation matrix R.
      transVect - Output 4x1 translation vector T.
      rotMatrixX - Optional 3x3 rotation matrix around x-axis.
      rotMatrixY - Optional 3x3 rotation matrix around y-axis.
      rotMatrixZ - Optional 3x3 rotation matrix around z-axis. degrees. The function computes a decomposition of a projection matrix into a calibration and a rotation matrix and the position of a camera. It optionally returns three rotation matrices, one for each axis, and three Euler angles that could be used in OpenGL. Note, there is always more than one sequence of rotations about the three principal axes that results in the same orientation of an object, e.g. see CITE: Slabaugh . Returned tree rotation matrices and corresponding three Euler angles are only one of the possible solutions. The function is based on #RQDecomp3x3 .
    • decomposeProjectionMatrix

      public static void decomposeProjectionMatrix​(Mat projMatrix, Mat cameraMatrix, Mat rotMatrix, Mat transVect, Mat rotMatrixX, Mat rotMatrixY)
      Decomposes a projection matrix into a rotation matrix and a camera intrinsic matrix.
      Parameters:
      projMatrix - 3x4 input projection matrix P.
      cameraMatrix - Output 3x3 camera intrinsic matrix \(\cameramatrix{A}\).
      rotMatrix - Output 3x3 external rotation matrix R.
      transVect - Output 4x1 translation vector T.
      rotMatrixX - Optional 3x3 rotation matrix around x-axis.
      rotMatrixY - Optional 3x3 rotation matrix around y-axis. degrees. The function computes a decomposition of a projection matrix into a calibration and a rotation matrix and the position of a camera. It optionally returns three rotation matrices, one for each axis, and three Euler angles that could be used in OpenGL. Note, there is always more than one sequence of rotations about the three principal axes that results in the same orientation of an object, e.g. see CITE: Slabaugh . Returned tree rotation matrices and corresponding three Euler angles are only one of the possible solutions. The function is based on #RQDecomp3x3 .
    • decomposeProjectionMatrix

      public static void decomposeProjectionMatrix​(Mat projMatrix, Mat cameraMatrix, Mat rotMatrix, Mat transVect, Mat rotMatrixX)
      Decomposes a projection matrix into a rotation matrix and a camera intrinsic matrix.
      Parameters:
      projMatrix - 3x4 input projection matrix P.
      cameraMatrix - Output 3x3 camera intrinsic matrix \(\cameramatrix{A}\).
      rotMatrix - Output 3x3 external rotation matrix R.
      transVect - Output 4x1 translation vector T.
      rotMatrixX - Optional 3x3 rotation matrix around x-axis. degrees. The function computes a decomposition of a projection matrix into a calibration and a rotation matrix and the position of a camera. It optionally returns three rotation matrices, one for each axis, and three Euler angles that could be used in OpenGL. Note, there is always more than one sequence of rotations about the three principal axes that results in the same orientation of an object, e.g. see CITE: Slabaugh . Returned tree rotation matrices and corresponding three Euler angles are only one of the possible solutions. The function is based on #RQDecomp3x3 .
    • decomposeProjectionMatrix

      public static void decomposeProjectionMatrix​(Mat projMatrix, Mat cameraMatrix, Mat rotMatrix, Mat transVect)
      Decomposes a projection matrix into a rotation matrix and a camera intrinsic matrix.
      Parameters:
      projMatrix - 3x4 input projection matrix P.
      cameraMatrix - Output 3x3 camera intrinsic matrix \(\cameramatrix{A}\).
      rotMatrix - Output 3x3 external rotation matrix R.
      transVect - Output 4x1 translation vector T. degrees. The function computes a decomposition of a projection matrix into a calibration and a rotation matrix and the position of a camera. It optionally returns three rotation matrices, one for each axis, and three Euler angles that could be used in OpenGL. Note, there is always more than one sequence of rotations about the three principal axes that results in the same orientation of an object, e.g. see CITE: Slabaugh . Returned tree rotation matrices and corresponding three Euler angles are only one of the possible solutions. The function is based on #RQDecomp3x3 .
    • matMulDeriv

      public static void matMulDeriv​(Mat A, Mat B, Mat dABdA, Mat dABdB)
      Computes partial derivatives of the matrix product for each multiplied matrix.
      Parameters:
      A - First multiplied matrix.
      B - Second multiplied matrix.
      dABdA - First output derivative matrix d(A\*B)/dA of size \(\texttt{A.rows*B.cols} \times {A.rows*A.cols}\) .
      dABdB - Second output derivative matrix d(A\*B)/dB of size \(\texttt{A.rows*B.cols} \times {B.rows*B.cols}\) . The function computes partial derivatives of the elements of the matrix product \(A*B\) with regard to the elements of each of the two input matrices. The function is used to compute the Jacobian matrices in #stereoCalibrate but can also be used in any other similar optimization function.
    • composeRT

      public static void composeRT​(Mat rvec1, Mat tvec1, Mat rvec2, Mat tvec2, Mat rvec3, Mat tvec3, Mat dr3dr1, Mat dr3dt1, Mat dr3dr2, Mat dr3dt2, Mat dt3dr1, Mat dt3dt1, Mat dt3dr2, Mat dt3dt2)
      Combines two rotation-and-shift transformations.
      Parameters:
      rvec1 - First rotation vector.
      tvec1 - First translation vector.
      rvec2 - Second rotation vector.
      tvec2 - Second translation vector.
      rvec3 - Output rotation vector of the superposition.
      tvec3 - Output translation vector of the superposition.
      dr3dr1 - Optional output derivative of rvec3 with regard to rvec1
      dr3dt1 - Optional output derivative of rvec3 with regard to tvec1
      dr3dr2 - Optional output derivative of rvec3 with regard to rvec2
      dr3dt2 - Optional output derivative of rvec3 with regard to tvec2
      dt3dr1 - Optional output derivative of tvec3 with regard to rvec1
      dt3dt1 - Optional output derivative of tvec3 with regard to tvec1
      dt3dr2 - Optional output derivative of tvec3 with regard to rvec2
      dt3dt2 - Optional output derivative of tvec3 with regard to tvec2 The functions compute: \(\begin{array}{l} \texttt{rvec3} = \mathrm{rodrigues} ^{-1} \left ( \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \mathrm{rodrigues} ( \texttt{rvec1} ) \right ) \\ \texttt{tvec3} = \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \texttt{tvec1} + \texttt{tvec2} \end{array} ,\) where \(\mathrm{rodrigues}\) denotes a rotation vector to a rotation matrix transformation, and \(\mathrm{rodrigues}^{-1}\) denotes the inverse transformation. See #Rodrigues for details. Also, the functions can compute the derivatives of the output vectors with regards to the input vectors (see #matMulDeriv ). The functions are used inside #stereoCalibrate but can also be used in your own code where Levenberg-Marquardt or another gradient-based solver is used to optimize a function that contains a matrix multiplication.
    • composeRT

      public static void composeRT​(Mat rvec1, Mat tvec1, Mat rvec2, Mat tvec2, Mat rvec3, Mat tvec3, Mat dr3dr1, Mat dr3dt1, Mat dr3dr2, Mat dr3dt2, Mat dt3dr1, Mat dt3dt1, Mat dt3dr2)
      Combines two rotation-and-shift transformations.
      Parameters:
      rvec1 - First rotation vector.
      tvec1 - First translation vector.
      rvec2 - Second rotation vector.
      tvec2 - Second translation vector.
      rvec3 - Output rotation vector of the superposition.
      tvec3 - Output translation vector of the superposition.
      dr3dr1 - Optional output derivative of rvec3 with regard to rvec1
      dr3dt1 - Optional output derivative of rvec3 with regard to tvec1
      dr3dr2 - Optional output derivative of rvec3 with regard to rvec2
      dr3dt2 - Optional output derivative of rvec3 with regard to tvec2
      dt3dr1 - Optional output derivative of tvec3 with regard to rvec1
      dt3dt1 - Optional output derivative of tvec3 with regard to tvec1
      dt3dr2 - Optional output derivative of tvec3 with regard to rvec2 The functions compute: \(\begin{array}{l} \texttt{rvec3} = \mathrm{rodrigues} ^{-1} \left ( \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \mathrm{rodrigues} ( \texttt{rvec1} ) \right ) \\ \texttt{tvec3} = \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \texttt{tvec1} + \texttt{tvec2} \end{array} ,\) where \(\mathrm{rodrigues}\) denotes a rotation vector to a rotation matrix transformation, and \(\mathrm{rodrigues}^{-1}\) denotes the inverse transformation. See #Rodrigues for details. Also, the functions can compute the derivatives of the output vectors with regards to the input vectors (see #matMulDeriv ). The functions are used inside #stereoCalibrate but can also be used in your own code where Levenberg-Marquardt or another gradient-based solver is used to optimize a function that contains a matrix multiplication.
    • composeRT

      public static void composeRT​(Mat rvec1, Mat tvec1, Mat rvec2, Mat tvec2, Mat rvec3, Mat tvec3, Mat dr3dr1, Mat dr3dt1, Mat dr3dr2, Mat dr3dt2, Mat dt3dr1, Mat dt3dt1)
      Combines two rotation-and-shift transformations.
      Parameters:
      rvec1 - First rotation vector.
      tvec1 - First translation vector.
      rvec2 - Second rotation vector.
      tvec2 - Second translation vector.
      rvec3 - Output rotation vector of the superposition.
      tvec3 - Output translation vector of the superposition.
      dr3dr1 - Optional output derivative of rvec3 with regard to rvec1
      dr3dt1 - Optional output derivative of rvec3 with regard to tvec1
      dr3dr2 - Optional output derivative of rvec3 with regard to rvec2
      dr3dt2 - Optional output derivative of rvec3 with regard to tvec2
      dt3dr1 - Optional output derivative of tvec3 with regard to rvec1
      dt3dt1 - Optional output derivative of tvec3 with regard to tvec1 The functions compute: \(\begin{array}{l} \texttt{rvec3} = \mathrm{rodrigues} ^{-1} \left ( \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \mathrm{rodrigues} ( \texttt{rvec1} ) \right ) \\ \texttt{tvec3} = \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \texttt{tvec1} + \texttt{tvec2} \end{array} ,\) where \(\mathrm{rodrigues}\) denotes a rotation vector to a rotation matrix transformation, and \(\mathrm{rodrigues}^{-1}\) denotes the inverse transformation. See #Rodrigues for details. Also, the functions can compute the derivatives of the output vectors with regards to the input vectors (see #matMulDeriv ). The functions are used inside #stereoCalibrate but can also be used in your own code where Levenberg-Marquardt or another gradient-based solver is used to optimize a function that contains a matrix multiplication.
    • composeRT

      public static void composeRT​(Mat rvec1, Mat tvec1, Mat rvec2, Mat tvec2, Mat rvec3, Mat tvec3, Mat dr3dr1, Mat dr3dt1, Mat dr3dr2, Mat dr3dt2, Mat dt3dr1)
      Combines two rotation-and-shift transformations.
      Parameters:
      rvec1 - First rotation vector.
      tvec1 - First translation vector.
      rvec2 - Second rotation vector.
      tvec2 - Second translation vector.
      rvec3 - Output rotation vector of the superposition.
      tvec3 - Output translation vector of the superposition.
      dr3dr1 - Optional output derivative of rvec3 with regard to rvec1
      dr3dt1 - Optional output derivative of rvec3 with regard to tvec1
      dr3dr2 - Optional output derivative of rvec3 with regard to rvec2
      dr3dt2 - Optional output derivative of rvec3 with regard to tvec2
      dt3dr1 - Optional output derivative of tvec3 with regard to rvec1 The functions compute: \(\begin{array}{l} \texttt{rvec3} = \mathrm{rodrigues} ^{-1} \left ( \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \mathrm{rodrigues} ( \texttt{rvec1} ) \right ) \\ \texttt{tvec3} = \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \texttt{tvec1} + \texttt{tvec2} \end{array} ,\) where \(\mathrm{rodrigues}\) denotes a rotation vector to a rotation matrix transformation, and \(\mathrm{rodrigues}^{-1}\) denotes the inverse transformation. See #Rodrigues for details. Also, the functions can compute the derivatives of the output vectors with regards to the input vectors (see #matMulDeriv ). The functions are used inside #stereoCalibrate but can also be used in your own code where Levenberg-Marquardt or another gradient-based solver is used to optimize a function that contains a matrix multiplication.
    • composeRT

      public static void composeRT​(Mat rvec1, Mat tvec1, Mat rvec2, Mat tvec2, Mat rvec3, Mat tvec3, Mat dr3dr1, Mat dr3dt1, Mat dr3dr2, Mat dr3dt2)
      Combines two rotation-and-shift transformations.
      Parameters:
      rvec1 - First rotation vector.
      tvec1 - First translation vector.
      rvec2 - Second rotation vector.
      tvec2 - Second translation vector.
      rvec3 - Output rotation vector of the superposition.
      tvec3 - Output translation vector of the superposition.
      dr3dr1 - Optional output derivative of rvec3 with regard to rvec1
      dr3dt1 - Optional output derivative of rvec3 with regard to tvec1
      dr3dr2 - Optional output derivative of rvec3 with regard to rvec2
      dr3dt2 - Optional output derivative of rvec3 with regard to tvec2 The functions compute: \(\begin{array}{l} \texttt{rvec3} = \mathrm{rodrigues} ^{-1} \left ( \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \mathrm{rodrigues} ( \texttt{rvec1} ) \right ) \\ \texttt{tvec3} = \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \texttt{tvec1} + \texttt{tvec2} \end{array} ,\) where \(\mathrm{rodrigues}\) denotes a rotation vector to a rotation matrix transformation, and \(\mathrm{rodrigues}^{-1}\) denotes the inverse transformation. See #Rodrigues for details. Also, the functions can compute the derivatives of the output vectors with regards to the input vectors (see #matMulDeriv ). The functions are used inside #stereoCalibrate but can also be used in your own code where Levenberg-Marquardt or another gradient-based solver is used to optimize a function that contains a matrix multiplication.
    • composeRT

      public static void composeRT​(Mat rvec1, Mat tvec1, Mat rvec2, Mat tvec2, Mat rvec3, Mat tvec3, Mat dr3dr1, Mat dr3dt1, Mat dr3dr2)
      Combines two rotation-and-shift transformations.
      Parameters:
      rvec1 - First rotation vector.
      tvec1 - First translation vector.
      rvec2 - Second rotation vector.
      tvec2 - Second translation vector.
      rvec3 - Output rotation vector of the superposition.
      tvec3 - Output translation vector of the superposition.
      dr3dr1 - Optional output derivative of rvec3 with regard to rvec1
      dr3dt1 - Optional output derivative of rvec3 with regard to tvec1
      dr3dr2 - Optional output derivative of rvec3 with regard to rvec2 The functions compute: \(\begin{array}{l} \texttt{rvec3} = \mathrm{rodrigues} ^{-1} \left ( \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \mathrm{rodrigues} ( \texttt{rvec1} ) \right ) \\ \texttt{tvec3} = \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \texttt{tvec1} + \texttt{tvec2} \end{array} ,\) where \(\mathrm{rodrigues}\) denotes a rotation vector to a rotation matrix transformation, and \(\mathrm{rodrigues}^{-1}\) denotes the inverse transformation. See #Rodrigues for details. Also, the functions can compute the derivatives of the output vectors with regards to the input vectors (see #matMulDeriv ). The functions are used inside #stereoCalibrate but can also be used in your own code where Levenberg-Marquardt or another gradient-based solver is used to optimize a function that contains a matrix multiplication.
    • composeRT

      public static void composeRT​(Mat rvec1, Mat tvec1, Mat rvec2, Mat tvec2, Mat rvec3, Mat tvec3, Mat dr3dr1, Mat dr3dt1)
      Combines two rotation-and-shift transformations.
      Parameters:
      rvec1 - First rotation vector.
      tvec1 - First translation vector.
      rvec2 - Second rotation vector.
      tvec2 - Second translation vector.
      rvec3 - Output rotation vector of the superposition.
      tvec3 - Output translation vector of the superposition.
      dr3dr1 - Optional output derivative of rvec3 with regard to rvec1
      dr3dt1 - Optional output derivative of rvec3 with regard to tvec1 The functions compute: \(\begin{array}{l} \texttt{rvec3} = \mathrm{rodrigues} ^{-1} \left ( \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \mathrm{rodrigues} ( \texttt{rvec1} ) \right ) \\ \texttt{tvec3} = \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \texttt{tvec1} + \texttt{tvec2} \end{array} ,\) where \(\mathrm{rodrigues}\) denotes a rotation vector to a rotation matrix transformation, and \(\mathrm{rodrigues}^{-1}\) denotes the inverse transformation. See #Rodrigues for details. Also, the functions can compute the derivatives of the output vectors with regards to the input vectors (see #matMulDeriv ). The functions are used inside #stereoCalibrate but can also be used in your own code where Levenberg-Marquardt or another gradient-based solver is used to optimize a function that contains a matrix multiplication.
    • composeRT

      public static void composeRT​(Mat rvec1, Mat tvec1, Mat rvec2, Mat tvec2, Mat rvec3, Mat tvec3, Mat dr3dr1)
      Combines two rotation-and-shift transformations.
      Parameters:
      rvec1 - First rotation vector.
      tvec1 - First translation vector.
      rvec2 - Second rotation vector.
      tvec2 - Second translation vector.
      rvec3 - Output rotation vector of the superposition.
      tvec3 - Output translation vector of the superposition.
      dr3dr1 - Optional output derivative of rvec3 with regard to rvec1 The functions compute: \(\begin{array}{l} \texttt{rvec3} = \mathrm{rodrigues} ^{-1} \left ( \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \mathrm{rodrigues} ( \texttt{rvec1} ) \right ) \\ \texttt{tvec3} = \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \texttt{tvec1} + \texttt{tvec2} \end{array} ,\) where \(\mathrm{rodrigues}\) denotes a rotation vector to a rotation matrix transformation, and \(\mathrm{rodrigues}^{-1}\) denotes the inverse transformation. See #Rodrigues for details. Also, the functions can compute the derivatives of the output vectors with regards to the input vectors (see #matMulDeriv ). The functions are used inside #stereoCalibrate but can also be used in your own code where Levenberg-Marquardt or another gradient-based solver is used to optimize a function that contains a matrix multiplication.
    • composeRT

      public static void composeRT​(Mat rvec1, Mat tvec1, Mat rvec2, Mat tvec2, Mat rvec3, Mat tvec3)
      Combines two rotation-and-shift transformations.
      Parameters:
      rvec1 - First rotation vector.
      tvec1 - First translation vector.
      rvec2 - Second rotation vector.
      tvec2 - Second translation vector.
      rvec3 - Output rotation vector of the superposition.
      tvec3 - Output translation vector of the superposition. The functions compute: \(\begin{array}{l} \texttt{rvec3} = \mathrm{rodrigues} ^{-1} \left ( \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \mathrm{rodrigues} ( \texttt{rvec1} ) \right ) \\ \texttt{tvec3} = \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \texttt{tvec1} + \texttt{tvec2} \end{array} ,\) where \(\mathrm{rodrigues}\) denotes a rotation vector to a rotation matrix transformation, and \(\mathrm{rodrigues}^{-1}\) denotes the inverse transformation. See #Rodrigues for details. Also, the functions can compute the derivatives of the output vectors with regards to the input vectors (see #matMulDeriv ). The functions are used inside #stereoCalibrate but can also be used in your own code where Levenberg-Marquardt or another gradient-based solver is used to optimize a function that contains a matrix multiplication.
    • projectPoints

      public static void projectPoints​(MatOfPoint3f objectPoints, Mat rvec, Mat tvec, Mat cameraMatrix, MatOfDouble distCoeffs, MatOfPoint2f imagePoints, Mat jacobian, double aspectRatio)
      Projects 3D points to an image plane.
      Parameters:
      objectPoints - Array of object points expressed wrt. the world coordinate frame. A 3xN/Nx3 1-channel or 1xN/Nx1 3-channel (or vector<Point3f> ), where N is the number of points in the view.
      rvec - The rotation vector (REF: Rodrigues) that, together with tvec, performs a change of basis from world to camera coordinate system, see REF: calibrateCamera for details.
      tvec - The translation vector, see parameter description above.
      cameraMatrix - Camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\) . If the vector is empty, the zero distortion coefficients are assumed.
      imagePoints - Output array of image points, 1xN/Nx1 2-channel, or vector<Point2f> .
      jacobian - Optional output 2Nx(10+<numDistCoeffs>) jacobian matrix of derivatives of image points with respect to components of the rotation vector, translation vector, focal lengths, coordinates of the principal point and the distortion coefficients. In the old interface different components of the jacobian are returned via different output parameters.
      aspectRatio - Optional "fixed aspect ratio" parameter. If the parameter is not 0, the function assumes that the aspect ratio (\(f_x / f_y\)) is fixed and correspondingly adjusts the jacobian matrix. The function computes the 2D projections of 3D points to the image plane, given intrinsic and extrinsic camera parameters. Optionally, the function computes Jacobians -matrices of partial derivatives of image points coordinates (as functions of all the input parameters) with respect to the particular parameters, intrinsic and/or extrinsic. The Jacobians are used during the global optimization in REF: calibrateCamera, REF: solvePnP, and REF: stereoCalibrate. The function itself can also be used to compute a re-projection error, given the current intrinsic and extrinsic parameters. Note: By setting rvec = tvec = \([0, 0, 0]\), or by setting cameraMatrix to a 3x3 identity matrix, or by passing zero distortion coefficients, one can get various useful partial cases of the function. This means, one can compute the distorted coordinates for a sparse set of points or apply a perspective transformation (and also compute the derivatives) in the ideal zero-distortion setup.
    • projectPoints

      public static void projectPoints​(MatOfPoint3f objectPoints, Mat rvec, Mat tvec, Mat cameraMatrix, MatOfDouble distCoeffs, MatOfPoint2f imagePoints, Mat jacobian)
      Projects 3D points to an image plane.
      Parameters:
      objectPoints - Array of object points expressed wrt. the world coordinate frame. A 3xN/Nx3 1-channel or 1xN/Nx1 3-channel (or vector<Point3f> ), where N is the number of points in the view.
      rvec - The rotation vector (REF: Rodrigues) that, together with tvec, performs a change of basis from world to camera coordinate system, see REF: calibrateCamera for details.
      tvec - The translation vector, see parameter description above.
      cameraMatrix - Camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\) . If the vector is empty, the zero distortion coefficients are assumed.
      imagePoints - Output array of image points, 1xN/Nx1 2-channel, or vector<Point2f> .
      jacobian - Optional output 2Nx(10+<numDistCoeffs>) jacobian matrix of derivatives of image points with respect to components of the rotation vector, translation vector, focal lengths, coordinates of the principal point and the distortion coefficients. In the old interface different components of the jacobian are returned via different output parameters. function assumes that the aspect ratio (\(f_x / f_y\)) is fixed and correspondingly adjusts the jacobian matrix. The function computes the 2D projections of 3D points to the image plane, given intrinsic and extrinsic camera parameters. Optionally, the function computes Jacobians -matrices of partial derivatives of image points coordinates (as functions of all the input parameters) with respect to the particular parameters, intrinsic and/or extrinsic. The Jacobians are used during the global optimization in REF: calibrateCamera, REF: solvePnP, and REF: stereoCalibrate. The function itself can also be used to compute a re-projection error, given the current intrinsic and extrinsic parameters. Note: By setting rvec = tvec = \([0, 0, 0]\), or by setting cameraMatrix to a 3x3 identity matrix, or by passing zero distortion coefficients, one can get various useful partial cases of the function. This means, one can compute the distorted coordinates for a sparse set of points or apply a perspective transformation (and also compute the derivatives) in the ideal zero-distortion setup.
    • projectPoints

      public static void projectPoints​(MatOfPoint3f objectPoints, Mat rvec, Mat tvec, Mat cameraMatrix, MatOfDouble distCoeffs, MatOfPoint2f imagePoints)
      Projects 3D points to an image plane.
      Parameters:
      objectPoints - Array of object points expressed wrt. the world coordinate frame. A 3xN/Nx3 1-channel or 1xN/Nx1 3-channel (or vector<Point3f> ), where N is the number of points in the view.
      rvec - The rotation vector (REF: Rodrigues) that, together with tvec, performs a change of basis from world to camera coordinate system, see REF: calibrateCamera for details.
      tvec - The translation vector, see parameter description above.
      cameraMatrix - Camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\) . If the vector is empty, the zero distortion coefficients are assumed.
      imagePoints - Output array of image points, 1xN/Nx1 2-channel, or vector<Point2f> . points with respect to components of the rotation vector, translation vector, focal lengths, coordinates of the principal point and the distortion coefficients. In the old interface different components of the jacobian are returned via different output parameters. function assumes that the aspect ratio (\(f_x / f_y\)) is fixed and correspondingly adjusts the jacobian matrix. The function computes the 2D projections of 3D points to the image plane, given intrinsic and extrinsic camera parameters. Optionally, the function computes Jacobians -matrices of partial derivatives of image points coordinates (as functions of all the input parameters) with respect to the particular parameters, intrinsic and/or extrinsic. The Jacobians are used during the global optimization in REF: calibrateCamera, REF: solvePnP, and REF: stereoCalibrate. The function itself can also be used to compute a re-projection error, given the current intrinsic and extrinsic parameters. Note: By setting rvec = tvec = \([0, 0, 0]\), or by setting cameraMatrix to a 3x3 identity matrix, or by passing zero distortion coefficients, one can get various useful partial cases of the function. This means, one can compute the distorted coordinates for a sparse set of points or apply a perspective transformation (and also compute the derivatives) in the ideal zero-distortion setup.
    • solvePnP

      public static boolean solvePnP​(MatOfPoint3f objectPoints, MatOfPoint2f imagePoints, Mat cameraMatrix, MatOfDouble distCoeffs, Mat rvec, Mat tvec, boolean useExtrinsicGuess, int flags)
      Finds an object pose from 3D-2D point correspondences. SEE: REF: calib3d_solvePnP This function returns the rotation and the translation vectors that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame, using different methods:
      • P3P methods (REF: SOLVEPNP_P3P, REF: SOLVEPNP_AP3P): need 4 input points to return a unique solution.
      • REF: SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar.
      • REF: SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation. Number of input points must be 4. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
      • for all the other flags, number of input points must be >= 4 and object points can be in any configuration.
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvec - Output rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system.
      tvec - Output translation vector.
      useExtrinsicGuess - Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them.
      flags - Method for solving a PnP problem: see REF: calib3d_solvePnP_flags More information about Perspective-n-Points is described in REF: calib3d_solvePnP Note:
      • An example of how to use solvePnP for planar augmented reality can be found at opencv_source_code/samples/python/plane_ar.py
      • If you are using Python:
        • Numpy array slices won't work as input because solvePnP requires contiguous arrays (enforced by the assertion using cv::Mat::checkVector() around line 55 of modules/calib3d/src/solvepnp.cpp version 2.4.9)
        • The P3P algorithm requires image points to be in an array of shape (N,1,2) due to its calling of #undistortPoints (around line 75 of modules/calib3d/src/solvepnp.cpp version 2.4.9) which requires 2-channel information.
        • Thus, given some data D = np.array(...) where D.shape = (N,M), in order to use a subset of it as, e.g., imagePoints, one must effectively copy it into a new array: imagePoints = np.ascontiguousarray(D[:,:2]).reshape((N,1,2))
      • The methods REF: SOLVEPNP_DLS and REF: SOLVEPNP_UPNP cannot be used as the current implementations are unstable and sometimes give completely wrong results. If you pass one of these two flags, REF: SOLVEPNP_EPNP method will be used instead.
      • The minimum number of points is 4 in the general case. In the case of REF: SOLVEPNP_P3P and REF: SOLVEPNP_AP3P methods, it is required to use exactly 4 points (the first 3 points are used to estimate all the solutions of the P3P problem, the last one is used to retain the best solution that minimizes the reprojection error).
      • With REF: SOLVEPNP_ITERATIVE method and useExtrinsicGuess=true, the minimum number of points is 3 (3 points are sufficient to compute a pose but there are up to 4 solutions). The initial solution should be close to the global solution to converge.
      • With REF: SOLVEPNP_IPPE input points must be >= 4 and object points must be coplanar.
      • With REF: SOLVEPNP_IPPE_SQUARE this is a special case suitable for marker pose estimation. Number of input points must be 4. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
        • With REF: SOLVEPNP_SQPNP input points must be >= 3
      Returns:
      automatically generated
    • solvePnP

      public static boolean solvePnP​(MatOfPoint3f objectPoints, MatOfPoint2f imagePoints, Mat cameraMatrix, MatOfDouble distCoeffs, Mat rvec, Mat tvec, boolean useExtrinsicGuess)
      Finds an object pose from 3D-2D point correspondences. SEE: REF: calib3d_solvePnP This function returns the rotation and the translation vectors that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame, using different methods:
      • P3P methods (REF: SOLVEPNP_P3P, REF: SOLVEPNP_AP3P): need 4 input points to return a unique solution.
      • REF: SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar.
      • REF: SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation. Number of input points must be 4. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
      • for all the other flags, number of input points must be >= 4 and object points can be in any configuration.
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvec - Output rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system.
      tvec - Output translation vector.
      useExtrinsicGuess - Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them. More information about Perspective-n-Points is described in REF: calib3d_solvePnP Note:
      • An example of how to use solvePnP for planar augmented reality can be found at opencv_source_code/samples/python/plane_ar.py
      • If you are using Python:
        • Numpy array slices won't work as input because solvePnP requires contiguous arrays (enforced by the assertion using cv::Mat::checkVector() around line 55 of modules/calib3d/src/solvepnp.cpp version 2.4.9)
        • The P3P algorithm requires image points to be in an array of shape (N,1,2) due to its calling of #undistortPoints (around line 75 of modules/calib3d/src/solvepnp.cpp version 2.4.9) which requires 2-channel information.
        • Thus, given some data D = np.array(...) where D.shape = (N,M), in order to use a subset of it as, e.g., imagePoints, one must effectively copy it into a new array: imagePoints = np.ascontiguousarray(D[:,:2]).reshape((N,1,2))
      • The methods REF: SOLVEPNP_DLS and REF: SOLVEPNP_UPNP cannot be used as the current implementations are unstable and sometimes give completely wrong results. If you pass one of these two flags, REF: SOLVEPNP_EPNP method will be used instead.
      • The minimum number of points is 4 in the general case. In the case of REF: SOLVEPNP_P3P and REF: SOLVEPNP_AP3P methods, it is required to use exactly 4 points (the first 3 points are used to estimate all the solutions of the P3P problem, the last one is used to retain the best solution that minimizes the reprojection error).
      • With REF: SOLVEPNP_ITERATIVE method and useExtrinsicGuess=true, the minimum number of points is 3 (3 points are sufficient to compute a pose but there are up to 4 solutions). The initial solution should be close to the global solution to converge.
      • With REF: SOLVEPNP_IPPE input points must be >= 4 and object points must be coplanar.
      • With REF: SOLVEPNP_IPPE_SQUARE this is a special case suitable for marker pose estimation. Number of input points must be 4. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
        • With REF: SOLVEPNP_SQPNP input points must be >= 3
      Returns:
      automatically generated
    • solvePnP

      public static boolean solvePnP​(MatOfPoint3f objectPoints, MatOfPoint2f imagePoints, Mat cameraMatrix, MatOfDouble distCoeffs, Mat rvec, Mat tvec)
      Finds an object pose from 3D-2D point correspondences. SEE: REF: calib3d_solvePnP This function returns the rotation and the translation vectors that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame, using different methods:
      • P3P methods (REF: SOLVEPNP_P3P, REF: SOLVEPNP_AP3P): need 4 input points to return a unique solution.
      • REF: SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar.
      • REF: SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation. Number of input points must be 4. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
      • for all the other flags, number of input points must be >= 4 and object points can be in any configuration.
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvec - Output rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system.
      tvec - Output translation vector. the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them. More information about Perspective-n-Points is described in REF: calib3d_solvePnP Note:
      • An example of how to use solvePnP for planar augmented reality can be found at opencv_source_code/samples/python/plane_ar.py
      • If you are using Python:
        • Numpy array slices won't work as input because solvePnP requires contiguous arrays (enforced by the assertion using cv::Mat::checkVector() around line 55 of modules/calib3d/src/solvepnp.cpp version 2.4.9)
        • The P3P algorithm requires image points to be in an array of shape (N,1,2) due to its calling of #undistortPoints (around line 75 of modules/calib3d/src/solvepnp.cpp version 2.4.9) which requires 2-channel information.
        • Thus, given some data D = np.array(...) where D.shape = (N,M), in order to use a subset of it as, e.g., imagePoints, one must effectively copy it into a new array: imagePoints = np.ascontiguousarray(D[:,:2]).reshape((N,1,2))
      • The methods REF: SOLVEPNP_DLS and REF: SOLVEPNP_UPNP cannot be used as the current implementations are unstable and sometimes give completely wrong results. If you pass one of these two flags, REF: SOLVEPNP_EPNP method will be used instead.
      • The minimum number of points is 4 in the general case. In the case of REF: SOLVEPNP_P3P and REF: SOLVEPNP_AP3P methods, it is required to use exactly 4 points (the first 3 points are used to estimate all the solutions of the P3P problem, the last one is used to retain the best solution that minimizes the reprojection error).
      • With REF: SOLVEPNP_ITERATIVE method and useExtrinsicGuess=true, the minimum number of points is 3 (3 points are sufficient to compute a pose but there are up to 4 solutions). The initial solution should be close to the global solution to converge.
      • With REF: SOLVEPNP_IPPE input points must be >= 4 and object points must be coplanar.
      • With REF: SOLVEPNP_IPPE_SQUARE this is a special case suitable for marker pose estimation. Number of input points must be 4. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
        • With REF: SOLVEPNP_SQPNP input points must be >= 3
      Returns:
      automatically generated
    • solvePnPRansac

      public static boolean solvePnPRansac​(MatOfPoint3f objectPoints, MatOfPoint2f imagePoints, Mat cameraMatrix, MatOfDouble distCoeffs, Mat rvec, Mat tvec, boolean useExtrinsicGuess, int iterationsCount, float reprojectionError, double confidence, Mat inliers, int flags)
      Finds an object pose from 3D-2D point correspondences using the RANSAC scheme. SEE: REF: calib3d_solvePnP
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvec - Output rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system.
      tvec - Output translation vector.
      useExtrinsicGuess - Parameter used for REF: SOLVEPNP_ITERATIVE. If true (1), the function uses the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them.
      iterationsCount - Number of iterations.
      reprojectionError - Inlier threshold value used by the RANSAC procedure. The parameter value is the maximum allowed distance between the observed and computed point projections to consider it an inlier.
      confidence - The probability that the algorithm produces a useful result.
      inliers - Output vector that contains indices of inliers in objectPoints and imagePoints .
      flags - Method for solving a PnP problem (see REF: solvePnP ). The function estimates an object pose given a set of object points, their corresponding image projections, as well as the camera intrinsic matrix and the distortion coefficients. This function finds such a pose that minimizes reprojection error, that is, the sum of squared distances between the observed projections imagePoints and the projected (using REF: projectPoints ) objectPoints. The use of RANSAC makes the function resistant to outliers. Note:
      • An example of how to use solvePNPRansac for object detection can be found at opencv_source_code/samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/
      • The default method used to estimate the camera pose for the Minimal Sample Sets step is #SOLVEPNP_EPNP. Exceptions are:
        • if you choose #SOLVEPNP_P3P or #SOLVEPNP_AP3P, these methods will be used.
        • if the number of input points is equal to 4, #SOLVEPNP_P3P is used.
      • The method used to estimate the camera pose using all the inliers is defined by the flags parameters unless it is equal to #SOLVEPNP_P3P or #SOLVEPNP_AP3P. In this case, the method #SOLVEPNP_EPNP will be used instead.
      Returns:
      automatically generated
    • solvePnPRansac

      public static boolean solvePnPRansac​(MatOfPoint3f objectPoints, MatOfPoint2f imagePoints, Mat cameraMatrix, MatOfDouble distCoeffs, Mat rvec, Mat tvec, boolean useExtrinsicGuess, int iterationsCount, float reprojectionError, double confidence, Mat inliers)
      Finds an object pose from 3D-2D point correspondences using the RANSAC scheme. SEE: REF: calib3d_solvePnP
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvec - Output rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system.
      tvec - Output translation vector.
      useExtrinsicGuess - Parameter used for REF: SOLVEPNP_ITERATIVE. If true (1), the function uses the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them.
      iterationsCount - Number of iterations.
      reprojectionError - Inlier threshold value used by the RANSAC procedure. The parameter value is the maximum allowed distance between the observed and computed point projections to consider it an inlier.
      confidence - The probability that the algorithm produces a useful result.
      inliers - Output vector that contains indices of inliers in objectPoints and imagePoints . The function estimates an object pose given a set of object points, their corresponding image projections, as well as the camera intrinsic matrix and the distortion coefficients. This function finds such a pose that minimizes reprojection error, that is, the sum of squared distances between the observed projections imagePoints and the projected (using REF: projectPoints ) objectPoints. The use of RANSAC makes the function resistant to outliers. Note:
      • An example of how to use solvePNPRansac for object detection can be found at opencv_source_code/samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/
      • The default method used to estimate the camera pose for the Minimal Sample Sets step is #SOLVEPNP_EPNP. Exceptions are:
        • if you choose #SOLVEPNP_P3P or #SOLVEPNP_AP3P, these methods will be used.
        • if the number of input points is equal to 4, #SOLVEPNP_P3P is used.
      • The method used to estimate the camera pose using all the inliers is defined by the flags parameters unless it is equal to #SOLVEPNP_P3P or #SOLVEPNP_AP3P. In this case, the method #SOLVEPNP_EPNP will be used instead.
      Returns:
      automatically generated
    • solvePnPRansac

      public static boolean solvePnPRansac​(MatOfPoint3f objectPoints, MatOfPoint2f imagePoints, Mat cameraMatrix, MatOfDouble distCoeffs, Mat rvec, Mat tvec, boolean useExtrinsicGuess, int iterationsCount, float reprojectionError, double confidence)
      Finds an object pose from 3D-2D point correspondences using the RANSAC scheme. SEE: REF: calib3d_solvePnP
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvec - Output rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system.
      tvec - Output translation vector.
      useExtrinsicGuess - Parameter used for REF: SOLVEPNP_ITERATIVE. If true (1), the function uses the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them.
      iterationsCount - Number of iterations.
      reprojectionError - Inlier threshold value used by the RANSAC procedure. The parameter value is the maximum allowed distance between the observed and computed point projections to consider it an inlier.
      confidence - The probability that the algorithm produces a useful result. The function estimates an object pose given a set of object points, their corresponding image projections, as well as the camera intrinsic matrix and the distortion coefficients. This function finds such a pose that minimizes reprojection error, that is, the sum of squared distances between the observed projections imagePoints and the projected (using REF: projectPoints ) objectPoints. The use of RANSAC makes the function resistant to outliers. Note:
      • An example of how to use solvePNPRansac for object detection can be found at opencv_source_code/samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/
      • The default method used to estimate the camera pose for the Minimal Sample Sets step is #SOLVEPNP_EPNP. Exceptions are:
        • if you choose #SOLVEPNP_P3P or #SOLVEPNP_AP3P, these methods will be used.
        • if the number of input points is equal to 4, #SOLVEPNP_P3P is used.
      • The method used to estimate the camera pose using all the inliers is defined by the flags parameters unless it is equal to #SOLVEPNP_P3P or #SOLVEPNP_AP3P. In this case, the method #SOLVEPNP_EPNP will be used instead.
      Returns:
      automatically generated
    • solvePnPRansac

      public static boolean solvePnPRansac​(MatOfPoint3f objectPoints, MatOfPoint2f imagePoints, Mat cameraMatrix, MatOfDouble distCoeffs, Mat rvec, Mat tvec, boolean useExtrinsicGuess, int iterationsCount, float reprojectionError)
      Finds an object pose from 3D-2D point correspondences using the RANSAC scheme. SEE: REF: calib3d_solvePnP
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvec - Output rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system.
      tvec - Output translation vector.
      useExtrinsicGuess - Parameter used for REF: SOLVEPNP_ITERATIVE. If true (1), the function uses the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them.
      iterationsCount - Number of iterations.
      reprojectionError - Inlier threshold value used by the RANSAC procedure. The parameter value is the maximum allowed distance between the observed and computed point projections to consider it an inlier. The function estimates an object pose given a set of object points, their corresponding image projections, as well as the camera intrinsic matrix and the distortion coefficients. This function finds such a pose that minimizes reprojection error, that is, the sum of squared distances between the observed projections imagePoints and the projected (using REF: projectPoints ) objectPoints. The use of RANSAC makes the function resistant to outliers. Note:
      • An example of how to use solvePNPRansac for object detection can be found at opencv_source_code/samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/
      • The default method used to estimate the camera pose for the Minimal Sample Sets step is #SOLVEPNP_EPNP. Exceptions are:
        • if you choose #SOLVEPNP_P3P or #SOLVEPNP_AP3P, these methods will be used.
        • if the number of input points is equal to 4, #SOLVEPNP_P3P is used.
      • The method used to estimate the camera pose using all the inliers is defined by the flags parameters unless it is equal to #SOLVEPNP_P3P or #SOLVEPNP_AP3P. In this case, the method #SOLVEPNP_EPNP will be used instead.
      Returns:
      automatically generated
    • solvePnPRansac

      public static boolean solvePnPRansac​(MatOfPoint3f objectPoints, MatOfPoint2f imagePoints, Mat cameraMatrix, MatOfDouble distCoeffs, Mat rvec, Mat tvec, boolean useExtrinsicGuess, int iterationsCount)
      Finds an object pose from 3D-2D point correspondences using the RANSAC scheme. SEE: REF: calib3d_solvePnP
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvec - Output rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system.
      tvec - Output translation vector.
      useExtrinsicGuess - Parameter used for REF: SOLVEPNP_ITERATIVE. If true (1), the function uses the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them.
      iterationsCount - Number of iterations. is the maximum allowed distance between the observed and computed point projections to consider it an inlier. The function estimates an object pose given a set of object points, their corresponding image projections, as well as the camera intrinsic matrix and the distortion coefficients. This function finds such a pose that minimizes reprojection error, that is, the sum of squared distances between the observed projections imagePoints and the projected (using REF: projectPoints ) objectPoints. The use of RANSAC makes the function resistant to outliers. Note:
      • An example of how to use solvePNPRansac for object detection can be found at opencv_source_code/samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/
      • The default method used to estimate the camera pose for the Minimal Sample Sets step is #SOLVEPNP_EPNP. Exceptions are:
        • if you choose #SOLVEPNP_P3P or #SOLVEPNP_AP3P, these methods will be used.
        • if the number of input points is equal to 4, #SOLVEPNP_P3P is used.
      • The method used to estimate the camera pose using all the inliers is defined by the flags parameters unless it is equal to #SOLVEPNP_P3P or #SOLVEPNP_AP3P. In this case, the method #SOLVEPNP_EPNP will be used instead.
      Returns:
      automatically generated
    • solvePnPRansac

      public static boolean solvePnPRansac​(MatOfPoint3f objectPoints, MatOfPoint2f imagePoints, Mat cameraMatrix, MatOfDouble distCoeffs, Mat rvec, Mat tvec, boolean useExtrinsicGuess)
      Finds an object pose from 3D-2D point correspondences using the RANSAC scheme. SEE: REF: calib3d_solvePnP
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvec - Output rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system.
      tvec - Output translation vector.
      useExtrinsicGuess - Parameter used for REF: SOLVEPNP_ITERATIVE. If true (1), the function uses the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them. is the maximum allowed distance between the observed and computed point projections to consider it an inlier. The function estimates an object pose given a set of object points, their corresponding image projections, as well as the camera intrinsic matrix and the distortion coefficients. This function finds such a pose that minimizes reprojection error, that is, the sum of squared distances between the observed projections imagePoints and the projected (using REF: projectPoints ) objectPoints. The use of RANSAC makes the function resistant to outliers. Note:
      • An example of how to use solvePNPRansac for object detection can be found at opencv_source_code/samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/
      • The default method used to estimate the camera pose for the Minimal Sample Sets step is #SOLVEPNP_EPNP. Exceptions are:
        • if you choose #SOLVEPNP_P3P or #SOLVEPNP_AP3P, these methods will be used.
        • if the number of input points is equal to 4, #SOLVEPNP_P3P is used.
      • The method used to estimate the camera pose using all the inliers is defined by the flags parameters unless it is equal to #SOLVEPNP_P3P or #SOLVEPNP_AP3P. In this case, the method #SOLVEPNP_EPNP will be used instead.
      Returns:
      automatically generated
    • solvePnPRansac

      public static boolean solvePnPRansac​(MatOfPoint3f objectPoints, MatOfPoint2f imagePoints, Mat cameraMatrix, MatOfDouble distCoeffs, Mat rvec, Mat tvec)
      Finds an object pose from 3D-2D point correspondences using the RANSAC scheme. SEE: REF: calib3d_solvePnP
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvec - Output rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system.
      tvec - Output translation vector. the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them. is the maximum allowed distance between the observed and computed point projections to consider it an inlier. The function estimates an object pose given a set of object points, their corresponding image projections, as well as the camera intrinsic matrix and the distortion coefficients. This function finds such a pose that minimizes reprojection error, that is, the sum of squared distances between the observed projections imagePoints and the projected (using REF: projectPoints ) objectPoints. The use of RANSAC makes the function resistant to outliers. Note:
      • An example of how to use solvePNPRansac for object detection can be found at opencv_source_code/samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/
      • The default method used to estimate the camera pose for the Minimal Sample Sets step is #SOLVEPNP_EPNP. Exceptions are:
        • if you choose #SOLVEPNP_P3P or #SOLVEPNP_AP3P, these methods will be used.
        • if the number of input points is equal to 4, #SOLVEPNP_P3P is used.
      • The method used to estimate the camera pose using all the inliers is defined by the flags parameters unless it is equal to #SOLVEPNP_P3P or #SOLVEPNP_AP3P. In this case, the method #SOLVEPNP_EPNP will be used instead.
      Returns:
      automatically generated
    • solvePnPRansac

      public static boolean solvePnPRansac​(MatOfPoint3f objectPoints, MatOfPoint2f imagePoints, Mat cameraMatrix, MatOfDouble distCoeffs, Mat rvec, Mat tvec, Mat inliers, UsacParams params)
    • solvePnPRansac

      public static boolean solvePnPRansac​(MatOfPoint3f objectPoints, MatOfPoint2f imagePoints, Mat cameraMatrix, MatOfDouble distCoeffs, Mat rvec, Mat tvec, Mat inliers)
    • solveP3P

      public static int solveP3P​(Mat objectPoints, Mat imagePoints, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, int flags)
      Finds an object pose from 3 3D-2D point correspondences. SEE: REF: calib3d_solvePnP
      Parameters:
      objectPoints - Array of object points in the object coordinate space, 3x3 1-channel or 1x3/3x1 3-channel. vector<Point3f> can be also passed here.
      imagePoints - Array of corresponding image points, 3x2 1-channel or 1x3/3x1 2-channel. vector<Point2f> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvecs - Output rotation vectors (see REF: Rodrigues ) that, together with tvecs, brings points from the model coordinate system to the camera coordinate system. A P3P problem has up to 4 solutions.
      tvecs - Output translation vectors.
      flags - Method for solving a P3P problem:
      • REF: SOLVEPNP_P3P Method is based on the paper of X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang "Complete Solution Classification for the Perspective-Three-Point Problem" (CITE: gao2003complete).
      • REF: SOLVEPNP_AP3P Method is based on the paper of T. Ke and S. Roumeliotis. "An Efficient Algebraic Solution to the Perspective-Three-Point Problem" (CITE: Ke17).
      The function estimates the object pose given 3 object points, their corresponding image projections, as well as the camera intrinsic matrix and the distortion coefficients. Note: The solutions are sorted by reprojection errors (lowest to highest).
      Returns:
      automatically generated
    • solvePnPRefineLM

      public static void solvePnPRefineLM​(Mat objectPoints, Mat imagePoints, Mat cameraMatrix, Mat distCoeffs, Mat rvec, Mat tvec, TermCriteria criteria)
      Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution. SEE: REF: calib3d_solvePnP
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can also be passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can also be passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvec - Input/Output rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system. Input values are used as an initial solution.
      tvec - Input/Output translation vector. Input values are used as an initial solution.
      criteria - Criteria when to stop the Levenberg-Marquard iterative algorithm. The function refines the object pose given at least 3 object points, their corresponding image projections, an initial solution for the rotation and translation vector, as well as the camera intrinsic matrix and the distortion coefficients. The function minimizes the projection error with respect to the rotation and the translation vectors, according to a Levenberg-Marquardt iterative minimization CITE: Madsen04 CITE: Eade13 process.
    • solvePnPRefineLM

      public static void solvePnPRefineLM​(Mat objectPoints, Mat imagePoints, Mat cameraMatrix, Mat distCoeffs, Mat rvec, Mat tvec)
      Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution. SEE: REF: calib3d_solvePnP
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can also be passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can also be passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvec - Input/Output rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system. Input values are used as an initial solution.
      tvec - Input/Output translation vector. Input values are used as an initial solution. The function refines the object pose given at least 3 object points, their corresponding image projections, an initial solution for the rotation and translation vector, as well as the camera intrinsic matrix and the distortion coefficients. The function minimizes the projection error with respect to the rotation and the translation vectors, according to a Levenberg-Marquardt iterative minimization CITE: Madsen04 CITE: Eade13 process.
    • solvePnPRefineVVS

      public static void solvePnPRefineVVS​(Mat objectPoints, Mat imagePoints, Mat cameraMatrix, Mat distCoeffs, Mat rvec, Mat tvec, TermCriteria criteria, double VVSlambda)
      Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution. SEE: REF: calib3d_solvePnP
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can also be passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can also be passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvec - Input/Output rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system. Input values are used as an initial solution.
      tvec - Input/Output translation vector. Input values are used as an initial solution.
      criteria - Criteria when to stop the Levenberg-Marquard iterative algorithm.
      VVSlambda - Gain for the virtual visual servoing control law, equivalent to the \(\alpha\) gain in the Damped Gauss-Newton formulation. The function refines the object pose given at least 3 object points, their corresponding image projections, an initial solution for the rotation and translation vector, as well as the camera intrinsic matrix and the distortion coefficients. The function minimizes the projection error with respect to the rotation and the translation vectors, using a virtual visual servoing (VVS) CITE: Chaumette06 CITE: Marchand16 scheme.
    • solvePnPRefineVVS

      public static void solvePnPRefineVVS​(Mat objectPoints, Mat imagePoints, Mat cameraMatrix, Mat distCoeffs, Mat rvec, Mat tvec, TermCriteria criteria)
      Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution. SEE: REF: calib3d_solvePnP
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can also be passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can also be passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvec - Input/Output rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system. Input values are used as an initial solution.
      tvec - Input/Output translation vector. Input values are used as an initial solution.
      criteria - Criteria when to stop the Levenberg-Marquard iterative algorithm. gain in the Damped Gauss-Newton formulation. The function refines the object pose given at least 3 object points, their corresponding image projections, an initial solution for the rotation and translation vector, as well as the camera intrinsic matrix and the distortion coefficients. The function minimizes the projection error with respect to the rotation and the translation vectors, using a virtual visual servoing (VVS) CITE: Chaumette06 CITE: Marchand16 scheme.
    • solvePnPRefineVVS

      public static void solvePnPRefineVVS​(Mat objectPoints, Mat imagePoints, Mat cameraMatrix, Mat distCoeffs, Mat rvec, Mat tvec)
      Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution. SEE: REF: calib3d_solvePnP
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can also be passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can also be passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvec - Input/Output rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system. Input values are used as an initial solution.
      tvec - Input/Output translation vector. Input values are used as an initial solution. gain in the Damped Gauss-Newton formulation. The function refines the object pose given at least 3 object points, their corresponding image projections, an initial solution for the rotation and translation vector, as well as the camera intrinsic matrix and the distortion coefficients. The function minimizes the projection error with respect to the rotation and the translation vectors, using a virtual visual servoing (VVS) CITE: Chaumette06 CITE: Marchand16 scheme.
    • solvePnPGeneric

      public static int solvePnPGeneric​(Mat objectPoints, Mat imagePoints, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, boolean useExtrinsicGuess, int flags, Mat rvec, Mat tvec, Mat reprojectionError)
      Finds an object pose from 3D-2D point correspondences. SEE: REF: calib3d_solvePnP This function returns a list of all the possible solutions (a solution is a <rotation vector, translation vector> couple), depending on the number of input points and the chosen method:
      • P3P methods (REF: SOLVEPNP_P3P, REF: SOLVEPNP_AP3P): 3 or 4 input points. Number of returned solutions can be between 0 and 4 with 3 input points.
      • REF: SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar. Returns 2 solutions.
      • REF: SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation. Number of input points must be 4 and 2 solutions are returned. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
      • for all the other flags, number of input points must be >= 4 and object points can be in any configuration. Only 1 solution is returned.
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvecs - Vector of output rotation vectors (see REF: Rodrigues ) that, together with tvecs, brings points from the model coordinate system to the camera coordinate system.
      tvecs - Vector of output translation vectors.
      useExtrinsicGuess - Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them.
      flags - Method for solving a PnP problem: see REF: calib3d_solvePnP_flags
      rvec - Rotation vector used to initialize an iterative PnP refinement algorithm, when flag is REF: SOLVEPNP_ITERATIVE and useExtrinsicGuess is set to true.
      tvec - Translation vector used to initialize an iterative PnP refinement algorithm, when flag is REF: SOLVEPNP_ITERATIVE and useExtrinsicGuess is set to true.
      reprojectionError - Optional vector of reprojection error, that is the RMS error (\( \text{RMSE} = \sqrt{\frac{\sum_{i}^{N} \left ( \hat{y_i} - y_i \right )^2}{N}} \)) between the input image points and the 3D object points projected with the estimated pose. More information is described in REF: calib3d_solvePnP Note:
      • An example of how to use solvePnP for planar augmented reality can be found at opencv_source_code/samples/python/plane_ar.py
      • If you are using Python:
        • Numpy array slices won't work as input because solvePnP requires contiguous arrays (enforced by the assertion using cv::Mat::checkVector() around line 55 of modules/calib3d/src/solvepnp.cpp version 2.4.9)
        • The P3P algorithm requires image points to be in an array of shape (N,1,2) due to its calling of #undistortPoints (around line 75 of modules/calib3d/src/solvepnp.cpp version 2.4.9) which requires 2-channel information.
        • Thus, given some data D = np.array(...) where D.shape = (N,M), in order to use a subset of it as, e.g., imagePoints, one must effectively copy it into a new array: imagePoints = np.ascontiguousarray(D[:,:2]).reshape((N,1,2))
      • The methods REF: SOLVEPNP_DLS and REF: SOLVEPNP_UPNP cannot be used as the current implementations are unstable and sometimes give completely wrong results. If you pass one of these two flags, REF: SOLVEPNP_EPNP method will be used instead.
      • The minimum number of points is 4 in the general case. In the case of REF: SOLVEPNP_P3P and REF: SOLVEPNP_AP3P methods, it is required to use exactly 4 points (the first 3 points are used to estimate all the solutions of the P3P problem, the last one is used to retain the best solution that minimizes the reprojection error).
      • With REF: SOLVEPNP_ITERATIVE method and useExtrinsicGuess=true, the minimum number of points is 3 (3 points are sufficient to compute a pose but there are up to 4 solutions). The initial solution should be close to the global solution to converge.
      • With REF: SOLVEPNP_IPPE input points must be >= 4 and object points must be coplanar.
      • With REF: SOLVEPNP_IPPE_SQUARE this is a special case suitable for marker pose estimation. Number of input points must be 4. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
      Returns:
      automatically generated
    • solvePnPGeneric

      public static int solvePnPGeneric​(Mat objectPoints, Mat imagePoints, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, boolean useExtrinsicGuess, int flags, Mat rvec, Mat tvec)
      Finds an object pose from 3D-2D point correspondences. SEE: REF: calib3d_solvePnP This function returns a list of all the possible solutions (a solution is a <rotation vector, translation vector> couple), depending on the number of input points and the chosen method:
      • P3P methods (REF: SOLVEPNP_P3P, REF: SOLVEPNP_AP3P): 3 or 4 input points. Number of returned solutions can be between 0 and 4 with 3 input points.
      • REF: SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar. Returns 2 solutions.
      • REF: SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation. Number of input points must be 4 and 2 solutions are returned. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
      • for all the other flags, number of input points must be >= 4 and object points can be in any configuration. Only 1 solution is returned.
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvecs - Vector of output rotation vectors (see REF: Rodrigues ) that, together with tvecs, brings points from the model coordinate system to the camera coordinate system.
      tvecs - Vector of output translation vectors.
      useExtrinsicGuess - Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them.
      flags - Method for solving a PnP problem: see REF: calib3d_solvePnP_flags
      rvec - Rotation vector used to initialize an iterative PnP refinement algorithm, when flag is REF: SOLVEPNP_ITERATIVE and useExtrinsicGuess is set to true.
      tvec - Translation vector used to initialize an iterative PnP refinement algorithm, when flag is REF: SOLVEPNP_ITERATIVE and useExtrinsicGuess is set to true. (\( \text{RMSE} = \sqrt{\frac{\sum_{i}^{N} \left ( \hat{y_i} - y_i \right )^2}{N}} \)) between the input image points and the 3D object points projected with the estimated pose. More information is described in REF: calib3d_solvePnP Note:
      • An example of how to use solvePnP for planar augmented reality can be found at opencv_source_code/samples/python/plane_ar.py
      • If you are using Python:
        • Numpy array slices won't work as input because solvePnP requires contiguous arrays (enforced by the assertion using cv::Mat::checkVector() around line 55 of modules/calib3d/src/solvepnp.cpp version 2.4.9)
        • The P3P algorithm requires image points to be in an array of shape (N,1,2) due to its calling of #undistortPoints (around line 75 of modules/calib3d/src/solvepnp.cpp version 2.4.9) which requires 2-channel information.
        • Thus, given some data D = np.array(...) where D.shape = (N,M), in order to use a subset of it as, e.g., imagePoints, one must effectively copy it into a new array: imagePoints = np.ascontiguousarray(D[:,:2]).reshape((N,1,2))
      • The methods REF: SOLVEPNP_DLS and REF: SOLVEPNP_UPNP cannot be used as the current implementations are unstable and sometimes give completely wrong results. If you pass one of these two flags, REF: SOLVEPNP_EPNP method will be used instead.
      • The minimum number of points is 4 in the general case. In the case of REF: SOLVEPNP_P3P and REF: SOLVEPNP_AP3P methods, it is required to use exactly 4 points (the first 3 points are used to estimate all the solutions of the P3P problem, the last one is used to retain the best solution that minimizes the reprojection error).
      • With REF: SOLVEPNP_ITERATIVE method and useExtrinsicGuess=true, the minimum number of points is 3 (3 points are sufficient to compute a pose but there are up to 4 solutions). The initial solution should be close to the global solution to converge.
      • With REF: SOLVEPNP_IPPE input points must be >= 4 and object points must be coplanar.
      • With REF: SOLVEPNP_IPPE_SQUARE this is a special case suitable for marker pose estimation. Number of input points must be 4. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
      Returns:
      automatically generated
    • solvePnPGeneric

      public static int solvePnPGeneric​(Mat objectPoints, Mat imagePoints, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, boolean useExtrinsicGuess, int flags, Mat rvec)
      Finds an object pose from 3D-2D point correspondences. SEE: REF: calib3d_solvePnP This function returns a list of all the possible solutions (a solution is a <rotation vector, translation vector> couple), depending on the number of input points and the chosen method:
      • P3P methods (REF: SOLVEPNP_P3P, REF: SOLVEPNP_AP3P): 3 or 4 input points. Number of returned solutions can be between 0 and 4 with 3 input points.
      • REF: SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar. Returns 2 solutions.
      • REF: SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation. Number of input points must be 4 and 2 solutions are returned. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
      • for all the other flags, number of input points must be >= 4 and object points can be in any configuration. Only 1 solution is returned.
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvecs - Vector of output rotation vectors (see REF: Rodrigues ) that, together with tvecs, brings points from the model coordinate system to the camera coordinate system.
      tvecs - Vector of output translation vectors.
      useExtrinsicGuess - Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them.
      flags - Method for solving a PnP problem: see REF: calib3d_solvePnP_flags
      rvec - Rotation vector used to initialize an iterative PnP refinement algorithm, when flag is REF: SOLVEPNP_ITERATIVE and useExtrinsicGuess is set to true. and useExtrinsicGuess is set to true. (\( \text{RMSE} = \sqrt{\frac{\sum_{i}^{N} \left ( \hat{y_i} - y_i \right )^2}{N}} \)) between the input image points and the 3D object points projected with the estimated pose. More information is described in REF: calib3d_solvePnP Note:
      • An example of how to use solvePnP for planar augmented reality can be found at opencv_source_code/samples/python/plane_ar.py
      • If you are using Python:
        • Numpy array slices won't work as input because solvePnP requires contiguous arrays (enforced by the assertion using cv::Mat::checkVector() around line 55 of modules/calib3d/src/solvepnp.cpp version 2.4.9)
        • The P3P algorithm requires image points to be in an array of shape (N,1,2) due to its calling of #undistortPoints (around line 75 of modules/calib3d/src/solvepnp.cpp version 2.4.9) which requires 2-channel information.
        • Thus, given some data D = np.array(...) where D.shape = (N,M), in order to use a subset of it as, e.g., imagePoints, one must effectively copy it into a new array: imagePoints = np.ascontiguousarray(D[:,:2]).reshape((N,1,2))
      • The methods REF: SOLVEPNP_DLS and REF: SOLVEPNP_UPNP cannot be used as the current implementations are unstable and sometimes give completely wrong results. If you pass one of these two flags, REF: SOLVEPNP_EPNP method will be used instead.
      • The minimum number of points is 4 in the general case. In the case of REF: SOLVEPNP_P3P and REF: SOLVEPNP_AP3P methods, it is required to use exactly 4 points (the first 3 points are used to estimate all the solutions of the P3P problem, the last one is used to retain the best solution that minimizes the reprojection error).
      • With REF: SOLVEPNP_ITERATIVE method and useExtrinsicGuess=true, the minimum number of points is 3 (3 points are sufficient to compute a pose but there are up to 4 solutions). The initial solution should be close to the global solution to converge.
      • With REF: SOLVEPNP_IPPE input points must be >= 4 and object points must be coplanar.
      • With REF: SOLVEPNP_IPPE_SQUARE this is a special case suitable for marker pose estimation. Number of input points must be 4. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
      Returns:
      automatically generated
    • solvePnPGeneric

      public static int solvePnPGeneric​(Mat objectPoints, Mat imagePoints, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, boolean useExtrinsicGuess, int flags)
      Finds an object pose from 3D-2D point correspondences. SEE: REF: calib3d_solvePnP This function returns a list of all the possible solutions (a solution is a <rotation vector, translation vector> couple), depending on the number of input points and the chosen method:
      • P3P methods (REF: SOLVEPNP_P3P, REF: SOLVEPNP_AP3P): 3 or 4 input points. Number of returned solutions can be between 0 and 4 with 3 input points.
      • REF: SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar. Returns 2 solutions.
      • REF: SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation. Number of input points must be 4 and 2 solutions are returned. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
      • for all the other flags, number of input points must be >= 4 and object points can be in any configuration. Only 1 solution is returned.
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvecs - Vector of output rotation vectors (see REF: Rodrigues ) that, together with tvecs, brings points from the model coordinate system to the camera coordinate system.
      tvecs - Vector of output translation vectors.
      useExtrinsicGuess - Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them.
      flags - Method for solving a PnP problem: see REF: calib3d_solvePnP_flags and useExtrinsicGuess is set to true. and useExtrinsicGuess is set to true. (\( \text{RMSE} = \sqrt{\frac{\sum_{i}^{N} \left ( \hat{y_i} - y_i \right )^2}{N}} \)) between the input image points and the 3D object points projected with the estimated pose. More information is described in REF: calib3d_solvePnP Note:
      • An example of how to use solvePnP for planar augmented reality can be found at opencv_source_code/samples/python/plane_ar.py
      • If you are using Python:
        • Numpy array slices won't work as input because solvePnP requires contiguous arrays (enforced by the assertion using cv::Mat::checkVector() around line 55 of modules/calib3d/src/solvepnp.cpp version 2.4.9)
        • The P3P algorithm requires image points to be in an array of shape (N,1,2) due to its calling of #undistortPoints (around line 75 of modules/calib3d/src/solvepnp.cpp version 2.4.9) which requires 2-channel information.
        • Thus, given some data D = np.array(...) where D.shape = (N,M), in order to use a subset of it as, e.g., imagePoints, one must effectively copy it into a new array: imagePoints = np.ascontiguousarray(D[:,:2]).reshape((N,1,2))
      • The methods REF: SOLVEPNP_DLS and REF: SOLVEPNP_UPNP cannot be used as the current implementations are unstable and sometimes give completely wrong results. If you pass one of these two flags, REF: SOLVEPNP_EPNP method will be used instead.
      • The minimum number of points is 4 in the general case. In the case of REF: SOLVEPNP_P3P and REF: SOLVEPNP_AP3P methods, it is required to use exactly 4 points (the first 3 points are used to estimate all the solutions of the P3P problem, the last one is used to retain the best solution that minimizes the reprojection error).
      • With REF: SOLVEPNP_ITERATIVE method and useExtrinsicGuess=true, the minimum number of points is 3 (3 points are sufficient to compute a pose but there are up to 4 solutions). The initial solution should be close to the global solution to converge.
      • With REF: SOLVEPNP_IPPE input points must be >= 4 and object points must be coplanar.
      • With REF: SOLVEPNP_IPPE_SQUARE this is a special case suitable for marker pose estimation. Number of input points must be 4. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
      Returns:
      automatically generated
    • solvePnPGeneric

      public static int solvePnPGeneric​(Mat objectPoints, Mat imagePoints, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, boolean useExtrinsicGuess)
      Finds an object pose from 3D-2D point correspondences. SEE: REF: calib3d_solvePnP This function returns a list of all the possible solutions (a solution is a <rotation vector, translation vector> couple), depending on the number of input points and the chosen method:
      • P3P methods (REF: SOLVEPNP_P3P, REF: SOLVEPNP_AP3P): 3 or 4 input points. Number of returned solutions can be between 0 and 4 with 3 input points.
      • REF: SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar. Returns 2 solutions.
      • REF: SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation. Number of input points must be 4 and 2 solutions are returned. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
      • for all the other flags, number of input points must be >= 4 and object points can be in any configuration. Only 1 solution is returned.
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvecs - Vector of output rotation vectors (see REF: Rodrigues ) that, together with tvecs, brings points from the model coordinate system to the camera coordinate system.
      tvecs - Vector of output translation vectors.
      useExtrinsicGuess - Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them. and useExtrinsicGuess is set to true. and useExtrinsicGuess is set to true. (\( \text{RMSE} = \sqrt{\frac{\sum_{i}^{N} \left ( \hat{y_i} - y_i \right )^2}{N}} \)) between the input image points and the 3D object points projected with the estimated pose. More information is described in REF: calib3d_solvePnP Note:
      • An example of how to use solvePnP for planar augmented reality can be found at opencv_source_code/samples/python/plane_ar.py
      • If you are using Python:
        • Numpy array slices won't work as input because solvePnP requires contiguous arrays (enforced by the assertion using cv::Mat::checkVector() around line 55 of modules/calib3d/src/solvepnp.cpp version 2.4.9)
        • The P3P algorithm requires image points to be in an array of shape (N,1,2) due to its calling of #undistortPoints (around line 75 of modules/calib3d/src/solvepnp.cpp version 2.4.9) which requires 2-channel information.
        • Thus, given some data D = np.array(...) where D.shape = (N,M), in order to use a subset of it as, e.g., imagePoints, one must effectively copy it into a new array: imagePoints = np.ascontiguousarray(D[:,:2]).reshape((N,1,2))
      • The methods REF: SOLVEPNP_DLS and REF: SOLVEPNP_UPNP cannot be used as the current implementations are unstable and sometimes give completely wrong results. If you pass one of these two flags, REF: SOLVEPNP_EPNP method will be used instead.
      • The minimum number of points is 4 in the general case. In the case of REF: SOLVEPNP_P3P and REF: SOLVEPNP_AP3P methods, it is required to use exactly 4 points (the first 3 points are used to estimate all the solutions of the P3P problem, the last one is used to retain the best solution that minimizes the reprojection error).
      • With REF: SOLVEPNP_ITERATIVE method and useExtrinsicGuess=true, the minimum number of points is 3 (3 points are sufficient to compute a pose but there are up to 4 solutions). The initial solution should be close to the global solution to converge.
      • With REF: SOLVEPNP_IPPE input points must be >= 4 and object points must be coplanar.
      • With REF: SOLVEPNP_IPPE_SQUARE this is a special case suitable for marker pose estimation. Number of input points must be 4. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
      Returns:
      automatically generated
    • solvePnPGeneric

      public static int solvePnPGeneric​(Mat objectPoints, Mat imagePoints, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs)
      Finds an object pose from 3D-2D point correspondences. SEE: REF: calib3d_solvePnP This function returns a list of all the possible solutions (a solution is a <rotation vector, translation vector> couple), depending on the number of input points and the chosen method:
      • P3P methods (REF: SOLVEPNP_P3P, REF: SOLVEPNP_AP3P): 3 or 4 input points. Number of returned solutions can be between 0 and 4 with 3 input points.
      • REF: SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar. Returns 2 solutions.
      • REF: SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation. Number of input points must be 4 and 2 solutions are returned. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
      • for all the other flags, number of input points must be >= 4 and object points can be in any configuration. Only 1 solution is returned.
      Parameters:
      objectPoints - Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. vector<Point3d> can be also passed here.
      imagePoints - Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. vector<Point2d> can be also passed here.
      cameraMatrix - Input camera intrinsic matrix \(\cameramatrix{A}\) .
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      rvecs - Vector of output rotation vectors (see REF: Rodrigues ) that, together with tvecs, brings points from the model coordinate system to the camera coordinate system.
      tvecs - Vector of output translation vectors. the provided rvec and tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them. and useExtrinsicGuess is set to true. and useExtrinsicGuess is set to true. (\( \text{RMSE} = \sqrt{\frac{\sum_{i}^{N} \left ( \hat{y_i} - y_i \right )^2}{N}} \)) between the input image points and the 3D object points projected with the estimated pose. More information is described in REF: calib3d_solvePnP Note:
      • An example of how to use solvePnP for planar augmented reality can be found at opencv_source_code/samples/python/plane_ar.py
      • If you are using Python:
        • Numpy array slices won't work as input because solvePnP requires contiguous arrays (enforced by the assertion using cv::Mat::checkVector() around line 55 of modules/calib3d/src/solvepnp.cpp version 2.4.9)
        • The P3P algorithm requires image points to be in an array of shape (N,1,2) due to its calling of #undistortPoints (around line 75 of modules/calib3d/src/solvepnp.cpp version 2.4.9) which requires 2-channel information.
        • Thus, given some data D = np.array(...) where D.shape = (N,M), in order to use a subset of it as, e.g., imagePoints, one must effectively copy it into a new array: imagePoints = np.ascontiguousarray(D[:,:2]).reshape((N,1,2))
      • The methods REF: SOLVEPNP_DLS and REF: SOLVEPNP_UPNP cannot be used as the current implementations are unstable and sometimes give completely wrong results. If you pass one of these two flags, REF: SOLVEPNP_EPNP method will be used instead.
      • The minimum number of points is 4 in the general case. In the case of REF: SOLVEPNP_P3P and REF: SOLVEPNP_AP3P methods, it is required to use exactly 4 points (the first 3 points are used to estimate all the solutions of the P3P problem, the last one is used to retain the best solution that minimizes the reprojection error).
      • With REF: SOLVEPNP_ITERATIVE method and useExtrinsicGuess=true, the minimum number of points is 3 (3 points are sufficient to compute a pose but there are up to 4 solutions). The initial solution should be close to the global solution to converge.
      • With REF: SOLVEPNP_IPPE input points must be >= 4 and object points must be coplanar.
      • With REF: SOLVEPNP_IPPE_SQUARE this is a special case suitable for marker pose estimation. Number of input points must be 4. Object points must be defined in the following order:
        • point 0: [-squareLength / 2, squareLength / 2, 0]
        • point 1: [ squareLength / 2, squareLength / 2, 0]
        • point 2: [ squareLength / 2, -squareLength / 2, 0]
        • point 3: [-squareLength / 2, -squareLength / 2, 0]
      Returns:
      automatically generated
    • initCameraMatrix2D

      public static Mat initCameraMatrix2D​(List<MatOfPoint3f> objectPoints, List<MatOfPoint2f> imagePoints, Size imageSize, double aspectRatio)
      Finds an initial camera intrinsic matrix from 3D-2D point correspondences.
      Parameters:
      objectPoints - Vector of vectors of the calibration pattern points in the calibration pattern coordinate space. In the old interface all the per-view vectors are concatenated. See #calibrateCamera for details.
      imagePoints - Vector of vectors of the projections of the calibration pattern points. In the old interface all the per-view vectors are concatenated.
      imageSize - Image size in pixels used to initialize the principal point.
      aspectRatio - If it is zero or negative, both \(f_x\) and \(f_y\) are estimated independently. Otherwise, \(f_x = f_y \cdot \texttt{aspectRatio}\) . The function estimates and returns an initial camera intrinsic matrix for the camera calibration process. Currently, the function only supports planar calibration patterns, which are patterns where each object point has z-coordinate =0.
      Returns:
      automatically generated
    • initCameraMatrix2D

      public static Mat initCameraMatrix2D​(List<MatOfPoint3f> objectPoints, List<MatOfPoint2f> imagePoints, Size imageSize)
      Finds an initial camera intrinsic matrix from 3D-2D point correspondences.
      Parameters:
      objectPoints - Vector of vectors of the calibration pattern points in the calibration pattern coordinate space. In the old interface all the per-view vectors are concatenated. See #calibrateCamera for details.
      imagePoints - Vector of vectors of the projections of the calibration pattern points. In the old interface all the per-view vectors are concatenated.
      imageSize - Image size in pixels used to initialize the principal point. Otherwise, \(f_x = f_y \cdot \texttt{aspectRatio}\) . The function estimates and returns an initial camera intrinsic matrix for the camera calibration process. Currently, the function only supports planar calibration patterns, which are patterns where each object point has z-coordinate =0.
      Returns:
      automatically generated
    • findChessboardCorners

      public static boolean findChessboardCorners​(Mat image, Size patternSize, MatOfPoint2f corners, int flags)
      Finds the positions of internal corners of the chessboard.
      Parameters:
      image - Source chessboard view. It must be an 8-bit grayscale or color image.
      patternSize - Number of inner corners per a chessboard row and column ( patternSize = cv::Size(points_per_row,points_per_colum) = cv::Size(columns,rows) ).
      corners - Output array of detected corners.
      flags - Various operation flags that can be zero or a combination of the following values:
      • REF: CALIB_CB_ADAPTIVE_THRESH Use adaptive thresholding to convert the image to black and white, rather than a fixed threshold level (computed from the average image brightness).
      • REF: CALIB_CB_NORMALIZE_IMAGE Normalize the image gamma with #equalizeHist before applying fixed or adaptive thresholding.
      • REF: CALIB_CB_FILTER_QUADS Use additional criteria (like contour area, perimeter, square-like shape) to filter out false quads extracted at the contour retrieval stage.
      • REF: CALIB_CB_FAST_CHECK Run a fast check on the image that looks for chessboard corners, and shortcut the call if none is found. This can drastically speed up the call in the degenerate condition when no chessboard is observed.
      The function attempts to determine whether the input image is a view of the chessboard pattern and locate the internal chessboard corners. The function returns a non-zero value if all of the corners are found and they are placed in a certain order (row by row, left to right in every row). Otherwise, if the function fails to find all the corners or reorder them, it returns 0. For example, a regular chessboard has 8 x 8 squares and 7 x 7 internal corners, that is, points where the black squares touch each other. The detected coordinates are approximate, and to determine their positions more accurately, the function calls #cornerSubPix. You also may use the function #cornerSubPix with different parameters if returned coordinates are not accurate enough. Sample usage of detecting and drawing chessboard corners: : Size patternsize(8,6); //interior number of corners Mat gray = ....; //source image vector<Point2f> corners; //this will be filled by the detected corners //CALIB_CB_FAST_CHECK saves a lot of time on images //that do not contain any chessboard corners bool patternfound = findChessboardCorners(gray, patternsize, corners, CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE + CALIB_CB_FAST_CHECK); if(patternfound) cornerSubPix(gray, corners, Size(11, 11), Size(-1, -1), TermCriteria(CV_TERMCRIT_EPS + CV_TERMCRIT_ITER, 30, 0.1)); drawChessboardCorners(img, patternsize, Mat(corners), patternfound); Note: The function requires white space (like a square-thick border, the wider the better) around the board to make the detection more robust in various environments. Otherwise, if there is no border and the background is dark, the outer black squares cannot be segmented properly and so the square grouping and ordering algorithm fails. Use gen_pattern.py (REF: tutorial_camera_calibration_pattern) to create checkerboard.
      Returns:
      automatically generated
    • findChessboardCorners

      public static boolean findChessboardCorners​(Mat image, Size patternSize, MatOfPoint2f corners)
      Finds the positions of internal corners of the chessboard.
      Parameters:
      image - Source chessboard view. It must be an 8-bit grayscale or color image.
      patternSize - Number of inner corners per a chessboard row and column ( patternSize = cv::Size(points_per_row,points_per_colum) = cv::Size(columns,rows) ).
      corners - Output array of detected corners.
      • REF: CALIB_CB_ADAPTIVE_THRESH Use adaptive thresholding to convert the image to black and white, rather than a fixed threshold level (computed from the average image brightness).
      • REF: CALIB_CB_NORMALIZE_IMAGE Normalize the image gamma with #equalizeHist before applying fixed or adaptive thresholding.
      • REF: CALIB_CB_FILTER_QUADS Use additional criteria (like contour area, perimeter, square-like shape) to filter out false quads extracted at the contour retrieval stage.
      • REF: CALIB_CB_FAST_CHECK Run a fast check on the image that looks for chessboard corners, and shortcut the call if none is found. This can drastically speed up the call in the degenerate condition when no chessboard is observed.
      The function attempts to determine whether the input image is a view of the chessboard pattern and locate the internal chessboard corners. The function returns a non-zero value if all of the corners are found and they are placed in a certain order (row by row, left to right in every row). Otherwise, if the function fails to find all the corners or reorder them, it returns 0. For example, a regular chessboard has 8 x 8 squares and 7 x 7 internal corners, that is, points where the black squares touch each other. The detected coordinates are approximate, and to determine their positions more accurately, the function calls #cornerSubPix. You also may use the function #cornerSubPix with different parameters if returned coordinates are not accurate enough. Sample usage of detecting and drawing chessboard corners: : Size patternsize(8,6); //interior number of corners Mat gray = ....; //source image vector<Point2f> corners; //this will be filled by the detected corners //CALIB_CB_FAST_CHECK saves a lot of time on images //that do not contain any chessboard corners bool patternfound = findChessboardCorners(gray, patternsize, corners, CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE + CALIB_CB_FAST_CHECK); if(patternfound) cornerSubPix(gray, corners, Size(11, 11), Size(-1, -1), TermCriteria(CV_TERMCRIT_EPS + CV_TERMCRIT_ITER, 30, 0.1)); drawChessboardCorners(img, patternsize, Mat(corners), patternfound); Note: The function requires white space (like a square-thick border, the wider the better) around the board to make the detection more robust in various environments. Otherwise, if there is no border and the background is dark, the outer black squares cannot be segmented properly and so the square grouping and ordering algorithm fails. Use gen_pattern.py (REF: tutorial_camera_calibration_pattern) to create checkerboard.
      Returns:
      automatically generated
    • checkChessboard

      public static boolean checkChessboard​(Mat img, Size size)
    • findChessboardCornersSBWithMeta

      public static boolean findChessboardCornersSBWithMeta​(Mat image, Size patternSize, Mat corners, int flags, Mat meta)
      Finds the positions of internal corners of the chessboard using a sector based approach.
      Parameters:
      image - Source chessboard view. It must be an 8-bit grayscale or color image.
      patternSize - Number of inner corners per a chessboard row and column ( patternSize = cv::Size(points_per_row,points_per_colum) = cv::Size(columns,rows) ).
      corners - Output array of detected corners.
      flags - Various operation flags that can be zero or a combination of the following values:
      • REF: CALIB_CB_NORMALIZE_IMAGE Normalize the image gamma with equalizeHist before detection.
      • REF: CALIB_CB_EXHAUSTIVE Run an exhaustive search to improve detection rate.
      • REF: CALIB_CB_ACCURACY Up sample input image to improve sub-pixel accuracy due to aliasing effects.
      • REF: CALIB_CB_LARGER The detected pattern is allowed to be larger than patternSize (see description).
      • REF: CALIB_CB_MARKER The detected pattern must have a marker (see description). This should be used if an accurate camera calibration is required.
      meta - Optional output arrray of detected corners (CV_8UC1 and size = cv::Size(columns,rows)). Each entry stands for one corner of the pattern and can have one of the following values:
      • 0 = no meta data attached
      • 1 = left-top corner of a black cell
      • 2 = left-top corner of a white cell
      • 3 = left-top corner of a black cell with a white marker dot
      • 4 = left-top corner of a white cell with a black marker dot (pattern origin in case of markers otherwise first corner)
      The function is analog to #findChessboardCorners but uses a localized radon transformation approximated by box filters being more robust to all sort of noise, faster on larger images and is able to directly return the sub-pixel position of the internal chessboard corners. The Method is based on the paper CITE: duda2018 "Accurate Detection and Localization of Checkerboard Corners for Calibration" demonstrating that the returned sub-pixel positions are more accurate than the one returned by cornerSubPix allowing a precise camera calibration for demanding applications. In the case, the flags REF: CALIB_CB_LARGER or REF: CALIB_CB_MARKER are given, the result can be recovered from the optional meta array. Both flags are helpful to use calibration patterns exceeding the field of view of the camera. These oversized patterns allow more accurate calibrations as corners can be utilized, which are as close as possible to the image borders. For a consistent coordinate system across all images, the optional marker (see image below) can be used to move the origin of the board to the location where the black circle is located. Note: The function requires a white boarder with roughly the same width as one of the checkerboard fields around the whole board to improve the detection in various environments. In addition, because of the localized radon transformation it is beneficial to use round corners for the field corners which are located on the outside of the board. The following figure illustrates a sample checkerboard optimized for the detection. However, any other checkerboard can be used as well. Use gen_pattern.py (REF: tutorial_camera_calibration_pattern) to create checkerboard. ![Checkerboard](pics/checkerboard_radon.png)
      Returns:
      automatically generated
    • findChessboardCornersSB

      public static boolean findChessboardCornersSB​(Mat image, Size patternSize, Mat corners, int flags)
    • findChessboardCornersSB

      public static boolean findChessboardCornersSB​(Mat image, Size patternSize, Mat corners)
    • estimateChessboardSharpness

      public static Scalar estimateChessboardSharpness​(Mat image, Size patternSize, Mat corners, float rise_distance, boolean vertical, Mat sharpness)
      Estimates the sharpness of a detected chessboard. Image sharpness, as well as brightness, are a critical parameter for accuracte camera calibration. For accessing these parameters for filtering out problematic calibraiton images, this method calculates edge profiles by traveling from black to white chessboard cell centers. Based on this, the number of pixels is calculated required to transit from black to white. This width of the transition area is a good indication of how sharp the chessboard is imaged and should be below ~3.0 pixels.
      Parameters:
      image - Gray image used to find chessboard corners
      patternSize - Size of a found chessboard pattern
      corners - Corners found by #findChessboardCornersSB
      rise_distance - Rise distance 0.8 means 10% ... 90% of the final signal strength
      vertical - By default edge responses for horizontal lines are calculated
      sharpness - Optional output array with a sharpness value for calculated edge responses (see description) The optional sharpness array is of type CV_32FC1 and has for each calculated profile one row with the following five entries: 0 = x coordinate of the underlying edge in the image 1 = y coordinate of the underlying edge in the image 2 = width of the transition area (sharpness) 3 = signal strength in the black cell (min brightness) 4 = signal strength in the white cell (max brightness)
      Returns:
      Scalar(average sharpness, average min brightness, average max brightness,0)
    • estimateChessboardSharpness

      public static Scalar estimateChessboardSharpness​(Mat image, Size patternSize, Mat corners, float rise_distance, boolean vertical)
      Estimates the sharpness of a detected chessboard. Image sharpness, as well as brightness, are a critical parameter for accuracte camera calibration. For accessing these parameters for filtering out problematic calibraiton images, this method calculates edge profiles by traveling from black to white chessboard cell centers. Based on this, the number of pixels is calculated required to transit from black to white. This width of the transition area is a good indication of how sharp the chessboard is imaged and should be below ~3.0 pixels.
      Parameters:
      image - Gray image used to find chessboard corners
      patternSize - Size of a found chessboard pattern
      corners - Corners found by #findChessboardCornersSB
      rise_distance - Rise distance 0.8 means 10% ... 90% of the final signal strength
      vertical - By default edge responses for horizontal lines are calculated The optional sharpness array is of type CV_32FC1 and has for each calculated profile one row with the following five entries: 0 = x coordinate of the underlying edge in the image 1 = y coordinate of the underlying edge in the image 2 = width of the transition area (sharpness) 3 = signal strength in the black cell (min brightness) 4 = signal strength in the white cell (max brightness)
      Returns:
      Scalar(average sharpness, average min brightness, average max brightness,0)
    • estimateChessboardSharpness

      public static Scalar estimateChessboardSharpness​(Mat image, Size patternSize, Mat corners, float rise_distance)
      Estimates the sharpness of a detected chessboard. Image sharpness, as well as brightness, are a critical parameter for accuracte camera calibration. For accessing these parameters for filtering out problematic calibraiton images, this method calculates edge profiles by traveling from black to white chessboard cell centers. Based on this, the number of pixels is calculated required to transit from black to white. This width of the transition area is a good indication of how sharp the chessboard is imaged and should be below ~3.0 pixels.
      Parameters:
      image - Gray image used to find chessboard corners
      patternSize - Size of a found chessboard pattern
      corners - Corners found by #findChessboardCornersSB
      rise_distance - Rise distance 0.8 means 10% ... 90% of the final signal strength The optional sharpness array is of type CV_32FC1 and has for each calculated profile one row with the following five entries: 0 = x coordinate of the underlying edge in the image 1 = y coordinate of the underlying edge in the image 2 = width of the transition area (sharpness) 3 = signal strength in the black cell (min brightness) 4 = signal strength in the white cell (max brightness)
      Returns:
      Scalar(average sharpness, average min brightness, average max brightness,0)
    • estimateChessboardSharpness

      public static Scalar estimateChessboardSharpness​(Mat image, Size patternSize, Mat corners)
      Estimates the sharpness of a detected chessboard. Image sharpness, as well as brightness, are a critical parameter for accuracte camera calibration. For accessing these parameters for filtering out problematic calibraiton images, this method calculates edge profiles by traveling from black to white chessboard cell centers. Based on this, the number of pixels is calculated required to transit from black to white. This width of the transition area is a good indication of how sharp the chessboard is imaged and should be below ~3.0 pixels.
      Parameters:
      image - Gray image used to find chessboard corners
      patternSize - Size of a found chessboard pattern
      corners - Corners found by #findChessboardCornersSB The optional sharpness array is of type CV_32FC1 and has for each calculated profile one row with the following five entries: 0 = x coordinate of the underlying edge in the image 1 = y coordinate of the underlying edge in the image 2 = width of the transition area (sharpness) 3 = signal strength in the black cell (min brightness) 4 = signal strength in the white cell (max brightness)
      Returns:
      Scalar(average sharpness, average min brightness, average max brightness,0)
    • find4QuadCornerSubpix

      public static boolean find4QuadCornerSubpix​(Mat img, Mat corners, Size region_size)
    • drawChessboardCorners

      public static void drawChessboardCorners​(Mat image, Size patternSize, MatOfPoint2f corners, boolean patternWasFound)
      Renders the detected chessboard corners.
      Parameters:
      image - Destination image. It must be an 8-bit color image.
      patternSize - Number of inner corners per a chessboard row and column (patternSize = cv::Size(points_per_row,points_per_column)).
      corners - Array of detected corners, the output of #findChessboardCorners.
      patternWasFound - Parameter indicating whether the complete board was found or not. The return value of #findChessboardCorners should be passed here. The function draws individual chessboard corners detected either as red circles if the board was not found, or as colored corners connected with lines if the board was found.
    • drawFrameAxes

      public static void drawFrameAxes​(Mat image, Mat cameraMatrix, Mat distCoeffs, Mat rvec, Mat tvec, float length, int thickness)
      Draw axes of the world/object coordinate system from pose estimation. SEE: solvePnP
      Parameters:
      image - Input/output image. It must have 1 or 3 channels. The number of channels is not altered.
      cameraMatrix - Input 3x3 floating-point matrix of camera intrinsic parameters. \(\cameramatrix{A}\)
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is empty, the zero distortion coefficients are assumed.
      rvec - Rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system.
      tvec - Translation vector.
      length - Length of the painted axes in the same unit than tvec (usually in meters).
      thickness - Line thickness of the painted axes. This function draws the axes of the world/object coordinate system w.r.t. to the camera frame. OX is drawn in red, OY in green and OZ in blue.
    • drawFrameAxes

      public static void drawFrameAxes​(Mat image, Mat cameraMatrix, Mat distCoeffs, Mat rvec, Mat tvec, float length)
      Draw axes of the world/object coordinate system from pose estimation. SEE: solvePnP
      Parameters:
      image - Input/output image. It must have 1 or 3 channels. The number of channels is not altered.
      cameraMatrix - Input 3x3 floating-point matrix of camera intrinsic parameters. \(\cameramatrix{A}\)
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is empty, the zero distortion coefficients are assumed.
      rvec - Rotation vector (see REF: Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system.
      tvec - Translation vector.
      length - Length of the painted axes in the same unit than tvec (usually in meters). This function draws the axes of the world/object coordinate system w.r.t. to the camera frame. OX is drawn in red, OY in green and OZ in blue.
    • findCirclesGrid

      public static boolean findCirclesGrid​(Mat image, Size patternSize, Mat centers, int flags)
    • findCirclesGrid

      public static boolean findCirclesGrid​(Mat image, Size patternSize, Mat centers)
    • calibrateCameraExtended

      public static double calibrateCameraExtended​(List<Mat> objectPoints, List<Mat> imagePoints, Size imageSize, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, Mat stdDeviationsIntrinsics, Mat stdDeviationsExtrinsics, Mat perViewErrors, int flags, TermCriteria criteria)
      Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.
      Parameters:
      objectPoints - In the new interface it is a vector of vectors of calibration pattern points in the calibration pattern coordinate space (e.g. std::vector<std::vector<cv::Vec3f>>). The outer vector contains as many elements as the number of pattern views. If the same calibration pattern is shown in each view and it is fully visible, all the vectors will be the same. Although, it is possible to use partially occluded patterns or even different patterns in different views. Then, the vectors will be different. Although the points are 3D, they all lie in the calibration pattern's XY coordinate plane (thus 0 in the Z-coordinate), if the used calibration pattern is a planar rig. In the old interface all the vectors of object points from different views are concatenated together.
      imagePoints - In the new interface it is a vector of vectors of the projections of calibration pattern points (e.g. std::vector<std::vector<cv::Vec2f>>). imagePoints.size() and objectPoints.size(), and imagePoints[i].size() and objectPoints[i].size() for each i, must be equal, respectively. In the old interface all the vectors of object points from different views are concatenated together.
      imageSize - Size of the image used only to initialize the camera intrinsic matrix.
      cameraMatrix - Input/output 3x3 floating-point camera intrinsic matrix \(\cameramatrix{A}\) . If REF: CALIB_USE_INTRINSIC_GUESS and/or REF: CALIB_FIX_ASPECT_RATIO, REF: CALIB_FIX_PRINCIPAL_POINT or REF: CALIB_FIX_FOCAL_LENGTH are specified, some or all of fx, fy, cx, cy must be initialized before calling the function.
      distCoeffs - Input/output vector of distortion coefficients \(\distcoeffs\).
      rvecs - Output vector of rotation vectors (REF: Rodrigues ) estimated for each pattern view (e.g. std::vector<cv::Mat>>). That is, each i-th rotation vector together with the corresponding i-th translation vector (see the next output parameter description) brings the calibration pattern from the object coordinate space (in which object points are specified) to the camera coordinate space. In more technical terms, the tuple of the i-th rotation and translation vector performs a change of basis from object coordinate space to camera coordinate space. Due to its duality, this tuple is equivalent to the position of the calibration pattern with respect to the camera coordinate space.
      tvecs - Output vector of translation vectors estimated for each pattern view, see parameter describtion above.
      stdDeviationsIntrinsics - Output vector of standard deviations estimated for intrinsic parameters. Order of deviations values: \((f_x, f_y, c_x, c_y, k_1, k_2, p_1, p_2, k_3, k_4, k_5, k_6 , s_1, s_2, s_3, s_4, \tau_x, \tau_y)\) If one of parameters is not estimated, it's deviation is equals to zero.
      stdDeviationsExtrinsics - Output vector of standard deviations estimated for extrinsic parameters. Order of deviations values: \((R_0, T_0, \dotsc , R_{M - 1}, T_{M - 1})\) where M is the number of pattern views. \(R_i, T_i\) are concatenated 1x3 vectors.
      perViewErrors - Output vector of the RMS re-projection error estimated for each pattern view.
      flags - Different flags that may be zero or a combination of the following values:
      • REF: CALIB_USE_INTRINSIC_GUESS cameraMatrix contains valid initial values of fx, fy, cx, cy that are optimized further. Otherwise, (cx, cy) is initially set to the image center ( imageSize is used), and focal distances are computed in a least-squares fashion. Note, that if intrinsic parameters are known, there is no need to use this function just to estimate extrinsic parameters. Use REF: solvePnP instead.
      • REF: CALIB_FIX_PRINCIPAL_POINT The principal point is not changed during the global optimization. It stays at the center or at a different location specified when REF: CALIB_USE_INTRINSIC_GUESS is set too.
      • REF: CALIB_FIX_ASPECT_RATIO The functions consider only fy as a free parameter. The ratio fx/fy stays the same as in the input cameraMatrix . When REF: CALIB_USE_INTRINSIC_GUESS is not set, the actual input values of fx and fy are ignored, only their ratio is computed and used further.
      • REF: CALIB_ZERO_TANGENT_DIST Tangential distortion coefficients \((p_1, p_2)\) are set to zeros and stay zero.
      • REF: CALIB_FIX_FOCAL_LENGTH The focal length is not changed during the global optimization if REF: CALIB_USE_INTRINSIC_GUESS is set.
      • REF: CALIB_FIX_K1,..., REF: CALIB_FIX_K6 The corresponding radial distortion coefficient is not changed during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      • REF: CALIB_RATIONAL_MODEL Coefficients k4, k5, and k6 are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the rational model and return 8 coefficients or more.
      • REF: CALIB_THIN_PRISM_MODEL Coefficients s1, s2, s3 and s4 are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the thin prism model and return 12 coefficients or more.
      • REF: CALIB_FIX_S1_S2_S3_S4 The thin prism distortion coefficients are not changed during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      • REF: CALIB_TILTED_MODEL Coefficients tauX and tauY are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the tilted sensor model and return 14 coefficients.
      • REF: CALIB_FIX_TAUX_TAUY The coefficients of the tilted sensor model are not changed during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      criteria - Termination criteria for the iterative optimization algorithm.
      Returns:
      the overall RMS re-projection error. The function estimates the intrinsic camera parameters and extrinsic parameters for each of the views. The algorithm is based on CITE: Zhang2000 and CITE: BouguetMCT . The coordinates of 3D object points and their corresponding 2D projections in each view must be specified. That may be achieved by using an object with known geometry and easily detectable feature points. Such an object is called a calibration rig or calibration pattern, and OpenCV has built-in support for a chessboard as a calibration rig (see REF: findChessboardCorners). Currently, initialization of intrinsic parameters (when REF: CALIB_USE_INTRINSIC_GUESS is not set) is only implemented for planar calibration patterns (where Z-coordinates of the object points must be all zeros). 3D calibration rigs can also be used as long as initial cameraMatrix is provided. The algorithm performs the following steps:
      • Compute the initial intrinsic parameters (the option only available for planar calibration patterns) or read them from the input parameters. The distortion coefficients are all set to zeros initially unless some of CALIB_FIX_K? are specified.
      • Estimate the initial camera pose as if the intrinsic parameters have been already known. This is done using REF: solvePnP .
      • Run the global Levenberg-Marquardt optimization algorithm to minimize the reprojection error, that is, the total sum of squared distances between the observed feature points imagePoints and the projected (using the current estimates for camera parameters and the poses) object points objectPoints. See REF: projectPoints for details.
      Note: If you use a non-square (i.e. non-N-by-N) grid and REF: findChessboardCorners for calibration, and REF: calibrateCamera returns bad values (zero distortion coefficients, \(c_x\) and \(c_y\) very far from the image center, and/or large differences between \(f_x\) and \(f_y\) (ratios of 10:1 or more)), then you are probably using patternSize=cvSize(rows,cols) instead of using patternSize=cvSize(cols,rows) in REF: findChessboardCorners. SEE: calibrateCameraRO, findChessboardCorners, solvePnP, initCameraMatrix2D, stereoCalibrate, undistort
    • calibrateCameraExtended

      public static double calibrateCameraExtended​(List<Mat> objectPoints, List<Mat> imagePoints, Size imageSize, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, Mat stdDeviationsIntrinsics, Mat stdDeviationsExtrinsics, Mat perViewErrors, int flags)
      Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.
      Parameters:
      objectPoints - In the new interface it is a vector of vectors of calibration pattern points in the calibration pattern coordinate space (e.g. std::vector<std::vector<cv::Vec3f>>). The outer vector contains as many elements as the number of pattern views. If the same calibration pattern is shown in each view and it is fully visible, all the vectors will be the same. Although, it is possible to use partially occluded patterns or even different patterns in different views. Then, the vectors will be different. Although the points are 3D, they all lie in the calibration pattern's XY coordinate plane (thus 0 in the Z-coordinate), if the used calibration pattern is a planar rig. In the old interface all the vectors of object points from different views are concatenated together.
      imagePoints - In the new interface it is a vector of vectors of the projections of calibration pattern points (e.g. std::vector<std::vector<cv::Vec2f>>). imagePoints.size() and objectPoints.size(), and imagePoints[i].size() and objectPoints[i].size() for each i, must be equal, respectively. In the old interface all the vectors of object points from different views are concatenated together.
      imageSize - Size of the image used only to initialize the camera intrinsic matrix.
      cameraMatrix - Input/output 3x3 floating-point camera intrinsic matrix \(\cameramatrix{A}\) . If REF: CALIB_USE_INTRINSIC_GUESS and/or REF: CALIB_FIX_ASPECT_RATIO, REF: CALIB_FIX_PRINCIPAL_POINT or REF: CALIB_FIX_FOCAL_LENGTH are specified, some or all of fx, fy, cx, cy must be initialized before calling the function.
      distCoeffs - Input/output vector of distortion coefficients \(\distcoeffs\).
      rvecs - Output vector of rotation vectors (REF: Rodrigues ) estimated for each pattern view (e.g. std::vector<cv::Mat>>). That is, each i-th rotation vector together with the corresponding i-th translation vector (see the next output parameter description) brings the calibration pattern from the object coordinate space (in which object points are specified) to the camera coordinate space. In more technical terms, the tuple of the i-th rotation and translation vector performs a change of basis from object coordinate space to camera coordinate space. Due to its duality, this tuple is equivalent to the position of the calibration pattern with respect to the camera coordinate space.
      tvecs - Output vector of translation vectors estimated for each pattern view, see parameter describtion above.
      stdDeviationsIntrinsics - Output vector of standard deviations estimated for intrinsic parameters. Order of deviations values: \((f_x, f_y, c_x, c_y, k_1, k_2, p_1, p_2, k_3, k_4, k_5, k_6 , s_1, s_2, s_3, s_4, \tau_x, \tau_y)\) If one of parameters is not estimated, it's deviation is equals to zero.
      stdDeviationsExtrinsics - Output vector of standard deviations estimated for extrinsic parameters. Order of deviations values: \((R_0, T_0, \dotsc , R_{M - 1}, T_{M - 1})\) where M is the number of pattern views. \(R_i, T_i\) are concatenated 1x3 vectors.
      perViewErrors - Output vector of the RMS re-projection error estimated for each pattern view.
      flags - Different flags that may be zero or a combination of the following values:
      • REF: CALIB_USE_INTRINSIC_GUESS cameraMatrix contains valid initial values of fx, fy, cx, cy that are optimized further. Otherwise, (cx, cy) is initially set to the image center ( imageSize is used), and focal distances are computed in a least-squares fashion. Note, that if intrinsic parameters are known, there is no need to use this function just to estimate extrinsic parameters. Use REF: solvePnP instead.
      • REF: CALIB_FIX_PRINCIPAL_POINT The principal point is not changed during the global optimization. It stays at the center or at a different location specified when REF: CALIB_USE_INTRINSIC_GUESS is set too.
      • REF: CALIB_FIX_ASPECT_RATIO The functions consider only fy as a free parameter. The ratio fx/fy stays the same as in the input cameraMatrix . When REF: CALIB_USE_INTRINSIC_GUESS is not set, the actual input values of fx and fy are ignored, only their ratio is computed and used further.
      • REF: CALIB_ZERO_TANGENT_DIST Tangential distortion coefficients \((p_1, p_2)\) are set to zeros and stay zero.
      • REF: CALIB_FIX_FOCAL_LENGTH The focal length is not changed during the global optimization if REF: CALIB_USE_INTRINSIC_GUESS is set.
      • REF: CALIB_FIX_K1,..., REF: CALIB_FIX_K6 The corresponding radial distortion coefficient is not changed during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      • REF: CALIB_RATIONAL_MODEL Coefficients k4, k5, and k6 are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the rational model and return 8 coefficients or more.
      • REF: CALIB_THIN_PRISM_MODEL Coefficients s1, s2, s3 and s4 are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the thin prism model and return 12 coefficients or more.
      • REF: CALIB_FIX_S1_S2_S3_S4 The thin prism distortion coefficients are not changed during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      • REF: CALIB_TILTED_MODEL Coefficients tauX and tauY are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the tilted sensor model and return 14 coefficients.
      • REF: CALIB_FIX_TAUX_TAUY The coefficients of the tilted sensor model are not changed during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      Returns:
      the overall RMS re-projection error. The function estimates the intrinsic camera parameters and extrinsic parameters for each of the views. The algorithm is based on CITE: Zhang2000 and CITE: BouguetMCT . The coordinates of 3D object points and their corresponding 2D projections in each view must be specified. That may be achieved by using an object with known geometry and easily detectable feature points. Such an object is called a calibration rig or calibration pattern, and OpenCV has built-in support for a chessboard as a calibration rig (see REF: findChessboardCorners). Currently, initialization of intrinsic parameters (when REF: CALIB_USE_INTRINSIC_GUESS is not set) is only implemented for planar calibration patterns (where Z-coordinates of the object points must be all zeros). 3D calibration rigs can also be used as long as initial cameraMatrix is provided. The algorithm performs the following steps:
      • Compute the initial intrinsic parameters (the option only available for planar calibration patterns) or read them from the input parameters. The distortion coefficients are all set to zeros initially unless some of CALIB_FIX_K? are specified.
      • Estimate the initial camera pose as if the intrinsic parameters have been already known. This is done using REF: solvePnP .
      • Run the global Levenberg-Marquardt optimization algorithm to minimize the reprojection error, that is, the total sum of squared distances between the observed feature points imagePoints and the projected (using the current estimates for camera parameters and the poses) object points objectPoints. See REF: projectPoints for details.
      Note: If you use a non-square (i.e. non-N-by-N) grid and REF: findChessboardCorners for calibration, and REF: calibrateCamera returns bad values (zero distortion coefficients, \(c_x\) and \(c_y\) very far from the image center, and/or large differences between \(f_x\) and \(f_y\) (ratios of 10:1 or more)), then you are probably using patternSize=cvSize(rows,cols) instead of using patternSize=cvSize(cols,rows) in REF: findChessboardCorners. SEE: calibrateCameraRO, findChessboardCorners, solvePnP, initCameraMatrix2D, stereoCalibrate, undistort
    • calibrateCameraExtended

      public static double calibrateCameraExtended​(List<Mat> objectPoints, List<Mat> imagePoints, Size imageSize, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, Mat stdDeviationsIntrinsics, Mat stdDeviationsExtrinsics, Mat perViewErrors)
      Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.
      Parameters:
      objectPoints - In the new interface it is a vector of vectors of calibration pattern points in the calibration pattern coordinate space (e.g. std::vector<std::vector<cv::Vec3f>>). The outer vector contains as many elements as the number of pattern views. If the same calibration pattern is shown in each view and it is fully visible, all the vectors will be the same. Although, it is possible to use partially occluded patterns or even different patterns in different views. Then, the vectors will be different. Although the points are 3D, they all lie in the calibration pattern's XY coordinate plane (thus 0 in the Z-coordinate), if the used calibration pattern is a planar rig. In the old interface all the vectors of object points from different views are concatenated together.
      imagePoints - In the new interface it is a vector of vectors of the projections of calibration pattern points (e.g. std::vector<std::vector<cv::Vec2f>>). imagePoints.size() and objectPoints.size(), and imagePoints[i].size() and objectPoints[i].size() for each i, must be equal, respectively. In the old interface all the vectors of object points from different views are concatenated together.
      imageSize - Size of the image used only to initialize the camera intrinsic matrix.
      cameraMatrix - Input/output 3x3 floating-point camera intrinsic matrix \(\cameramatrix{A}\) . If REF: CALIB_USE_INTRINSIC_GUESS and/or REF: CALIB_FIX_ASPECT_RATIO, REF: CALIB_FIX_PRINCIPAL_POINT or REF: CALIB_FIX_FOCAL_LENGTH are specified, some or all of fx, fy, cx, cy must be initialized before calling the function.
      distCoeffs - Input/output vector of distortion coefficients \(\distcoeffs\).
      rvecs - Output vector of rotation vectors (REF: Rodrigues ) estimated for each pattern view (e.g. std::vector<cv::Mat>>). That is, each i-th rotation vector together with the corresponding i-th translation vector (see the next output parameter description) brings the calibration pattern from the object coordinate space (in which object points are specified) to the camera coordinate space. In more technical terms, the tuple of the i-th rotation and translation vector performs a change of basis from object coordinate space to camera coordinate space. Due to its duality, this tuple is equivalent to the position of the calibration pattern with respect to the camera coordinate space.
      tvecs - Output vector of translation vectors estimated for each pattern view, see parameter describtion above.
      stdDeviationsIntrinsics - Output vector of standard deviations estimated for intrinsic parameters. Order of deviations values: \((f_x, f_y, c_x, c_y, k_1, k_2, p_1, p_2, k_3, k_4, k_5, k_6 , s_1, s_2, s_3, s_4, \tau_x, \tau_y)\) If one of parameters is not estimated, it's deviation is equals to zero.
      stdDeviationsExtrinsics - Output vector of standard deviations estimated for extrinsic parameters. Order of deviations values: \((R_0, T_0, \dotsc , R_{M - 1}, T_{M - 1})\) where M is the number of pattern views. \(R_i, T_i\) are concatenated 1x3 vectors.
      perViewErrors - Output vector of the RMS re-projection error estimated for each pattern view.
      • REF: CALIB_USE_INTRINSIC_GUESS cameraMatrix contains valid initial values of fx, fy, cx, cy that are optimized further. Otherwise, (cx, cy) is initially set to the image center ( imageSize is used), and focal distances are computed in a least-squares fashion. Note, that if intrinsic parameters are known, there is no need to use this function just to estimate extrinsic parameters. Use REF: solvePnP instead.
      • REF: CALIB_FIX_PRINCIPAL_POINT The principal point is not changed during the global optimization. It stays at the center or at a different location specified when REF: CALIB_USE_INTRINSIC_GUESS is set too.
      • REF: CALIB_FIX_ASPECT_RATIO The functions consider only fy as a free parameter. The ratio fx/fy stays the same as in the input cameraMatrix . When REF: CALIB_USE_INTRINSIC_GUESS is not set, the actual input values of fx and fy are ignored, only their ratio is computed and used further.
      • REF: CALIB_ZERO_TANGENT_DIST Tangential distortion coefficients \((p_1, p_2)\) are set to zeros and stay zero.
      • REF: CALIB_FIX_FOCAL_LENGTH The focal length is not changed during the global optimization if REF: CALIB_USE_INTRINSIC_GUESS is set.
      • REF: CALIB_FIX_K1,..., REF: CALIB_FIX_K6 The corresponding radial distortion coefficient is not changed during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      • REF: CALIB_RATIONAL_MODEL Coefficients k4, k5, and k6 are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the rational model and return 8 coefficients or more.
      • REF: CALIB_THIN_PRISM_MODEL Coefficients s1, s2, s3 and s4 are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the thin prism model and return 12 coefficients or more.
      • REF: CALIB_FIX_S1_S2_S3_S4 The thin prism distortion coefficients are not changed during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      • REF: CALIB_TILTED_MODEL Coefficients tauX and tauY are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the tilted sensor model and return 14 coefficients.
      • REF: CALIB_FIX_TAUX_TAUY The coefficients of the tilted sensor model are not changed during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      Returns:
      the overall RMS re-projection error. The function estimates the intrinsic camera parameters and extrinsic parameters for each of the views. The algorithm is based on CITE: Zhang2000 and CITE: BouguetMCT . The coordinates of 3D object points and their corresponding 2D projections in each view must be specified. That may be achieved by using an object with known geometry and easily detectable feature points. Such an object is called a calibration rig or calibration pattern, and OpenCV has built-in support for a chessboard as a calibration rig (see REF: findChessboardCorners). Currently, initialization of intrinsic parameters (when REF: CALIB_USE_INTRINSIC_GUESS is not set) is only implemented for planar calibration patterns (where Z-coordinates of the object points must be all zeros). 3D calibration rigs can also be used as long as initial cameraMatrix is provided. The algorithm performs the following steps:
      • Compute the initial intrinsic parameters (the option only available for planar calibration patterns) or read them from the input parameters. The distortion coefficients are all set to zeros initially unless some of CALIB_FIX_K? are specified.
      • Estimate the initial camera pose as if the intrinsic parameters have been already known. This is done using REF: solvePnP .
      • Run the global Levenberg-Marquardt optimization algorithm to minimize the reprojection error, that is, the total sum of squared distances between the observed feature points imagePoints and the projected (using the current estimates for camera parameters and the poses) object points objectPoints. See REF: projectPoints for details.
      Note: If you use a non-square (i.e. non-N-by-N) grid and REF: findChessboardCorners for calibration, and REF: calibrateCamera returns bad values (zero distortion coefficients, \(c_x\) and \(c_y\) very far from the image center, and/or large differences between \(f_x\) and \(f_y\) (ratios of 10:1 or more)), then you are probably using patternSize=cvSize(rows,cols) instead of using patternSize=cvSize(cols,rows) in REF: findChessboardCorners. SEE: calibrateCameraRO, findChessboardCorners, solvePnP, initCameraMatrix2D, stereoCalibrate, undistort
    • calibrateCamera

      public static double calibrateCamera​(List<Mat> objectPoints, List<Mat> imagePoints, Size imageSize, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, int flags, TermCriteria criteria)
    • calibrateCamera

      public static double calibrateCamera​(List<Mat> objectPoints, List<Mat> imagePoints, Size imageSize, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, int flags)
    • calibrateCamera

      public static double calibrateCamera​(List<Mat> objectPoints, List<Mat> imagePoints, Size imageSize, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs)
    • calibrateCameraROExtended

      public static double calibrateCameraROExtended​(List<Mat> objectPoints, List<Mat> imagePoints, Size imageSize, int iFixedPoint, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, Mat newObjPoints, Mat stdDeviationsIntrinsics, Mat stdDeviationsExtrinsics, Mat stdDeviationsObjPoints, Mat perViewErrors, int flags, TermCriteria criteria)
      Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern. This function is an extension of #calibrateCamera with the method of releasing object which was proposed in CITE: strobl2011iccv. In many common cases with inaccurate, unmeasured, roughly planar targets (calibration plates), this method can dramatically improve the precision of the estimated camera parameters. Both the object-releasing method and standard method are supported by this function. Use the parameter iFixedPoint for method selection. In the internal implementation, #calibrateCamera is a wrapper for this function.
      Parameters:
      objectPoints - Vector of vectors of calibration pattern points in the calibration pattern coordinate space. See #calibrateCamera for details. If the method of releasing object to be used, the identical calibration board must be used in each view and it must be fully visible, and all objectPoints[i] must be the same and all points should be roughly close to a plane. The calibration target has to be rigid, or at least static if the camera (rather than the calibration target) is shifted for grabbing images.
      imagePoints - Vector of vectors of the projections of calibration pattern points. See #calibrateCamera for details.
      imageSize - Size of the image used only to initialize the intrinsic camera matrix.
      iFixedPoint - The index of the 3D object point in objectPoints[0] to be fixed. It also acts as a switch for calibration method selection. If object-releasing method to be used, pass in the parameter in the range of [1, objectPoints[0].size()-2], otherwise a value out of this range will make standard calibration method selected. Usually the top-right corner point of the calibration board grid is recommended to be fixed when object-releasing method being utilized. According to \cite strobl2011iccv, two other points are also fixed. In this implementation, objectPoints[0].front and objectPoints[0].back.z are used. With object-releasing method, accurate rvecs, tvecs and newObjPoints are only possible if coordinates of these three fixed points are accurate enough.
      cameraMatrix - Output 3x3 floating-point camera matrix. See #calibrateCamera for details.
      distCoeffs - Output vector of distortion coefficients. See #calibrateCamera for details.
      rvecs - Output vector of rotation vectors estimated for each pattern view. See #calibrateCamera for details.
      tvecs - Output vector of translation vectors estimated for each pattern view.
      newObjPoints - The updated output vector of calibration pattern points. The coordinates might be scaled based on three fixed points. The returned coordinates are accurate only if the above mentioned three fixed points are accurate. If not needed, noArray() can be passed in. This parameter is ignored with standard calibration method.
      stdDeviationsIntrinsics - Output vector of standard deviations estimated for intrinsic parameters. See #calibrateCamera for details.
      stdDeviationsExtrinsics - Output vector of standard deviations estimated for extrinsic parameters. See #calibrateCamera for details.
      stdDeviationsObjPoints - Output vector of standard deviations estimated for refined coordinates of calibration pattern points. It has the same size and order as objectPoints[0] vector. This parameter is ignored with standard calibration method.
      perViewErrors - Output vector of the RMS re-projection error estimated for each pattern view.
      flags - Different flags that may be zero or a combination of some predefined values. See #calibrateCamera for details. If the method of releasing object is used, the calibration time may be much longer. CALIB_USE_QR or CALIB_USE_LU could be used for faster calibration with potentially less precise and less stable in some rare cases.
      criteria - Termination criteria for the iterative optimization algorithm.
      Returns:
      the overall RMS re-projection error. The function estimates the intrinsic camera parameters and extrinsic parameters for each of the views. The algorithm is based on CITE: Zhang2000, CITE: BouguetMCT and CITE: strobl2011iccv. See #calibrateCamera for other detailed explanations. SEE: calibrateCamera, findChessboardCorners, solvePnP, initCameraMatrix2D, stereoCalibrate, undistort
    • calibrateCameraROExtended

      public static double calibrateCameraROExtended​(List<Mat> objectPoints, List<Mat> imagePoints, Size imageSize, int iFixedPoint, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, Mat newObjPoints, Mat stdDeviationsIntrinsics, Mat stdDeviationsExtrinsics, Mat stdDeviationsObjPoints, Mat perViewErrors, int flags)
      Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern. This function is an extension of #calibrateCamera with the method of releasing object which was proposed in CITE: strobl2011iccv. In many common cases with inaccurate, unmeasured, roughly planar targets (calibration plates), this method can dramatically improve the precision of the estimated camera parameters. Both the object-releasing method and standard method are supported by this function. Use the parameter iFixedPoint for method selection. In the internal implementation, #calibrateCamera is a wrapper for this function.
      Parameters:
      objectPoints - Vector of vectors of calibration pattern points in the calibration pattern coordinate space. See #calibrateCamera for details. If the method of releasing object to be used, the identical calibration board must be used in each view and it must be fully visible, and all objectPoints[i] must be the same and all points should be roughly close to a plane. The calibration target has to be rigid, or at least static if the camera (rather than the calibration target) is shifted for grabbing images.
      imagePoints - Vector of vectors of the projections of calibration pattern points. See #calibrateCamera for details.
      imageSize - Size of the image used only to initialize the intrinsic camera matrix.
      iFixedPoint - The index of the 3D object point in objectPoints[0] to be fixed. It also acts as a switch for calibration method selection. If object-releasing method to be used, pass in the parameter in the range of [1, objectPoints[0].size()-2], otherwise a value out of this range will make standard calibration method selected. Usually the top-right corner point of the calibration board grid is recommended to be fixed when object-releasing method being utilized. According to \cite strobl2011iccv, two other points are also fixed. In this implementation, objectPoints[0].front and objectPoints[0].back.z are used. With object-releasing method, accurate rvecs, tvecs and newObjPoints are only possible if coordinates of these three fixed points are accurate enough.
      cameraMatrix - Output 3x3 floating-point camera matrix. See #calibrateCamera for details.
      distCoeffs - Output vector of distortion coefficients. See #calibrateCamera for details.
      rvecs - Output vector of rotation vectors estimated for each pattern view. See #calibrateCamera for details.
      tvecs - Output vector of translation vectors estimated for each pattern view.
      newObjPoints - The updated output vector of calibration pattern points. The coordinates might be scaled based on three fixed points. The returned coordinates are accurate only if the above mentioned three fixed points are accurate. If not needed, noArray() can be passed in. This parameter is ignored with standard calibration method.
      stdDeviationsIntrinsics - Output vector of standard deviations estimated for intrinsic parameters. See #calibrateCamera for details.
      stdDeviationsExtrinsics - Output vector of standard deviations estimated for extrinsic parameters. See #calibrateCamera for details.
      stdDeviationsObjPoints - Output vector of standard deviations estimated for refined coordinates of calibration pattern points. It has the same size and order as objectPoints[0] vector. This parameter is ignored with standard calibration method.
      perViewErrors - Output vector of the RMS re-projection error estimated for each pattern view.
      flags - Different flags that may be zero or a combination of some predefined values. See #calibrateCamera for details. If the method of releasing object is used, the calibration time may be much longer. CALIB_USE_QR or CALIB_USE_LU could be used for faster calibration with potentially less precise and less stable in some rare cases.
      Returns:
      the overall RMS re-projection error. The function estimates the intrinsic camera parameters and extrinsic parameters for each of the views. The algorithm is based on CITE: Zhang2000, CITE: BouguetMCT and CITE: strobl2011iccv. See #calibrateCamera for other detailed explanations. SEE: calibrateCamera, findChessboardCorners, solvePnP, initCameraMatrix2D, stereoCalibrate, undistort
    • calibrateCameraROExtended

      public static double calibrateCameraROExtended​(List<Mat> objectPoints, List<Mat> imagePoints, Size imageSize, int iFixedPoint, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, Mat newObjPoints, Mat stdDeviationsIntrinsics, Mat stdDeviationsExtrinsics, Mat stdDeviationsObjPoints, Mat perViewErrors)
      Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern. This function is an extension of #calibrateCamera with the method of releasing object which was proposed in CITE: strobl2011iccv. In many common cases with inaccurate, unmeasured, roughly planar targets (calibration plates), this method can dramatically improve the precision of the estimated camera parameters. Both the object-releasing method and standard method are supported by this function. Use the parameter iFixedPoint for method selection. In the internal implementation, #calibrateCamera is a wrapper for this function.
      Parameters:
      objectPoints - Vector of vectors of calibration pattern points in the calibration pattern coordinate space. See #calibrateCamera for details. If the method of releasing object to be used, the identical calibration board must be used in each view and it must be fully visible, and all objectPoints[i] must be the same and all points should be roughly close to a plane. The calibration target has to be rigid, or at least static if the camera (rather than the calibration target) is shifted for grabbing images.
      imagePoints - Vector of vectors of the projections of calibration pattern points. See #calibrateCamera for details.
      imageSize - Size of the image used only to initialize the intrinsic camera matrix.
      iFixedPoint - The index of the 3D object point in objectPoints[0] to be fixed. It also acts as a switch for calibration method selection. If object-releasing method to be used, pass in the parameter in the range of [1, objectPoints[0].size()-2], otherwise a value out of this range will make standard calibration method selected. Usually the top-right corner point of the calibration board grid is recommended to be fixed when object-releasing method being utilized. According to \cite strobl2011iccv, two other points are also fixed. In this implementation, objectPoints[0].front and objectPoints[0].back.z are used. With object-releasing method, accurate rvecs, tvecs and newObjPoints are only possible if coordinates of these three fixed points are accurate enough.
      cameraMatrix - Output 3x3 floating-point camera matrix. See #calibrateCamera for details.
      distCoeffs - Output vector of distortion coefficients. See #calibrateCamera for details.
      rvecs - Output vector of rotation vectors estimated for each pattern view. See #calibrateCamera for details.
      tvecs - Output vector of translation vectors estimated for each pattern view.
      newObjPoints - The updated output vector of calibration pattern points. The coordinates might be scaled based on three fixed points. The returned coordinates are accurate only if the above mentioned three fixed points are accurate. If not needed, noArray() can be passed in. This parameter is ignored with standard calibration method.
      stdDeviationsIntrinsics - Output vector of standard deviations estimated for intrinsic parameters. See #calibrateCamera for details.
      stdDeviationsExtrinsics - Output vector of standard deviations estimated for extrinsic parameters. See #calibrateCamera for details.
      stdDeviationsObjPoints - Output vector of standard deviations estimated for refined coordinates of calibration pattern points. It has the same size and order as objectPoints[0] vector. This parameter is ignored with standard calibration method.
      perViewErrors - Output vector of the RMS re-projection error estimated for each pattern view. #calibrateCamera for details. If the method of releasing object is used, the calibration time may be much longer. CALIB_USE_QR or CALIB_USE_LU could be used for faster calibration with potentially less precise and less stable in some rare cases.
      Returns:
      the overall RMS re-projection error. The function estimates the intrinsic camera parameters and extrinsic parameters for each of the views. The algorithm is based on CITE: Zhang2000, CITE: BouguetMCT and CITE: strobl2011iccv. See #calibrateCamera for other detailed explanations. SEE: calibrateCamera, findChessboardCorners, solvePnP, initCameraMatrix2D, stereoCalibrate, undistort
    • calibrateCameraRO

      public static double calibrateCameraRO​(List<Mat> objectPoints, List<Mat> imagePoints, Size imageSize, int iFixedPoint, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, Mat newObjPoints, int flags, TermCriteria criteria)
    • calibrateCameraRO

      public static double calibrateCameraRO​(List<Mat> objectPoints, List<Mat> imagePoints, Size imageSize, int iFixedPoint, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, Mat newObjPoints, int flags)
    • calibrateCameraRO

      public static double calibrateCameraRO​(List<Mat> objectPoints, List<Mat> imagePoints, Size imageSize, int iFixedPoint, Mat cameraMatrix, Mat distCoeffs, List<Mat> rvecs, List<Mat> tvecs, Mat newObjPoints)
    • calibrationMatrixValues

      public static void calibrationMatrixValues​(Mat cameraMatrix, Size imageSize, double apertureWidth, double apertureHeight, double[] fovx, double[] fovy, double[] focalLength, Point principalPoint, double[] aspectRatio)
      Computes useful camera characteristics from the camera intrinsic matrix.
      Parameters:
      cameraMatrix - Input camera intrinsic matrix that can be estimated by #calibrateCamera or #stereoCalibrate .
      imageSize - Input image size in pixels.
      apertureWidth - Physical width in mm of the sensor.
      apertureHeight - Physical height in mm of the sensor.
      fovx - Output field of view in degrees along the horizontal sensor axis.
      fovy - Output field of view in degrees along the vertical sensor axis.
      focalLength - Focal length of the lens in mm.
      principalPoint - Principal point in mm.
      aspectRatio - \(f_y/f_x\) The function computes various useful camera characteristics from the previously estimated camera matrix. Note: Do keep in mind that the unity measure 'mm' stands for whatever unit of measure one chooses for the chessboard pitch (it can thus be any value).
    • stereoCalibrateExtended

      public static double stereoCalibrateExtended​(List<Mat> objectPoints, List<Mat> imagePoints1, List<Mat> imagePoints2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Size imageSize, Mat R, Mat T, Mat E, Mat F, List<Mat> rvecs, List<Mat> tvecs, Mat perViewErrors, int flags, TermCriteria criteria)
      Calibrates a stereo camera set up. This function finds the intrinsic parameters for each of the two cameras and the extrinsic parameters between the two cameras.
      Parameters:
      objectPoints - Vector of vectors of the calibration pattern points. The same structure as in REF: calibrateCamera. For each pattern view, both cameras need to see the same object points. Therefore, objectPoints.size(), imagePoints1.size(), and imagePoints2.size() need to be equal as well as objectPoints[i].size(), imagePoints1[i].size(), and imagePoints2[i].size() need to be equal for each i.
      imagePoints1 - Vector of vectors of the projections of the calibration pattern points, observed by the first camera. The same structure as in REF: calibrateCamera.
      imagePoints2 - Vector of vectors of the projections of the calibration pattern points, observed by the second camera. The same structure as in REF: calibrateCamera.
      cameraMatrix1 - Input/output camera intrinsic matrix for the first camera, the same as in REF: calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
      distCoeffs1 - Input/output vector of distortion coefficients, the same as in REF: calibrateCamera.
      cameraMatrix2 - Input/output second camera intrinsic matrix for the second camera. See description for cameraMatrix1.
      distCoeffs2 - Input/output lens distortion coefficients for the second camera. See description for distCoeffs1.
      imageSize - Size of the image used only to initialize the camera intrinsic matrices.
      R - Output rotation matrix. Together with the translation vector T, this matrix brings points given in the first camera's coordinate system to points in the second camera's coordinate system. In more technical terms, the tuple of R and T performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Due to its duality, this tuple is equivalent to the position of the first camera with respect to the second camera coordinate system.
      T - Output translation vector, see description above.
      E - Output essential matrix.
      F - Output fundamental matrix.
      rvecs - Output vector of rotation vectors ( REF: Rodrigues ) estimated for each pattern view in the coordinate system of the first camera of the stereo pair (e.g. std::vector<cv::Mat>). More in detail, each i-th rotation vector together with the corresponding i-th translation vector (see the next output parameter description) brings the calibration pattern from the object coordinate space (in which object points are specified) to the camera coordinate space of the first camera of the stereo pair. In more technical terms, the tuple of the i-th rotation and translation vector performs a change of basis from object coordinate space to camera coordinate space of the first camera of the stereo pair.
      tvecs - Output vector of translation vectors estimated for each pattern view, see parameter description of previous output parameter ( rvecs ).
      perViewErrors - Output vector of the RMS re-projection error estimated for each pattern view.
      flags - Different flags that may be zero or a combination of the following values:
      • REF: CALIB_FIX_INTRINSIC Fix cameraMatrix? and distCoeffs? so that only R, T, E, and F matrices are estimated.
      • REF: CALIB_USE_INTRINSIC_GUESS Optimize some or all of the intrinsic parameters according to the specified flags. Initial values are provided by the user.
      • REF: CALIB_USE_EXTRINSIC_GUESS R and T contain valid initial values that are optimized further. Otherwise R and T are initialized to the median value of the pattern views (each dimension separately).
      • REF: CALIB_FIX_PRINCIPAL_POINT Fix the principal points during the optimization.
      • REF: CALIB_FIX_FOCAL_LENGTH Fix \(f^{(j)}_x\) and \(f^{(j)}_y\) .
      • REF: CALIB_FIX_ASPECT_RATIO Optimize \(f^{(j)}_y\) . Fix the ratio \(f^{(j)}_x/f^{(j)}_y\) .
      • REF: CALIB_SAME_FOCAL_LENGTH Enforce \(f^{(0)}_x=f^{(1)}_x\) and \(f^{(0)}_y=f^{(1)}_y\) .
      • REF: CALIB_ZERO_TANGENT_DIST Set tangential distortion coefficients for each camera to zeros and fix there.
      • REF: CALIB_FIX_K1,..., REF: CALIB_FIX_K6 Do not change the corresponding radial distortion coefficient during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      • REF: CALIB_RATIONAL_MODEL Enable coefficients k4, k5, and k6. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the rational model and return 8 coefficients. If the flag is not set, the function computes and returns only 5 distortion coefficients.
      • REF: CALIB_THIN_PRISM_MODEL Coefficients s1, s2, s3 and s4 are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the thin prism model and return 12 coefficients. If the flag is not set, the function computes and returns only 5 distortion coefficients.
      • REF: CALIB_FIX_S1_S2_S3_S4 The thin prism distortion coefficients are not changed during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      • REF: CALIB_TILTED_MODEL Coefficients tauX and tauY are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the tilted sensor model and return 14 coefficients. If the flag is not set, the function computes and returns only 5 distortion coefficients.
      • REF: CALIB_FIX_TAUX_TAUY The coefficients of the tilted sensor model are not changed during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      criteria - Termination criteria for the iterative optimization algorithm. The function estimates the transformation between two cameras making a stereo pair. If one computes the poses of an object relative to the first camera and to the second camera, ( \(R_1\),\(T_1\) ) and (\(R_2\),\(T_2\)), respectively, for a stereo camera where the relative position and orientation between the two cameras are fixed, then those poses definitely relate to each other. This means, if the relative position and orientation (\(R\),\(T\)) of the two cameras is known, it is possible to compute (\(R_2\),\(T_2\)) when (\(R_1\),\(T_1\)) is given. This is what the described function does. It computes (\(R\),\(T\)) such that: \(R_2=R R_1\) \(T_2=R T_1 + T.\) Therefore, one can compute the coordinate representation of a 3D point for the second camera's coordinate system when given the point's coordinate representation in the first camera's coordinate system: \(\begin{bmatrix} X_2 \\ Y_2 \\ Z_2 \\ 1 \end{bmatrix} = \begin{bmatrix} R & T \\ 0 & 1 \end{bmatrix} \begin{bmatrix} X_1 \\ Y_1 \\ Z_1 \\ 1 \end{bmatrix}.\) Optionally, it computes the essential matrix E: \(E= \vecthreethree{0}{-T_2}{T_1}{T_2}{0}{-T_0}{-T_1}{T_0}{0} R\) where \(T_i\) are components of the translation vector \(T\) : \(T=[T_0, T_1, T_2]^T\) . And the function can also compute the fundamental matrix F: \(F = cameraMatrix2^{-T}\cdot E \cdot cameraMatrix1^{-1}\) Besides the stereo-related information, the function can also perform a full calibration of each of the two cameras. However, due to the high dimensionality of the parameter space and noise in the input data, the function can diverge from the correct solution. If the intrinsic parameters can be estimated with high accuracy for each of the cameras individually (for example, using #calibrateCamera ), you are recommended to do so and then pass REF: CALIB_FIX_INTRINSIC flag to the function along with the computed intrinsic parameters. Otherwise, if all the parameters are estimated at once, it makes sense to restrict some parameters, for example, pass REF: CALIB_SAME_FOCAL_LENGTH and REF: CALIB_ZERO_TANGENT_DIST flags, which is usually a reasonable assumption. Similarly to #calibrateCamera, the function minimizes the total re-projection error for all the points in all the available views from both cameras. The function returns the final value of the re-projection error.
      Returns:
      automatically generated
    • stereoCalibrateExtended

      public static double stereoCalibrateExtended​(List<Mat> objectPoints, List<Mat> imagePoints1, List<Mat> imagePoints2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Size imageSize, Mat R, Mat T, Mat E, Mat F, List<Mat> rvecs, List<Mat> tvecs, Mat perViewErrors, int flags)
      Calibrates a stereo camera set up. This function finds the intrinsic parameters for each of the two cameras and the extrinsic parameters between the two cameras.
      Parameters:
      objectPoints - Vector of vectors of the calibration pattern points. The same structure as in REF: calibrateCamera. For each pattern view, both cameras need to see the same object points. Therefore, objectPoints.size(), imagePoints1.size(), and imagePoints2.size() need to be equal as well as objectPoints[i].size(), imagePoints1[i].size(), and imagePoints2[i].size() need to be equal for each i.
      imagePoints1 - Vector of vectors of the projections of the calibration pattern points, observed by the first camera. The same structure as in REF: calibrateCamera.
      imagePoints2 - Vector of vectors of the projections of the calibration pattern points, observed by the second camera. The same structure as in REF: calibrateCamera.
      cameraMatrix1 - Input/output camera intrinsic matrix for the first camera, the same as in REF: calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
      distCoeffs1 - Input/output vector of distortion coefficients, the same as in REF: calibrateCamera.
      cameraMatrix2 - Input/output second camera intrinsic matrix for the second camera. See description for cameraMatrix1.
      distCoeffs2 - Input/output lens distortion coefficients for the second camera. See description for distCoeffs1.
      imageSize - Size of the image used only to initialize the camera intrinsic matrices.
      R - Output rotation matrix. Together with the translation vector T, this matrix brings points given in the first camera's coordinate system to points in the second camera's coordinate system. In more technical terms, the tuple of R and T performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Due to its duality, this tuple is equivalent to the position of the first camera with respect to the second camera coordinate system.
      T - Output translation vector, see description above.
      E - Output essential matrix.
      F - Output fundamental matrix.
      rvecs - Output vector of rotation vectors ( REF: Rodrigues ) estimated for each pattern view in the coordinate system of the first camera of the stereo pair (e.g. std::vector<cv::Mat>). More in detail, each i-th rotation vector together with the corresponding i-th translation vector (see the next output parameter description) brings the calibration pattern from the object coordinate space (in which object points are specified) to the camera coordinate space of the first camera of the stereo pair. In more technical terms, the tuple of the i-th rotation and translation vector performs a change of basis from object coordinate space to camera coordinate space of the first camera of the stereo pair.
      tvecs - Output vector of translation vectors estimated for each pattern view, see parameter description of previous output parameter ( rvecs ).
      perViewErrors - Output vector of the RMS re-projection error estimated for each pattern view.
      flags - Different flags that may be zero or a combination of the following values:
      • REF: CALIB_FIX_INTRINSIC Fix cameraMatrix? and distCoeffs? so that only R, T, E, and F matrices are estimated.
      • REF: CALIB_USE_INTRINSIC_GUESS Optimize some or all of the intrinsic parameters according to the specified flags. Initial values are provided by the user.
      • REF: CALIB_USE_EXTRINSIC_GUESS R and T contain valid initial values that are optimized further. Otherwise R and T are initialized to the median value of the pattern views (each dimension separately).
      • REF: CALIB_FIX_PRINCIPAL_POINT Fix the principal points during the optimization.
      • REF: CALIB_FIX_FOCAL_LENGTH Fix \(f^{(j)}_x\) and \(f^{(j)}_y\) .
      • REF: CALIB_FIX_ASPECT_RATIO Optimize \(f^{(j)}_y\) . Fix the ratio \(f^{(j)}_x/f^{(j)}_y\) .
      • REF: CALIB_SAME_FOCAL_LENGTH Enforce \(f^{(0)}_x=f^{(1)}_x\) and \(f^{(0)}_y=f^{(1)}_y\) .
      • REF: CALIB_ZERO_TANGENT_DIST Set tangential distortion coefficients for each camera to zeros and fix there.
      • REF: CALIB_FIX_K1,..., REF: CALIB_FIX_K6 Do not change the corresponding radial distortion coefficient during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      • REF: CALIB_RATIONAL_MODEL Enable coefficients k4, k5, and k6. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the rational model and return 8 coefficients. If the flag is not set, the function computes and returns only 5 distortion coefficients.
      • REF: CALIB_THIN_PRISM_MODEL Coefficients s1, s2, s3 and s4 are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the thin prism model and return 12 coefficients. If the flag is not set, the function computes and returns only 5 distortion coefficients.
      • REF: CALIB_FIX_S1_S2_S3_S4 The thin prism distortion coefficients are not changed during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      • REF: CALIB_TILTED_MODEL Coefficients tauX and tauY are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the tilted sensor model and return 14 coefficients. If the flag is not set, the function computes and returns only 5 distortion coefficients.
      • REF: CALIB_FIX_TAUX_TAUY The coefficients of the tilted sensor model are not changed during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      The function estimates the transformation between two cameras making a stereo pair. If one computes the poses of an object relative to the first camera and to the second camera, ( \(R_1\),\(T_1\) ) and (\(R_2\),\(T_2\)), respectively, for a stereo camera where the relative position and orientation between the two cameras are fixed, then those poses definitely relate to each other. This means, if the relative position and orientation (\(R\),\(T\)) of the two cameras is known, it is possible to compute (\(R_2\),\(T_2\)) when (\(R_1\),\(T_1\)) is given. This is what the described function does. It computes (\(R\),\(T\)) such that: \(R_2=R R_1\) \(T_2=R T_1 + T.\) Therefore, one can compute the coordinate representation of a 3D point for the second camera's coordinate system when given the point's coordinate representation in the first camera's coordinate system: \(\begin{bmatrix} X_2 \\ Y_2 \\ Z_2 \\ 1 \end{bmatrix} = \begin{bmatrix} R & T \\ 0 & 1 \end{bmatrix} \begin{bmatrix} X_1 \\ Y_1 \\ Z_1 \\ 1 \end{bmatrix}.\) Optionally, it computes the essential matrix E: \(E= \vecthreethree{0}{-T_2}{T_1}{T_2}{0}{-T_0}{-T_1}{T_0}{0} R\) where \(T_i\) are components of the translation vector \(T\) : \(T=[T_0, T_1, T_2]^T\) . And the function can also compute the fundamental matrix F: \(F = cameraMatrix2^{-T}\cdot E \cdot cameraMatrix1^{-1}\) Besides the stereo-related information, the function can also perform a full calibration of each of the two cameras. However, due to the high dimensionality of the parameter space and noise in the input data, the function can diverge from the correct solution. If the intrinsic parameters can be estimated with high accuracy for each of the cameras individually (for example, using #calibrateCamera ), you are recommended to do so and then pass REF: CALIB_FIX_INTRINSIC flag to the function along with the computed intrinsic parameters. Otherwise, if all the parameters are estimated at once, it makes sense to restrict some parameters, for example, pass REF: CALIB_SAME_FOCAL_LENGTH and REF: CALIB_ZERO_TANGENT_DIST flags, which is usually a reasonable assumption. Similarly to #calibrateCamera, the function minimizes the total re-projection error for all the points in all the available views from both cameras. The function returns the final value of the re-projection error.
      Returns:
      automatically generated
    • stereoCalibrateExtended

      public static double stereoCalibrateExtended​(List<Mat> objectPoints, List<Mat> imagePoints1, List<Mat> imagePoints2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Size imageSize, Mat R, Mat T, Mat E, Mat F, List<Mat> rvecs, List<Mat> tvecs, Mat perViewErrors)
      Calibrates a stereo camera set up. This function finds the intrinsic parameters for each of the two cameras and the extrinsic parameters between the two cameras.
      Parameters:
      objectPoints - Vector of vectors of the calibration pattern points. The same structure as in REF: calibrateCamera. For each pattern view, both cameras need to see the same object points. Therefore, objectPoints.size(), imagePoints1.size(), and imagePoints2.size() need to be equal as well as objectPoints[i].size(), imagePoints1[i].size(), and imagePoints2[i].size() need to be equal for each i.
      imagePoints1 - Vector of vectors of the projections of the calibration pattern points, observed by the first camera. The same structure as in REF: calibrateCamera.
      imagePoints2 - Vector of vectors of the projections of the calibration pattern points, observed by the second camera. The same structure as in REF: calibrateCamera.
      cameraMatrix1 - Input/output camera intrinsic matrix for the first camera, the same as in REF: calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
      distCoeffs1 - Input/output vector of distortion coefficients, the same as in REF: calibrateCamera.
      cameraMatrix2 - Input/output second camera intrinsic matrix for the second camera. See description for cameraMatrix1.
      distCoeffs2 - Input/output lens distortion coefficients for the second camera. See description for distCoeffs1.
      imageSize - Size of the image used only to initialize the camera intrinsic matrices.
      R - Output rotation matrix. Together with the translation vector T, this matrix brings points given in the first camera's coordinate system to points in the second camera's coordinate system. In more technical terms, the tuple of R and T performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Due to its duality, this tuple is equivalent to the position of the first camera with respect to the second camera coordinate system.
      T - Output translation vector, see description above.
      E - Output essential matrix.
      F - Output fundamental matrix.
      rvecs - Output vector of rotation vectors ( REF: Rodrigues ) estimated for each pattern view in the coordinate system of the first camera of the stereo pair (e.g. std::vector<cv::Mat>). More in detail, each i-th rotation vector together with the corresponding i-th translation vector (see the next output parameter description) brings the calibration pattern from the object coordinate space (in which object points are specified) to the camera coordinate space of the first camera of the stereo pair. In more technical terms, the tuple of the i-th rotation and translation vector performs a change of basis from object coordinate space to camera coordinate space of the first camera of the stereo pair.
      tvecs - Output vector of translation vectors estimated for each pattern view, see parameter description of previous output parameter ( rvecs ).
      perViewErrors - Output vector of the RMS re-projection error estimated for each pattern view.
      • REF: CALIB_FIX_INTRINSIC Fix cameraMatrix? and distCoeffs? so that only R, T, E, and F matrices are estimated.
      • REF: CALIB_USE_INTRINSIC_GUESS Optimize some or all of the intrinsic parameters according to the specified flags. Initial values are provided by the user.
      • REF: CALIB_USE_EXTRINSIC_GUESS R and T contain valid initial values that are optimized further. Otherwise R and T are initialized to the median value of the pattern views (each dimension separately).
      • REF: CALIB_FIX_PRINCIPAL_POINT Fix the principal points during the optimization.
      • REF: CALIB_FIX_FOCAL_LENGTH Fix \(f^{(j)}_x\) and \(f^{(j)}_y\) .
      • REF: CALIB_FIX_ASPECT_RATIO Optimize \(f^{(j)}_y\) . Fix the ratio \(f^{(j)}_x/f^{(j)}_y\) .
      • REF: CALIB_SAME_FOCAL_LENGTH Enforce \(f^{(0)}_x=f^{(1)}_x\) and \(f^{(0)}_y=f^{(1)}_y\) .
      • REF: CALIB_ZERO_TANGENT_DIST Set tangential distortion coefficients for each camera to zeros and fix there.
      • REF: CALIB_FIX_K1,..., REF: CALIB_FIX_K6 Do not change the corresponding radial distortion coefficient during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      • REF: CALIB_RATIONAL_MODEL Enable coefficients k4, k5, and k6. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the rational model and return 8 coefficients. If the flag is not set, the function computes and returns only 5 distortion coefficients.
      • REF: CALIB_THIN_PRISM_MODEL Coefficients s1, s2, s3 and s4 are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the thin prism model and return 12 coefficients. If the flag is not set, the function computes and returns only 5 distortion coefficients.
      • REF: CALIB_FIX_S1_S2_S3_S4 The thin prism distortion coefficients are not changed during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      • REF: CALIB_TILTED_MODEL Coefficients tauX and tauY are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the tilted sensor model and return 14 coefficients. If the flag is not set, the function computes and returns only 5 distortion coefficients.
      • REF: CALIB_FIX_TAUX_TAUY The coefficients of the tilted sensor model are not changed during the optimization. If REF: CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
      The function estimates the transformation between two cameras making a stereo pair. If one computes the poses of an object relative to the first camera and to the second camera, ( \(R_1\),\(T_1\) ) and (\(R_2\),\(T_2\)), respectively, for a stereo camera where the relative position and orientation between the two cameras are fixed, then those poses definitely relate to each other. This means, if the relative position and orientation (\(R\),\(T\)) of the two cameras is known, it is possible to compute (\(R_2\),\(T_2\)) when (\(R_1\),\(T_1\)) is given. This is what the described function does. It computes (\(R\),\(T\)) such that: \(R_2=R R_1\) \(T_2=R T_1 + T.\) Therefore, one can compute the coordinate representation of a 3D point for the second camera's coordinate system when given the point's coordinate representation in the first camera's coordinate system: \(\begin{bmatrix} X_2 \\ Y_2 \\ Z_2 \\ 1 \end{bmatrix} = \begin{bmatrix} R & T \\ 0 & 1 \end{bmatrix} \begin{bmatrix} X_1 \\ Y_1 \\ Z_1 \\ 1 \end{bmatrix}.\) Optionally, it computes the essential matrix E: \(E= \vecthreethree{0}{-T_2}{T_1}{T_2}{0}{-T_0}{-T_1}{T_0}{0} R\) where \(T_i\) are components of the translation vector \(T\) : \(T=[T_0, T_1, T_2]^T\) . And the function can also compute the fundamental matrix F: \(F = cameraMatrix2^{-T}\cdot E \cdot cameraMatrix1^{-1}\) Besides the stereo-related information, the function can also perform a full calibration of each of the two cameras. However, due to the high dimensionality of the parameter space and noise in the input data, the function can diverge from the correct solution. If the intrinsic parameters can be estimated with high accuracy for each of the cameras individually (for example, using #calibrateCamera ), you are recommended to do so and then pass REF: CALIB_FIX_INTRINSIC flag to the function along with the computed intrinsic parameters. Otherwise, if all the parameters are estimated at once, it makes sense to restrict some parameters, for example, pass REF: CALIB_SAME_FOCAL_LENGTH and REF: CALIB_ZERO_TANGENT_DIST flags, which is usually a reasonable assumption. Similarly to #calibrateCamera, the function minimizes the total re-projection error for all the points in all the available views from both cameras. The function returns the final value of the re-projection error.
      Returns:
      automatically generated
    • stereoCalibrate

      public static double stereoCalibrate​(List<Mat> objectPoints, List<Mat> imagePoints1, List<Mat> imagePoints2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Size imageSize, Mat R, Mat T, Mat E, Mat F, int flags, TermCriteria criteria)
    • stereoCalibrate

      public static double stereoCalibrate​(List<Mat> objectPoints, List<Mat> imagePoints1, List<Mat> imagePoints2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Size imageSize, Mat R, Mat T, Mat E, Mat F, int flags)
    • stereoCalibrate

      public static double stereoCalibrate​(List<Mat> objectPoints, List<Mat> imagePoints1, List<Mat> imagePoints2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Size imageSize, Mat R, Mat T, Mat E, Mat F)
    • stereoCalibrate

      public static double stereoCalibrate​(List<Mat> objectPoints, List<Mat> imagePoints1, List<Mat> imagePoints2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Size imageSize, Mat R, Mat T, Mat E, Mat F, Mat perViewErrors, int flags, TermCriteria criteria)
    • stereoCalibrate

      public static double stereoCalibrate​(List<Mat> objectPoints, List<Mat> imagePoints1, List<Mat> imagePoints2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Size imageSize, Mat R, Mat T, Mat E, Mat F, Mat perViewErrors, int flags)
    • stereoCalibrate

      public static double stereoCalibrate​(List<Mat> objectPoints, List<Mat> imagePoints1, List<Mat> imagePoints2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Size imageSize, Mat R, Mat T, Mat E, Mat F, Mat perViewErrors)
    • stereoRectify

      public static void stereoRectify​(Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Size imageSize, Mat R, Mat T, Mat R1, Mat R2, Mat P1, Mat P2, Mat Q, int flags, double alpha, Size newImageSize, Rect validPixROI1, Rect validPixROI2)
      Computes rectification transforms for each head of a calibrated stereo camera.
      Parameters:
      cameraMatrix1 - First camera intrinsic matrix.
      distCoeffs1 - First camera distortion parameters.
      cameraMatrix2 - Second camera intrinsic matrix.
      distCoeffs2 - Second camera distortion parameters.
      imageSize - Size of the image used for stereo calibration.
      R - Rotation matrix from the coordinate system of the first camera to the second camera, see REF: stereoCalibrate.
      T - Translation vector from the coordinate system of the first camera to the second camera, see REF: stereoCalibrate.
      R1 - Output 3x3 rectification transform (rotation matrix) for the first camera. This matrix brings points given in the unrectified first camera's coordinate system to points in the rectified first camera's coordinate system. In more technical terms, it performs a change of basis from the unrectified first camera's coordinate system to the rectified first camera's coordinate system.
      R2 - Output 3x3 rectification transform (rotation matrix) for the second camera. This matrix brings points given in the unrectified second camera's coordinate system to points in the rectified second camera's coordinate system. In more technical terms, it performs a change of basis from the unrectified second camera's coordinate system to the rectified second camera's coordinate system.
      P1 - Output 3x4 projection matrix in the new (rectified) coordinate systems for the first camera, i.e. it projects points given in the rectified first camera coordinate system into the rectified first camera's image.
      P2 - Output 3x4 projection matrix in the new (rectified) coordinate systems for the second camera, i.e. it projects points given in the rectified first camera coordinate system into the rectified second camera's image.
      Q - Output \(4 \times 4\) disparity-to-depth mapping matrix (see REF: reprojectImageTo3D).
      flags - Operation flags that may be zero or REF: CALIB_ZERO_DISPARITY . If the flag is set, the function makes the principal points of each camera have the same pixel coordinates in the rectified views. And if the flag is not set, the function may still shift the images in the horizontal or vertical direction (depending on the orientation of epipolar lines) to maximize the useful image area.
      alpha - Free scaling parameter. If it is -1 or absent, the function performs the default scaling. Otherwise, the parameter should be between 0 and 1. alpha=0 means that the rectified images are zoomed and shifted so that only valid pixels are visible (no black areas after rectification). alpha=1 means that the rectified image is decimated and shifted so that all the pixels from the original images from the cameras are retained in the rectified images (no source image pixels are lost). Any intermediate value yields an intermediate result between those two extreme cases.
      newImageSize - New image resolution after rectification. The same size should be passed to #initUndistortRectifyMap (see the stereo_calib.cpp sample in OpenCV samples directory). When (0,0) is passed (default), it is set to the original imageSize . Setting it to a larger value can help you preserve details in the original image, especially when there is a big radial distortion.
      validPixROI1 - Optional output rectangles inside the rectified images where all the pixels are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below).
      validPixROI2 - Optional output rectangles inside the rectified images where all the pixels are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below). The function computes the rotation matrices for each camera that (virtually) make both camera image planes the same plane. Consequently, this makes all the epipolar lines parallel and thus simplifies the dense stereo correspondence problem. The function takes the matrices computed by #stereoCalibrate as input. As output, it provides two rotation matrices and also two projection matrices in the new coordinates. The function distinguishes the following two cases:
      • Horizontal stereo: the first and the second camera views are shifted relative to each other mainly along the x-axis (with possible small vertical shift). In the rectified images, the corresponding epipolar lines in the left and right cameras are horizontal and have the same y-coordinate. P1 and P2 look like:
      \(\texttt{P1} = \begin{bmatrix} f & 0 & cx_1 & 0 \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}\) \(\texttt{P2} = \begin{bmatrix} f & 0 & cx_2 & T_x \cdot f \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} ,\) \(\texttt{Q} = \begin{bmatrix} 1 & 0 & 0 & -cx_1 \\ 0 & 1 & 0 & -cy \\ 0 & 0 & 0 & f \\ 0 & 0 & -\frac{1}{T_x} & \frac{cx_1 - cx_2}{T_x} \end{bmatrix} \) where \(T_x\) is a horizontal shift between the cameras and \(cx_1=cx_2\) if REF: CALIB_ZERO_DISPARITY is set.
      • Vertical stereo: the first and the second camera views are shifted relative to each other mainly in the vertical direction (and probably a bit in the horizontal direction too). The epipolar lines in the rectified images are vertical and have the same x-coordinate. P1 and P2 look like:
      \(\texttt{P1} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_1 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}\) \(\texttt{P2} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_2 & T_y \cdot f \\ 0 & 0 & 1 & 0 \end{bmatrix},\) \(\texttt{Q} = \begin{bmatrix} 1 & 0 & 0 & -cx \\ 0 & 1 & 0 & -cy_1 \\ 0 & 0 & 0 & f \\ 0 & 0 & -\frac{1}{T_y} & \frac{cy_1 - cy_2}{T_y} \end{bmatrix} \) where \(T_y\) is a vertical shift between the cameras and \(cy_1=cy_2\) if REF: CALIB_ZERO_DISPARITY is set. As you can see, the first three columns of P1 and P2 will effectively be the new "rectified" camera matrices. The matrices, together with R1 and R2 , can then be passed to #initUndistortRectifyMap to initialize the rectification map for each camera. See below the screenshot from the stereo_calib.cpp sample. Some red horizontal lines pass through the corresponding image regions. This means that the images are well rectified, which is what most stereo correspondence algorithms rely on. The green rectangles are roi1 and roi2 . You see that their interiors are all valid pixels. ![image](pics/stereo_undistort.jpg)
    • stereoRectify

      public static void stereoRectify​(Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Size imageSize, Mat R, Mat T, Mat R1, Mat R2, Mat P1, Mat P2, Mat Q, int flags, double alpha, Size newImageSize, Rect validPixROI1)
      Computes rectification transforms for each head of a calibrated stereo camera.
      Parameters:
      cameraMatrix1 - First camera intrinsic matrix.
      distCoeffs1 - First camera distortion parameters.
      cameraMatrix2 - Second camera intrinsic matrix.
      distCoeffs2 - Second camera distortion parameters.
      imageSize - Size of the image used for stereo calibration.
      R - Rotation matrix from the coordinate system of the first camera to the second camera, see REF: stereoCalibrate.
      T - Translation vector from the coordinate system of the first camera to the second camera, see REF: stereoCalibrate.
      R1 - Output 3x3 rectification transform (rotation matrix) for the first camera. This matrix brings points given in the unrectified first camera's coordinate system to points in the rectified first camera's coordinate system. In more technical terms, it performs a change of basis from the unrectified first camera's coordinate system to the rectified first camera's coordinate system.
      R2 - Output 3x3 rectification transform (rotation matrix) for the second camera. This matrix brings points given in the unrectified second camera's coordinate system to points in the rectified second camera's coordinate system. In more technical terms, it performs a change of basis from the unrectified second camera's coordinate system to the rectified second camera's coordinate system.
      P1 - Output 3x4 projection matrix in the new (rectified) coordinate systems for the first camera, i.e. it projects points given in the rectified first camera coordinate system into the rectified first camera's image.
      P2 - Output 3x4 projection matrix in the new (rectified) coordinate systems for the second camera, i.e. it projects points given in the rectified first camera coordinate system into the rectified second camera's image.
      Q - Output \(4 \times 4\) disparity-to-depth mapping matrix (see REF: reprojectImageTo3D).
      flags - Operation flags that may be zero or REF: CALIB_ZERO_DISPARITY . If the flag is set, the function makes the principal points of each camera have the same pixel coordinates in the rectified views. And if the flag is not set, the function may still shift the images in the horizontal or vertical direction (depending on the orientation of epipolar lines) to maximize the useful image area.
      alpha - Free scaling parameter. If it is -1 or absent, the function performs the default scaling. Otherwise, the parameter should be between 0 and 1. alpha=0 means that the rectified images are zoomed and shifted so that only valid pixels are visible (no black areas after rectification). alpha=1 means that the rectified image is decimated and shifted so that all the pixels from the original images from the cameras are retained in the rectified images (no source image pixels are lost). Any intermediate value yields an intermediate result between those two extreme cases.
      newImageSize - New image resolution after rectification. The same size should be passed to #initUndistortRectifyMap (see the stereo_calib.cpp sample in OpenCV samples directory). When (0,0) is passed (default), it is set to the original imageSize . Setting it to a larger value can help you preserve details in the original image, especially when there is a big radial distortion.
      validPixROI1 - Optional output rectangles inside the rectified images where all the pixels are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below). are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below). The function computes the rotation matrices for each camera that (virtually) make both camera image planes the same plane. Consequently, this makes all the epipolar lines parallel and thus simplifies the dense stereo correspondence problem. The function takes the matrices computed by #stereoCalibrate as input. As output, it provides two rotation matrices and also two projection matrices in the new coordinates. The function distinguishes the following two cases:
      • Horizontal stereo: the first and the second camera views are shifted relative to each other mainly along the x-axis (with possible small vertical shift). In the rectified images, the corresponding epipolar lines in the left and right cameras are horizontal and have the same y-coordinate. P1 and P2 look like:
      \(\texttt{P1} = \begin{bmatrix} f & 0 & cx_1 & 0 \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}\) \(\texttt{P2} = \begin{bmatrix} f & 0 & cx_2 & T_x \cdot f \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} ,\) \(\texttt{Q} = \begin{bmatrix} 1 & 0 & 0 & -cx_1 \\ 0 & 1 & 0 & -cy \\ 0 & 0 & 0 & f \\ 0 & 0 & -\frac{1}{T_x} & \frac{cx_1 - cx_2}{T_x} \end{bmatrix} \) where \(T_x\) is a horizontal shift between the cameras and \(cx_1=cx_2\) if REF: CALIB_ZERO_DISPARITY is set.
      • Vertical stereo: the first and the second camera views are shifted relative to each other mainly in the vertical direction (and probably a bit in the horizontal direction too). The epipolar lines in the rectified images are vertical and have the same x-coordinate. P1 and P2 look like:
      \(\texttt{P1} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_1 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}\) \(\texttt{P2} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_2 & T_y \cdot f \\ 0 & 0 & 1 & 0 \end{bmatrix},\) \(\texttt{Q} = \begin{bmatrix} 1 & 0 & 0 & -cx \\ 0 & 1 & 0 & -cy_1 \\ 0 & 0 & 0 & f \\ 0 & 0 & -\frac{1}{T_y} & \frac{cy_1 - cy_2}{T_y} \end{bmatrix} \) where \(T_y\) is a vertical shift between the cameras and \(cy_1=cy_2\) if REF: CALIB_ZERO_DISPARITY is set. As you can see, the first three columns of P1 and P2 will effectively be the new "rectified" camera matrices. The matrices, together with R1 and R2 , can then be passed to #initUndistortRectifyMap to initialize the rectification map for each camera. See below the screenshot from the stereo_calib.cpp sample. Some red horizontal lines pass through the corresponding image regions. This means that the images are well rectified, which is what most stereo correspondence algorithms rely on. The green rectangles are roi1 and roi2 . You see that their interiors are all valid pixels. ![image](pics/stereo_undistort.jpg)
    • stereoRectify

      public static void stereoRectify​(Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Size imageSize, Mat R, Mat T, Mat R1, Mat R2, Mat P1, Mat P2, Mat Q, int flags, double alpha, Size newImageSize)
      Computes rectification transforms for each head of a calibrated stereo camera.
      Parameters:
      cameraMatrix1 - First camera intrinsic matrix.
      distCoeffs1 - First camera distortion parameters.
      cameraMatrix2 - Second camera intrinsic matrix.
      distCoeffs2 - Second camera distortion parameters.
      imageSize - Size of the image used for stereo calibration.
      R - Rotation matrix from the coordinate system of the first camera to the second camera, see REF: stereoCalibrate.
      T - Translation vector from the coordinate system of the first camera to the second camera, see REF: stereoCalibrate.
      R1 - Output 3x3 rectification transform (rotation matrix) for the first camera. This matrix brings points given in the unrectified first camera's coordinate system to points in the rectified first camera's coordinate system. In more technical terms, it performs a change of basis from the unrectified first camera's coordinate system to the rectified first camera's coordinate system.
      R2 - Output 3x3 rectification transform (rotation matrix) for the second camera. This matrix brings points given in the unrectified second camera's coordinate system to points in the rectified second camera's coordinate system. In more technical terms, it performs a change of basis from the unrectified second camera's coordinate system to the rectified second camera's coordinate system.
      P1 - Output 3x4 projection matrix in the new (rectified) coordinate systems for the first camera, i.e. it projects points given in the rectified first camera coordinate system into the rectified first camera's image.
      P2 - Output 3x4 projection matrix in the new (rectified) coordinate systems for the second camera, i.e. it projects points given in the rectified first camera coordinate system into the rectified second camera's image.
      Q - Output \(4 \times 4\) disparity-to-depth mapping matrix (see REF: reprojectImageTo3D).
      flags - Operation flags that may be zero or REF: CALIB_ZERO_DISPARITY . If the flag is set, the function makes the principal points of each camera have the same pixel coordinates in the rectified views. And if the flag is not set, the function may still shift the images in the horizontal or vertical direction (depending on the orientation of epipolar lines) to maximize the useful image area.
      alpha - Free scaling parameter. If it is -1 or absent, the function performs the default scaling. Otherwise, the parameter should be between 0 and 1. alpha=0 means that the rectified images are zoomed and shifted so that only valid pixels are visible (no black areas after rectification). alpha=1 means that the rectified image is decimated and shifted so that all the pixels from the original images from the cameras are retained in the rectified images (no source image pixels are lost). Any intermediate value yields an intermediate result between those two extreme cases.
      newImageSize - New image resolution after rectification. The same size should be passed to #initUndistortRectifyMap (see the stereo_calib.cpp sample in OpenCV samples directory). When (0,0) is passed (default), it is set to the original imageSize . Setting it to a larger value can help you preserve details in the original image, especially when there is a big radial distortion. are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below). are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below). The function computes the rotation matrices for each camera that (virtually) make both camera image planes the same plane. Consequently, this makes all the epipolar lines parallel and thus simplifies the dense stereo correspondence problem. The function takes the matrices computed by #stereoCalibrate as input. As output, it provides two rotation matrices and also two projection matrices in the new coordinates. The function distinguishes the following two cases:
      • Horizontal stereo: the first and the second camera views are shifted relative to each other mainly along the x-axis (with possible small vertical shift). In the rectified images, the corresponding epipolar lines in the left and right cameras are horizontal and have the same y-coordinate. P1 and P2 look like:
      \(\texttt{P1} = \begin{bmatrix} f & 0 & cx_1 & 0 \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}\) \(\texttt{P2} = \begin{bmatrix} f & 0 & cx_2 & T_x \cdot f \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} ,\) \(\texttt{Q} = \begin{bmatrix} 1 & 0 & 0 & -cx_1 \\ 0 & 1 & 0 & -cy \\ 0 & 0 & 0 & f \\ 0 & 0 & -\frac{1}{T_x} & \frac{cx_1 - cx_2}{T_x} \end{bmatrix} \) where \(T_x\) is a horizontal shift between the cameras and \(cx_1=cx_2\) if REF: CALIB_ZERO_DISPARITY is set.
      • Vertical stereo: the first and the second camera views are shifted relative to each other mainly in the vertical direction (and probably a bit in the horizontal direction too). The epipolar lines in the rectified images are vertical and have the same x-coordinate. P1 and P2 look like:
      \(\texttt{P1} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_1 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}\) \(\texttt{P2} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_2 & T_y \cdot f \\ 0 & 0 & 1 & 0 \end{bmatrix},\) \(\texttt{Q} = \begin{bmatrix} 1 & 0 & 0 & -cx \\ 0 & 1 & 0 & -cy_1 \\ 0 & 0 & 0 & f \\ 0 & 0 & -\frac{1}{T_y} & \frac{cy_1 - cy_2}{T_y} \end{bmatrix} \) where \(T_y\) is a vertical shift between the cameras and \(cy_1=cy_2\) if REF: CALIB_ZERO_DISPARITY is set. As you can see, the first three columns of P1 and P2 will effectively be the new "rectified" camera matrices. The matrices, together with R1 and R2 , can then be passed to #initUndistortRectifyMap to initialize the rectification map for each camera. See below the screenshot from the stereo_calib.cpp sample. Some red horizontal lines pass through the corresponding image regions. This means that the images are well rectified, which is what most stereo correspondence algorithms rely on. The green rectangles are roi1 and roi2 . You see that their interiors are all valid pixels. ![image](pics/stereo_undistort.jpg)
    • stereoRectify

      public static void stereoRectify​(Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Size imageSize, Mat R, Mat T, Mat R1, Mat R2, Mat P1, Mat P2, Mat Q, int flags, double alpha)
      Computes rectification transforms for each head of a calibrated stereo camera.
      Parameters:
      cameraMatrix1 - First camera intrinsic matrix.
      distCoeffs1 - First camera distortion parameters.
      cameraMatrix2 - Second camera intrinsic matrix.
      distCoeffs2 - Second camera distortion parameters.
      imageSize - Size of the image used for stereo calibration.
      R - Rotation matrix from the coordinate system of the first camera to the second camera, see REF: stereoCalibrate.
      T - Translation vector from the coordinate system of the first camera to the second camera, see REF: stereoCalibrate.
      R1 - Output 3x3 rectification transform (rotation matrix) for the first camera. This matrix brings points given in the unrectified first camera's coordinate system to points in the rectified first camera's coordinate system. In more technical terms, it performs a change of basis from the unrectified first camera's coordinate system to the rectified first camera's coordinate system.
      R2 - Output 3x3 rectification transform (rotation matrix) for the second camera. This matrix brings points given in the unrectified second camera's coordinate system to points in the rectified second camera's coordinate system. In more technical terms, it performs a change of basis from the unrectified second camera's coordinate system to the rectified second camera's coordinate system.
      P1 - Output 3x4 projection matrix in the new (rectified) coordinate systems for the first camera, i.e. it projects points given in the rectified first camera coordinate system into the rectified first camera's image.
      P2 - Output 3x4 projection matrix in the new (rectified) coordinate systems for the second camera, i.e. it projects points given in the rectified first camera coordinate system into the rectified second camera's image.
      Q - Output \(4 \times 4\) disparity-to-depth mapping matrix (see REF: reprojectImageTo3D).
      flags - Operation flags that may be zero or REF: CALIB_ZERO_DISPARITY . If the flag is set, the function makes the principal points of each camera have the same pixel coordinates in the rectified views. And if the flag is not set, the function may still shift the images in the horizontal or vertical direction (depending on the orientation of epipolar lines) to maximize the useful image area.
      alpha - Free scaling parameter. If it is -1 or absent, the function performs the default scaling. Otherwise, the parameter should be between 0 and 1. alpha=0 means that the rectified images are zoomed and shifted so that only valid pixels are visible (no black areas after rectification). alpha=1 means that the rectified image is decimated and shifted so that all the pixels from the original images from the cameras are retained in the rectified images (no source image pixels are lost). Any intermediate value yields an intermediate result between those two extreme cases. #initUndistortRectifyMap (see the stereo_calib.cpp sample in OpenCV samples directory). When (0,0) is passed (default), it is set to the original imageSize . Setting it to a larger value can help you preserve details in the original image, especially when there is a big radial distortion. are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below). are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below). The function computes the rotation matrices for each camera that (virtually) make both camera image planes the same plane. Consequently, this makes all the epipolar lines parallel and thus simplifies the dense stereo correspondence problem. The function takes the matrices computed by #stereoCalibrate as input. As output, it provides two rotation matrices and also two projection matrices in the new coordinates. The function distinguishes the following two cases:
      • Horizontal stereo: the first and the second camera views are shifted relative to each other mainly along the x-axis (with possible small vertical shift). In the rectified images, the corresponding epipolar lines in the left and right cameras are horizontal and have the same y-coordinate. P1 and P2 look like:
      \(\texttt{P1} = \begin{bmatrix} f & 0 & cx_1 & 0 \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}\) \(\texttt{P2} = \begin{bmatrix} f & 0 & cx_2 & T_x \cdot f \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} ,\) \(\texttt{Q} = \begin{bmatrix} 1 & 0 & 0 & -cx_1 \\ 0 & 1 & 0 & -cy \\ 0 & 0 & 0 & f \\ 0 & 0 & -\frac{1}{T_x} & \frac{cx_1 - cx_2}{T_x} \end{bmatrix} \) where \(T_x\) is a horizontal shift between the cameras and \(cx_1=cx_2\) if REF: CALIB_ZERO_DISPARITY is set.
      • Vertical stereo: the first and the second camera views are shifted relative to each other mainly in the vertical direction (and probably a bit in the horizontal direction too). The epipolar lines in the rectified images are vertical and have the same x-coordinate. P1 and P2 look like:
      \(\texttt{P1} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_1 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}\) \(\texttt{P2} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_2 & T_y \cdot f \\ 0 & 0 & 1 & 0 \end{bmatrix},\) \(\texttt{Q} = \begin{bmatrix} 1 & 0 & 0 & -cx \\ 0 & 1 & 0 & -cy_1 \\ 0 & 0 & 0 & f \\ 0 & 0 & -\frac{1}{T_y} & \frac{cy_1 - cy_2}{T_y} \end{bmatrix} \) where \(T_y\) is a vertical shift between the cameras and \(cy_1=cy_2\) if REF: CALIB_ZERO_DISPARITY is set. As you can see, the first three columns of P1 and P2 will effectively be the new "rectified" camera matrices. The matrices, together with R1 and R2 , can then be passed to #initUndistortRectifyMap to initialize the rectification map for each camera. See below the screenshot from the stereo_calib.cpp sample. Some red horizontal lines pass through the corresponding image regions. This means that the images are well rectified, which is what most stereo correspondence algorithms rely on. The green rectangles are roi1 and roi2 . You see that their interiors are all valid pixels. ![image](pics/stereo_undistort.jpg)
    • stereoRectify

      public static void stereoRectify​(Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Size imageSize, Mat R, Mat T, Mat R1, Mat R2, Mat P1, Mat P2, Mat Q, int flags)
      Computes rectification transforms for each head of a calibrated stereo camera.
      Parameters:
      cameraMatrix1 - First camera intrinsic matrix.
      distCoeffs1 - First camera distortion parameters.
      cameraMatrix2 - Second camera intrinsic matrix.
      distCoeffs2 - Second camera distortion parameters.
      imageSize - Size of the image used for stereo calibration.
      R - Rotation matrix from the coordinate system of the first camera to the second camera, see REF: stereoCalibrate.
      T - Translation vector from the coordinate system of the first camera to the second camera, see REF: stereoCalibrate.
      R1 - Output 3x3 rectification transform (rotation matrix) for the first camera. This matrix brings points given in the unrectified first camera's coordinate system to points in the rectified first camera's coordinate system. In more technical terms, it performs a change of basis from the unrectified first camera's coordinate system to the rectified first camera's coordinate system.
      R2 - Output 3x3 rectification transform (rotation matrix) for the second camera. This matrix brings points given in the unrectified second camera's coordinate system to points in the rectified second camera's coordinate system. In more technical terms, it performs a change of basis from the unrectified second camera's coordinate system to the rectified second camera's coordinate system.
      P1 - Output 3x4 projection matrix in the new (rectified) coordinate systems for the first camera, i.e. it projects points given in the rectified first camera coordinate system into the rectified first camera's image.
      P2 - Output 3x4 projection matrix in the new (rectified) coordinate systems for the second camera, i.e. it projects points given in the rectified first camera coordinate system into the rectified second camera's image.
      Q - Output \(4 \times 4\) disparity-to-depth mapping matrix (see REF: reprojectImageTo3D).
      flags - Operation flags that may be zero or REF: CALIB_ZERO_DISPARITY . If the flag is set, the function makes the principal points of each camera have the same pixel coordinates in the rectified views. And if the flag is not set, the function may still shift the images in the horizontal or vertical direction (depending on the orientation of epipolar lines) to maximize the useful image area. scaling. Otherwise, the parameter should be between 0 and 1. alpha=0 means that the rectified images are zoomed and shifted so that only valid pixels are visible (no black areas after rectification). alpha=1 means that the rectified image is decimated and shifted so that all the pixels from the original images from the cameras are retained in the rectified images (no source image pixels are lost). Any intermediate value yields an intermediate result between those two extreme cases. #initUndistortRectifyMap (see the stereo_calib.cpp sample in OpenCV samples directory). When (0,0) is passed (default), it is set to the original imageSize . Setting it to a larger value can help you preserve details in the original image, especially when there is a big radial distortion. are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below). are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below). The function computes the rotation matrices for each camera that (virtually) make both camera image planes the same plane. Consequently, this makes all the epipolar lines parallel and thus simplifies the dense stereo correspondence problem. The function takes the matrices computed by #stereoCalibrate as input. As output, it provides two rotation matrices and also two projection matrices in the new coordinates. The function distinguishes the following two cases:
      • Horizontal stereo: the first and the second camera views are shifted relative to each other mainly along the x-axis (with possible small vertical shift). In the rectified images, the corresponding epipolar lines in the left and right cameras are horizontal and have the same y-coordinate. P1 and P2 look like:
      \(\texttt{P1} = \begin{bmatrix} f & 0 & cx_1 & 0 \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}\) \(\texttt{P2} = \begin{bmatrix} f & 0 & cx_2 & T_x \cdot f \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} ,\) \(\texttt{Q} = \begin{bmatrix} 1 & 0 & 0 & -cx_1 \\ 0 & 1 & 0 & -cy \\ 0 & 0 & 0 & f \\ 0 & 0 & -\frac{1}{T_x} & \frac{cx_1 - cx_2}{T_x} \end{bmatrix} \) where \(T_x\) is a horizontal shift between the cameras and \(cx_1=cx_2\) if REF: CALIB_ZERO_DISPARITY is set.
      • Vertical stereo: the first and the second camera views are shifted relative to each other mainly in the vertical direction (and probably a bit in the horizontal direction too). The epipolar lines in the rectified images are vertical and have the same x-coordinate. P1 and P2 look like:
      \(\texttt{P1} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_1 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}\) \(\texttt{P2} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_2 & T_y \cdot f \\ 0 & 0 & 1 & 0 \end{bmatrix},\) \(\texttt{Q} = \begin{bmatrix} 1 & 0 & 0 & -cx \\ 0 & 1 & 0 & -cy_1 \\ 0 & 0 & 0 & f \\ 0 & 0 & -\frac{1}{T_y} & \frac{cy_1 - cy_2}{T_y} \end{bmatrix} \) where \(T_y\) is a vertical shift between the cameras and \(cy_1=cy_2\) if REF: CALIB_ZERO_DISPARITY is set. As you can see, the first three columns of P1 and P2 will effectively be the new "rectified" camera matrices. The matrices, together with R1 and R2 , can then be passed to #initUndistortRectifyMap to initialize the rectification map for each camera. See below the screenshot from the stereo_calib.cpp sample. Some red horizontal lines pass through the corresponding image regions. This means that the images are well rectified, which is what most stereo correspondence algorithms rely on. The green rectangles are roi1 and roi2 . You see that their interiors are all valid pixels. ![image](pics/stereo_undistort.jpg)
    • stereoRectify

      public static void stereoRectify​(Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Size imageSize, Mat R, Mat T, Mat R1, Mat R2, Mat P1, Mat P2, Mat Q)
      Computes rectification transforms for each head of a calibrated stereo camera.
      Parameters:
      cameraMatrix1 - First camera intrinsic matrix.
      distCoeffs1 - First camera distortion parameters.
      cameraMatrix2 - Second camera intrinsic matrix.
      distCoeffs2 - Second camera distortion parameters.
      imageSize - Size of the image used for stereo calibration.
      R - Rotation matrix from the coordinate system of the first camera to the second camera, see REF: stereoCalibrate.
      T - Translation vector from the coordinate system of the first camera to the second camera, see REF: stereoCalibrate.
      R1 - Output 3x3 rectification transform (rotation matrix) for the first camera. This matrix brings points given in the unrectified first camera's coordinate system to points in the rectified first camera's coordinate system. In more technical terms, it performs a change of basis from the unrectified first camera's coordinate system to the rectified first camera's coordinate system.
      R2 - Output 3x3 rectification transform (rotation matrix) for the second camera. This matrix brings points given in the unrectified second camera's coordinate system to points in the rectified second camera's coordinate system. In more technical terms, it performs a change of basis from the unrectified second camera's coordinate system to the rectified second camera's coordinate system.
      P1 - Output 3x4 projection matrix in the new (rectified) coordinate systems for the first camera, i.e. it projects points given in the rectified first camera coordinate system into the rectified first camera's image.
      P2 - Output 3x4 projection matrix in the new (rectified) coordinate systems for the second camera, i.e. it projects points given in the rectified first camera coordinate system into the rectified second camera's image.
      Q - Output \(4 \times 4\) disparity-to-depth mapping matrix (see REF: reprojectImageTo3D). the function makes the principal points of each camera have the same pixel coordinates in the rectified views. And if the flag is not set, the function may still shift the images in the horizontal or vertical direction (depending on the orientation of epipolar lines) to maximize the useful image area. scaling. Otherwise, the parameter should be between 0 and 1. alpha=0 means that the rectified images are zoomed and shifted so that only valid pixels are visible (no black areas after rectification). alpha=1 means that the rectified image is decimated and shifted so that all the pixels from the original images from the cameras are retained in the rectified images (no source image pixels are lost). Any intermediate value yields an intermediate result between those two extreme cases. #initUndistortRectifyMap (see the stereo_calib.cpp sample in OpenCV samples directory). When (0,0) is passed (default), it is set to the original imageSize . Setting it to a larger value can help you preserve details in the original image, especially when there is a big radial distortion. are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below). are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below). The function computes the rotation matrices for each camera that (virtually) make both camera image planes the same plane. Consequently, this makes all the epipolar lines parallel and thus simplifies the dense stereo correspondence problem. The function takes the matrices computed by #stereoCalibrate as input. As output, it provides two rotation matrices and also two projection matrices in the new coordinates. The function distinguishes the following two cases:
      • Horizontal stereo: the first and the second camera views are shifted relative to each other mainly along the x-axis (with possible small vertical shift). In the rectified images, the corresponding epipolar lines in the left and right cameras are horizontal and have the same y-coordinate. P1 and P2 look like:
      \(\texttt{P1} = \begin{bmatrix} f & 0 & cx_1 & 0 \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}\) \(\texttt{P2} = \begin{bmatrix} f & 0 & cx_2 & T_x \cdot f \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} ,\) \(\texttt{Q} = \begin{bmatrix} 1 & 0 & 0 & -cx_1 \\ 0 & 1 & 0 & -cy \\ 0 & 0 & 0 & f \\ 0 & 0 & -\frac{1}{T_x} & \frac{cx_1 - cx_2}{T_x} \end{bmatrix} \) where \(T_x\) is a horizontal shift between the cameras and \(cx_1=cx_2\) if REF: CALIB_ZERO_DISPARITY is set.
      • Vertical stereo: the first and the second camera views are shifted relative to each other mainly in the vertical direction (and probably a bit in the horizontal direction too). The epipolar lines in the rectified images are vertical and have the same x-coordinate. P1 and P2 look like:
      \(\texttt{P1} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_1 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}\) \(\texttt{P2} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_2 & T_y \cdot f \\ 0 & 0 & 1 & 0 \end{bmatrix},\) \(\texttt{Q} = \begin{bmatrix} 1 & 0 & 0 & -cx \\ 0 & 1 & 0 & -cy_1 \\ 0 & 0 & 0 & f \\ 0 & 0 & -\frac{1}{T_y} & \frac{cy_1 - cy_2}{T_y} \end{bmatrix} \) where \(T_y\) is a vertical shift between the cameras and \(cy_1=cy_2\) if REF: CALIB_ZERO_DISPARITY is set. As you can see, the first three columns of P1 and P2 will effectively be the new "rectified" camera matrices. The matrices, together with R1 and R2 , can then be passed to #initUndistortRectifyMap to initialize the rectification map for each camera. See below the screenshot from the stereo_calib.cpp sample. Some red horizontal lines pass through the corresponding image regions. This means that the images are well rectified, which is what most stereo correspondence algorithms rely on. The green rectangles are roi1 and roi2 . You see that their interiors are all valid pixels. ![image](pics/stereo_undistort.jpg)
    • stereoRectifyUncalibrated

      public static boolean stereoRectifyUncalibrated​(Mat points1, Mat points2, Mat F, Size imgSize, Mat H1, Mat H2, double threshold)
      Computes a rectification transform for an uncalibrated stereo camera.
      Parameters:
      points1 - Array of feature points in the first image.
      points2 - The corresponding points in the second image. The same formats as in #findFundamentalMat are supported.
      F - Input fundamental matrix. It can be computed from the same set of point pairs using #findFundamentalMat .
      imgSize - Size of the image.
      H1 - Output rectification homography matrix for the first image.
      H2 - Output rectification homography matrix for the second image.
      threshold - Optional threshold used to filter out the outliers. If the parameter is greater than zero, all the point pairs that do not comply with the epipolar geometry (that is, the points for which \(|\texttt{points2[i]}^T \cdot \texttt{F} \cdot \texttt{points1[i]}|>\texttt{threshold}\) ) are rejected prior to computing the homographies. Otherwise, all the points are considered inliers. The function computes the rectification transformations without knowing intrinsic parameters of the cameras and their relative position in the space, which explains the suffix "uncalibrated". Another related difference from #stereoRectify is that the function outputs not the rectification transformations in the object (3D) space, but the planar perspective transformations encoded by the homography matrices H1 and H2 . The function implements the algorithm CITE: Hartley99 . Note: While the algorithm does not need to know the intrinsic parameters of the cameras, it heavily depends on the epipolar geometry. Therefore, if the camera lenses have a significant distortion, it would be better to correct it before computing the fundamental matrix and calling this function. For example, distortion coefficients can be estimated for each head of stereo camera separately by using #calibrateCamera . Then, the images can be corrected using #undistort , or just the point coordinates can be corrected with #undistortPoints .
      Returns:
      automatically generated
    • stereoRectifyUncalibrated

      public static boolean stereoRectifyUncalibrated​(Mat points1, Mat points2, Mat F, Size imgSize, Mat H1, Mat H2)
      Computes a rectification transform for an uncalibrated stereo camera.
      Parameters:
      points1 - Array of feature points in the first image.
      points2 - The corresponding points in the second image. The same formats as in #findFundamentalMat are supported.
      F - Input fundamental matrix. It can be computed from the same set of point pairs using #findFundamentalMat .
      imgSize - Size of the image.
      H1 - Output rectification homography matrix for the first image.
      H2 - Output rectification homography matrix for the second image. than zero, all the point pairs that do not comply with the epipolar geometry (that is, the points for which \(|\texttt{points2[i]}^T \cdot \texttt{F} \cdot \texttt{points1[i]}|>\texttt{threshold}\) ) are rejected prior to computing the homographies. Otherwise, all the points are considered inliers. The function computes the rectification transformations without knowing intrinsic parameters of the cameras and their relative position in the space, which explains the suffix "uncalibrated". Another related difference from #stereoRectify is that the function outputs not the rectification transformations in the object (3D) space, but the planar perspective transformations encoded by the homography matrices H1 and H2 . The function implements the algorithm CITE: Hartley99 . Note: While the algorithm does not need to know the intrinsic parameters of the cameras, it heavily depends on the epipolar geometry. Therefore, if the camera lenses have a significant distortion, it would be better to correct it before computing the fundamental matrix and calling this function. For example, distortion coefficients can be estimated for each head of stereo camera separately by using #calibrateCamera . Then, the images can be corrected using #undistort , or just the point coordinates can be corrected with #undistortPoints .
      Returns:
      automatically generated
    • rectify3Collinear

      public static float rectify3Collinear​(Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Mat cameraMatrix3, Mat distCoeffs3, List<Mat> imgpt1, List<Mat> imgpt3, Size imageSize, Mat R12, Mat T12, Mat R13, Mat T13, Mat R1, Mat R2, Mat R3, Mat P1, Mat P2, Mat P3, Mat Q, double alpha, Size newImgSize, Rect roi1, Rect roi2, int flags)
    • getOptimalNewCameraMatrix

      public static Mat getOptimalNewCameraMatrix​(Mat cameraMatrix, Mat distCoeffs, Size imageSize, double alpha, Size newImgSize, Rect validPixROI, boolean centerPrincipalPoint)
      Returns the new camera intrinsic matrix based on the free scaling parameter.
      Parameters:
      cameraMatrix - Input camera intrinsic matrix.
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      imageSize - Original image size.
      alpha - Free scaling parameter between 0 (when all the pixels in the undistorted image are valid) and 1 (when all the source image pixels are retained in the undistorted image). See #stereoRectify for details.
      newImgSize - Image size after rectification. By default, it is set to imageSize .
      validPixROI - Optional output rectangle that outlines all-good-pixels region in the undistorted image. See roi1, roi2 description in #stereoRectify .
      centerPrincipalPoint - Optional flag that indicates whether in the new camera intrinsic matrix the principal point should be at the image center or not. By default, the principal point is chosen to best fit a subset of the source image (determined by alpha) to the corrected image.
      Returns:
      new_camera_matrix Output new camera intrinsic matrix. The function computes and returns the optimal new camera intrinsic matrix based on the free scaling parameter. By varying this parameter, you may retrieve only sensible pixels alpha=0 , keep all the original image pixels if there is valuable information in the corners alpha=1 , or get something in between. When alpha>0 , the undistorted result is likely to have some black pixels corresponding to "virtual" pixels outside of the captured distorted image. The original camera intrinsic matrix, distortion coefficients, the computed new camera intrinsic matrix, and newImageSize should be passed to #initUndistortRectifyMap to produce the maps for #remap .
    • getOptimalNewCameraMatrix

      public static Mat getOptimalNewCameraMatrix​(Mat cameraMatrix, Mat distCoeffs, Size imageSize, double alpha, Size newImgSize, Rect validPixROI)
      Returns the new camera intrinsic matrix based on the free scaling parameter.
      Parameters:
      cameraMatrix - Input camera intrinsic matrix.
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      imageSize - Original image size.
      alpha - Free scaling parameter between 0 (when all the pixels in the undistorted image are valid) and 1 (when all the source image pixels are retained in the undistorted image). See #stereoRectify for details.
      newImgSize - Image size after rectification. By default, it is set to imageSize .
      validPixROI - Optional output rectangle that outlines all-good-pixels region in the undistorted image. See roi1, roi2 description in #stereoRectify . principal point should be at the image center or not. By default, the principal point is chosen to best fit a subset of the source image (determined by alpha) to the corrected image.
      Returns:
      new_camera_matrix Output new camera intrinsic matrix. The function computes and returns the optimal new camera intrinsic matrix based on the free scaling parameter. By varying this parameter, you may retrieve only sensible pixels alpha=0 , keep all the original image pixels if there is valuable information in the corners alpha=1 , or get something in between. When alpha>0 , the undistorted result is likely to have some black pixels corresponding to "virtual" pixels outside of the captured distorted image. The original camera intrinsic matrix, distortion coefficients, the computed new camera intrinsic matrix, and newImageSize should be passed to #initUndistortRectifyMap to produce the maps for #remap .
    • getOptimalNewCameraMatrix

      public static Mat getOptimalNewCameraMatrix​(Mat cameraMatrix, Mat distCoeffs, Size imageSize, double alpha, Size newImgSize)
      Returns the new camera intrinsic matrix based on the free scaling parameter.
      Parameters:
      cameraMatrix - Input camera intrinsic matrix.
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      imageSize - Original image size.
      alpha - Free scaling parameter between 0 (when all the pixels in the undistorted image are valid) and 1 (when all the source image pixels are retained in the undistorted image). See #stereoRectify for details.
      newImgSize - Image size after rectification. By default, it is set to imageSize . undistorted image. See roi1, roi2 description in #stereoRectify . principal point should be at the image center or not. By default, the principal point is chosen to best fit a subset of the source image (determined by alpha) to the corrected image.
      Returns:
      new_camera_matrix Output new camera intrinsic matrix. The function computes and returns the optimal new camera intrinsic matrix based on the free scaling parameter. By varying this parameter, you may retrieve only sensible pixels alpha=0 , keep all the original image pixels if there is valuable information in the corners alpha=1 , or get something in between. When alpha>0 , the undistorted result is likely to have some black pixels corresponding to "virtual" pixels outside of the captured distorted image. The original camera intrinsic matrix, distortion coefficients, the computed new camera intrinsic matrix, and newImageSize should be passed to #initUndistortRectifyMap to produce the maps for #remap .
    • getOptimalNewCameraMatrix

      public static Mat getOptimalNewCameraMatrix​(Mat cameraMatrix, Mat distCoeffs, Size imageSize, double alpha)
      Returns the new camera intrinsic matrix based on the free scaling parameter.
      Parameters:
      cameraMatrix - Input camera intrinsic matrix.
      distCoeffs - Input vector of distortion coefficients \(\distcoeffs\). If the vector is NULL/empty, the zero distortion coefficients are assumed.
      imageSize - Original image size.
      alpha - Free scaling parameter between 0 (when all the pixels in the undistorted image are valid) and 1 (when all the source image pixels are retained in the undistorted image). See #stereoRectify for details. undistorted image. See roi1, roi2 description in #stereoRectify . principal point should be at the image center or not. By default, the principal point is chosen to best fit a subset of the source image (determined by alpha) to the corrected image.
      Returns:
      new_camera_matrix Output new camera intrinsic matrix. The function computes and returns the optimal new camera intrinsic matrix based on the free scaling parameter. By varying this parameter, you may retrieve only sensible pixels alpha=0 , keep all the original image pixels if there is valuable information in the corners alpha=1 , or get something in between. When alpha>0 , the undistorted result is likely to have some black pixels corresponding to "virtual" pixels outside of the captured distorted image. The original camera intrinsic matrix, distortion coefficients, the computed new camera intrinsic matrix, and newImageSize should be passed to #initUndistortRectifyMap to produce the maps for #remap .
    • calibrateHandEye

      public static void calibrateHandEye​(List<Mat> R_gripper2base, List<Mat> t_gripper2base, List<Mat> R_target2cam, List<Mat> t_target2cam, Mat R_cam2gripper, Mat t_cam2gripper, int method)
      Computes Hand-Eye calibration: \(_{}^{g}\textrm{T}_c\)
      Parameters:
      R_gripper2base - Rotation part extracted from the homogeneous matrix that transforms a point expressed in the gripper frame to the robot base frame (\(_{}^{b}\textrm{T}_g\)). This is a vector (vector&lt;Mat&gt;) that contains the rotation, (3x3) rotation matrices or (3x1) rotation vectors, for all the transformations from gripper frame to robot base frame.
      t_gripper2base - Translation part extracted from the homogeneous matrix that transforms a point expressed in the gripper frame to the robot base frame (\(_{}^{b}\textrm{T}_g\)). This is a vector (vector&lt;Mat&gt;) that contains the (3x1) translation vectors for all the transformations from gripper frame to robot base frame.
      R_target2cam - Rotation part extracted from the homogeneous matrix that transforms a point expressed in the target frame to the camera frame (\(_{}^{c}\textrm{T}_t\)). This is a vector (vector&lt;Mat&gt;) that contains the rotation, (3x3) rotation matrices or (3x1) rotation vectors, for all the transformations from calibration target frame to camera frame.
      t_target2cam - Rotation part extracted from the homogeneous matrix that transforms a point expressed in the target frame to the camera frame (\(_{}^{c}\textrm{T}_t\)). This is a vector (vector&lt;Mat&gt;) that contains the (3x1) translation vectors for all the transformations from calibration target frame to camera frame.
      R_cam2gripper - Estimated (3x3) rotation part extracted from the homogeneous matrix that transforms a point expressed in the camera frame to the gripper frame (\(_{}^{g}\textrm{T}_c\)).
      t_cam2gripper - Estimated (3x1) translation part extracted from the homogeneous matrix that transforms a point expressed in the camera frame to the gripper frame (\(_{}^{g}\textrm{T}_c\)).
      method - One of the implemented Hand-Eye calibration method, see cv::HandEyeCalibrationMethod The function performs the Hand-Eye calibration using various methods. One approach consists in estimating the rotation then the translation (separable solutions) and the following methods are implemented:
      • R. Tsai, R. Lenz A New Technique for Fully Autonomous and Efficient 3D Robotics Hand/EyeCalibration \cite Tsai89
      • F. Park, B. Martin Robot Sensor Calibration: Solving AX = XB on the Euclidean Group \cite Park94
      • R. Horaud, F. Dornaika Hand-Eye Calibration \cite Horaud95
      Another approach consists in estimating simultaneously the rotation and the translation (simultaneous solutions), with the following implemented methods:
      • N. Andreff, R. Horaud, B. Espiau On-line Hand-Eye Calibration \cite Andreff99
      • K. Daniilidis Hand-Eye Calibration Using Dual Quaternions \cite Daniilidis98
      The following picture describes the Hand-Eye calibration problem where the transformation between a camera ("eye") mounted on a robot gripper ("hand") has to be estimated. This configuration is called eye-in-hand. The eye-to-hand configuration consists in a static camera observing a calibration pattern mounted on the robot end-effector. The transformation from the camera to the robot base frame can then be estimated by inputting the suitable transformations to the function, see below. ![](pics/hand-eye_figure.png) The calibration procedure is the following:
      • a static calibration pattern is used to estimate the transformation between the target frame and the camera frame
      • the robot gripper is moved in order to acquire several poses
      • for each pose, the homogeneous transformation between the gripper frame and the robot base frame is recorded using for instance the robot kinematics \( \begin{bmatrix} X_b\\ Y_b\\ Z_b\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{b}\textrm{R}_g & _{}^{b}\textrm{t}_g \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_g\\ Y_g\\ Z_g\\ 1 \end{bmatrix} \)
      • for each pose, the homogeneous transformation between the calibration target frame and the camera frame is recorded using for instance a pose estimation method (PnP) from 2D-3D point correspondences \( \begin{bmatrix} X_c\\ Y_c\\ Z_c\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{c}\textrm{R}_t & _{}^{c}\textrm{t}_t \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_t\\ Y_t\\ Z_t\\ 1 \end{bmatrix} \)
      The Hand-Eye calibration procedure returns the following homogeneous transformation \( \begin{bmatrix} X_g\\ Y_g\\ Z_g\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{g}\textrm{R}_c & _{}^{g}\textrm{t}_c \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_c\\ Y_c\\ Z_c\\ 1 \end{bmatrix} \) This problem is also known as solving the \(\mathbf{A}\mathbf{X}=\mathbf{X}\mathbf{B}\) equation:
      • for an eye-in-hand configuration \( \begin{align*} ^{b}{\textrm{T}_g}^{(1)} \hspace{0.2em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(1)} &= \hspace{0.1em} ^{b}{\textrm{T}_g}^{(2)} \hspace{0.2em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} \\
      (^{b}{\textrm{T}_g}^{(2)})^{-1} \hspace{0.2em} ^{b}{\textrm{T}_g}^{(1)} \hspace{0.2em} ^{g}\textrm{T}_c &= \hspace{0.1em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} (^{c}{\textrm{T}_t}^{(1)})^{-1} \\ \textrm{A}_i \textrm{X} &= \textrm{X} \textrm{B}_i \\ \end{align*} \)
      • for an eye-to-hand configuration \( \begin{align*} ^{g}{\textrm{T}_b}^{(1)} \hspace{0.2em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(1)} &= \hspace{0.1em} ^{g}{\textrm{T}_b}^{(2)} \hspace{0.2em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} \\
      (^{g}{\textrm{T}_b}^{(2)})^{-1} \hspace{0.2em} ^{g}{\textrm{T}_b}^{(1)} \hspace{0.2em} ^{b}\textrm{T}_c &= \hspace{0.1em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} (^{c}{\textrm{T}_t}^{(1)})^{-1} \\ \textrm{A}_i \textrm{X} &= \textrm{X} \textrm{B}_i \\ \end{align*} \) \note Additional information can be found on this [website](http://campar.in.tum.de/Chair/HandEyeCalibration). \note A minimum of 2 motions with non parallel rotation axes are necessary to determine the hand-eye transformation. So at least 3 different poses are required, but it is strongly recommended to use many more poses.
    • calibrateHandEye

      public static void calibrateHandEye​(List<Mat> R_gripper2base, List<Mat> t_gripper2base, List<Mat> R_target2cam, List<Mat> t_target2cam, Mat R_cam2gripper, Mat t_cam2gripper)
      Computes Hand-Eye calibration: \(_{}^{g}\textrm{T}_c\)
      Parameters:
      R_gripper2base - Rotation part extracted from the homogeneous matrix that transforms a point expressed in the gripper frame to the robot base frame (\(_{}^{b}\textrm{T}_g\)). This is a vector (vector&lt;Mat&gt;) that contains the rotation, (3x3) rotation matrices or (3x1) rotation vectors, for all the transformations from gripper frame to robot base frame.
      t_gripper2base - Translation part extracted from the homogeneous matrix that transforms a point expressed in the gripper frame to the robot base frame (\(_{}^{b}\textrm{T}_g\)). This is a vector (vector&lt;Mat&gt;) that contains the (3x1) translation vectors for all the transformations from gripper frame to robot base frame.
      R_target2cam - Rotation part extracted from the homogeneous matrix that transforms a point expressed in the target frame to the camera frame (\(_{}^{c}\textrm{T}_t\)). This is a vector (vector&lt;Mat&gt;) that contains the rotation, (3x3) rotation matrices or (3x1) rotation vectors, for all the transformations from calibration target frame to camera frame.
      t_target2cam - Rotation part extracted from the homogeneous matrix that transforms a point expressed in the target frame to the camera frame (\(_{}^{c}\textrm{T}_t\)). This is a vector (vector&lt;Mat&gt;) that contains the (3x1) translation vectors for all the transformations from calibration target frame to camera frame.
      R_cam2gripper - Estimated (3x3) rotation part extracted from the homogeneous matrix that transforms a point expressed in the camera frame to the gripper frame (\(_{}^{g}\textrm{T}_c\)).
      t_cam2gripper - Estimated (3x1) translation part extracted from the homogeneous matrix that transforms a point expressed in the camera frame to the gripper frame (\(_{}^{g}\textrm{T}_c\)). The function performs the Hand-Eye calibration using various methods. One approach consists in estimating the rotation then the translation (separable solutions) and the following methods are implemented:
      • R. Tsai, R. Lenz A New Technique for Fully Autonomous and Efficient 3D Robotics Hand/EyeCalibration \cite Tsai89
      • F. Park, B. Martin Robot Sensor Calibration: Solving AX = XB on the Euclidean Group \cite Park94
      • R. Horaud, F. Dornaika Hand-Eye Calibration \cite Horaud95
      Another approach consists in estimating simultaneously the rotation and the translation (simultaneous solutions), with the following implemented methods:
      • N. Andreff, R. Horaud, B. Espiau On-line Hand-Eye Calibration \cite Andreff99
      • K. Daniilidis Hand-Eye Calibration Using Dual Quaternions \cite Daniilidis98
      The following picture describes the Hand-Eye calibration problem where the transformation between a camera ("eye") mounted on a robot gripper ("hand") has to be estimated. This configuration is called eye-in-hand. The eye-to-hand configuration consists in a static camera observing a calibration pattern mounted on the robot end-effector. The transformation from the camera to the robot base frame can then be estimated by inputting the suitable transformations to the function, see below. ![](pics/hand-eye_figure.png) The calibration procedure is the following:
      • a static calibration pattern is used to estimate the transformation between the target frame and the camera frame
      • the robot gripper is moved in order to acquire several poses
      • for each pose, the homogeneous transformation between the gripper frame and the robot base frame is recorded using for instance the robot kinematics \( \begin{bmatrix} X_b\\ Y_b\\ Z_b\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{b}\textrm{R}_g & _{}^{b}\textrm{t}_g \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_g\\ Y_g\\ Z_g\\ 1 \end{bmatrix} \)
      • for each pose, the homogeneous transformation between the calibration target frame and the camera frame is recorded using for instance a pose estimation method (PnP) from 2D-3D point correspondences \( \begin{bmatrix} X_c\\ Y_c\\ Z_c\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{c}\textrm{R}_t & _{}^{c}\textrm{t}_t \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_t\\ Y_t\\ Z_t\\ 1 \end{bmatrix} \)
      The Hand-Eye calibration procedure returns the following homogeneous transformation \( \begin{bmatrix} X_g\\ Y_g\\ Z_g\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{g}\textrm{R}_c & _{}^{g}\textrm{t}_c \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_c\\ Y_c\\ Z_c\\ 1 \end{bmatrix} \) This problem is also known as solving the \(\mathbf{A}\mathbf{X}=\mathbf{X}\mathbf{B}\) equation:
      • for an eye-in-hand configuration \( \begin{align*} ^{b}{\textrm{T}_g}^{(1)} \hspace{0.2em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(1)} &= \hspace{0.1em} ^{b}{\textrm{T}_g}^{(2)} \hspace{0.2em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} \\
      (^{b}{\textrm{T}_g}^{(2)})^{-1} \hspace{0.2em} ^{b}{\textrm{T}_g}^{(1)} \hspace{0.2em} ^{g}\textrm{T}_c &= \hspace{0.1em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} (^{c}{\textrm{T}_t}^{(1)})^{-1} \\ \textrm{A}_i \textrm{X} &= \textrm{X} \textrm{B}_i \\ \end{align*} \)
      • for an eye-to-hand configuration \( \begin{align*} ^{g}{\textrm{T}_b}^{(1)} \hspace{0.2em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(1)} &= \hspace{0.1em} ^{g}{\textrm{T}_b}^{(2)} \hspace{0.2em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} \\
      (^{g}{\textrm{T}_b}^{(2)})^{-1} \hspace{0.2em} ^{g}{\textrm{T}_b}^{(1)} \hspace{0.2em} ^{b}\textrm{T}_c &= \hspace{0.1em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} (^{c}{\textrm{T}_t}^{(1)})^{-1} \\ \textrm{A}_i \textrm{X} &= \textrm{X} \textrm{B}_i \\ \end{align*} \) \note Additional information can be found on this [website](http://campar.in.tum.de/Chair/HandEyeCalibration). \note A minimum of 2 motions with non parallel rotation axes are necessary to determine the hand-eye transformation. So at least 3 different poses are required, but it is strongly recommended to use many more poses.
    • calibrateRobotWorldHandEye

      public static void calibrateRobotWorldHandEye​(List<Mat> R_world2cam, List<Mat> t_world2cam, List<Mat> R_base2gripper, List<Mat> t_base2gripper, Mat R_base2world, Mat t_base2world, Mat R_gripper2cam, Mat t_gripper2cam, int method)
      Computes Robot-World/Hand-Eye calibration: \(_{}^{w}\textrm{T}_b\) and \(_{}^{c}\textrm{T}_g\)
      Parameters:
      R_world2cam - Rotation part extracted from the homogeneous matrix that transforms a point expressed in the world frame to the camera frame (\(_{}^{c}\textrm{T}_w\)). This is a vector (vector&lt;Mat&gt;) that contains the rotation, (3x3) rotation matrices or (3x1) rotation vectors, for all the transformations from world frame to the camera frame.
      t_world2cam - Translation part extracted from the homogeneous matrix that transforms a point expressed in the world frame to the camera frame (\(_{}^{c}\textrm{T}_w\)). This is a vector (vector&lt;Mat&gt;) that contains the (3x1) translation vectors for all the transformations from world frame to the camera frame.
      R_base2gripper - Rotation part extracted from the homogeneous matrix that transforms a point expressed in the robot base frame to the gripper frame (\(_{}^{g}\textrm{T}_b\)). This is a vector (vector&lt;Mat&gt;) that contains the rotation, (3x3) rotation matrices or (3x1) rotation vectors, for all the transformations from robot base frame to the gripper frame.
      t_base2gripper - Rotation part extracted from the homogeneous matrix that transforms a point expressed in the robot base frame to the gripper frame (\(_{}^{g}\textrm{T}_b\)). This is a vector (vector&lt;Mat&gt;) that contains the (3x1) translation vectors for all the transformations from robot base frame to the gripper frame.
      R_base2world - Estimated (3x3) rotation part extracted from the homogeneous matrix that transforms a point expressed in the robot base frame to the world frame (\(_{}^{w}\textrm{T}_b\)).
      t_base2world - Estimated (3x1) translation part extracted from the homogeneous matrix that transforms a point expressed in the robot base frame to the world frame (\(_{}^{w}\textrm{T}_b\)).
      R_gripper2cam - Estimated (3x3) rotation part extracted from the homogeneous matrix that transforms a point expressed in the gripper frame to the camera frame (\(_{}^{c}\textrm{T}_g\)).
      t_gripper2cam - Estimated (3x1) translation part extracted from the homogeneous matrix that transforms a point expressed in the gripper frame to the camera frame (\(_{}^{c}\textrm{T}_g\)).
      method - One of the implemented Robot-World/Hand-Eye calibration method, see cv::RobotWorldHandEyeCalibrationMethod The function performs the Robot-World/Hand-Eye calibration using various methods. One approach consists in estimating the rotation then the translation (separable solutions):
      • M. Shah, Solving the robot-world/hand-eye calibration problem using the kronecker product \cite Shah2013SolvingTR
      Another approach consists in estimating simultaneously the rotation and the translation (simultaneous solutions), with the following implemented method:
      • A. Li, L. Wang, and D. Wu, Simultaneous robot-world and hand-eye calibration using dual-quaternions and kronecker product \cite Li2010SimultaneousRA
      The following picture describes the Robot-World/Hand-Eye calibration problem where the transformations between a robot and a world frame and between a robot gripper ("hand") and a camera ("eye") mounted at the robot end-effector have to be estimated. ![](pics/robot-world_hand-eye_figure.png) The calibration procedure is the following:
      • a static calibration pattern is used to estimate the transformation between the target frame and the camera frame
      • the robot gripper is moved in order to acquire several poses
      • for each pose, the homogeneous transformation between the gripper frame and the robot base frame is recorded using for instance the robot kinematics \( \begin{bmatrix} X_g\\ Y_g\\ Z_g\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{g}\textrm{R}_b & _{}^{g}\textrm{t}_b \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_b\\ Y_b\\ Z_b\\ 1 \end{bmatrix} \)
      • for each pose, the homogeneous transformation between the calibration target frame (the world frame) and the camera frame is recorded using for instance a pose estimation method (PnP) from 2D-3D point correspondences \( \begin{bmatrix} X_c\\ Y_c\\ Z_c\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{c}\textrm{R}_w & _{}^{c}\textrm{t}_w \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_w\\ Y_w\\ Z_w\\ 1 \end{bmatrix} \)
      The Robot-World/Hand-Eye calibration procedure returns the following homogeneous transformations \( \begin{bmatrix} X_w\\ Y_w\\ Z_w\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{w}\textrm{R}_b & _{}^{w}\textrm{t}_b \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_b\\ Y_b\\ Z_b\\ 1 \end{bmatrix} \) \( \begin{bmatrix} X_c\\ Y_c\\ Z_c\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{c}\textrm{R}_g & _{}^{c}\textrm{t}_g \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_g\\ Y_g\\ Z_g\\ 1 \end{bmatrix} \) This problem is also known as solving the \(\mathbf{A}\mathbf{X}=\mathbf{Z}\mathbf{B}\) equation, with:
      • \(\mathbf{A} \Leftrightarrow \hspace{0.1em} _{}^{c}\textrm{T}_w\)
      • \(\mathbf{X} \Leftrightarrow \hspace{0.1em} _{}^{w}\textrm{T}_b\)
      • \(\mathbf{Z} \Leftrightarrow \hspace{0.1em} _{}^{c}\textrm{T}_g\)
      • \(\mathbf{B} \Leftrightarrow \hspace{0.1em} _{}^{g}\textrm{T}_b\)
      \note At least 3 measurements are required (input vectors size must be greater or equal to 3).
    • calibrateRobotWorldHandEye

      public static void calibrateRobotWorldHandEye​(List<Mat> R_world2cam, List<Mat> t_world2cam, List<Mat> R_base2gripper, List<Mat> t_base2gripper, Mat R_base2world, Mat t_base2world, Mat R_gripper2cam, Mat t_gripper2cam)
      Computes Robot-World/Hand-Eye calibration: \(_{}^{w}\textrm{T}_b\) and \(_{}^{c}\textrm{T}_g\)
      Parameters:
      R_world2cam - Rotation part extracted from the homogeneous matrix that transforms a point expressed in the world frame to the camera frame (\(_{}^{c}\textrm{T}_w\)). This is a vector (vector&lt;Mat&gt;) that contains the rotation, (3x3) rotation matrices or (3x1) rotation vectors, for all the transformations from world frame to the camera frame.
      t_world2cam - Translation part extracted from the homogeneous matrix that transforms a point expressed in the world frame to the camera frame (\(_{}^{c}\textrm{T}_w\)). This is a vector (vector&lt;Mat&gt;) that contains the (3x1) translation vectors for all the transformations from world frame to the camera frame.
      R_base2gripper - Rotation part extracted from the homogeneous matrix that transforms a point expressed in the robot base frame to the gripper frame (\(_{}^{g}\textrm{T}_b\)). This is a vector (vector&lt;Mat&gt;) that contains the rotation, (3x3) rotation matrices or (3x1) rotation vectors, for all the transformations from robot base frame to the gripper frame.
      t_base2gripper - Rotation part extracted from the homogeneous matrix that transforms a point expressed in the robot base frame to the gripper frame (\(_{}^{g}\textrm{T}_b\)). This is a vector (vector&lt;Mat&gt;) that contains the (3x1) translation vectors for all the transformations from robot base frame to the gripper frame.
      R_base2world - Estimated (3x3) rotation part extracted from the homogeneous matrix that transforms a point expressed in the robot base frame to the world frame (\(_{}^{w}\textrm{T}_b\)).
      t_base2world - Estimated (3x1) translation part extracted from the homogeneous matrix that transforms a point expressed in the robot base frame to the world frame (\(_{}^{w}\textrm{T}_b\)).
      R_gripper2cam - Estimated (3x3) rotation part extracted from the homogeneous matrix that transforms a point expressed in the gripper frame to the camera frame (\(_{}^{c}\textrm{T}_g\)).
      t_gripper2cam - Estimated (3x1) translation part extracted from the homogeneous matrix that transforms a point expressed in the gripper frame to the camera frame (\(_{}^{c}\textrm{T}_g\)). The function performs the Robot-World/Hand-Eye calibration using various methods. One approach consists in estimating the rotation then the translation (separable solutions):
      • M. Shah, Solving the robot-world/hand-eye calibration problem using the kronecker product \cite Shah2013SolvingTR
      Another approach consists in estimating simultaneously the rotation and the translation (simultaneous solutions), with the following implemented method:
      • A. Li, L. Wang, and D. Wu, Simultaneous robot-world and hand-eye calibration using dual-quaternions and kronecker product \cite Li2010SimultaneousRA
      The following picture describes the Robot-World/Hand-Eye calibration problem where the transformations between a robot and a world frame and between a robot gripper ("hand") and a camera ("eye") mounted at the robot end-effector have to be estimated. ![](pics/robot-world_hand-eye_figure.png) The calibration procedure is the following:
      • a static calibration pattern is used to estimate the transformation between the target frame and the camera frame
      • the robot gripper is moved in order to acquire several poses
      • for each pose, the homogeneous transformation between the gripper frame and the robot base frame is recorded using for instance the robot kinematics \( \begin{bmatrix} X_g\\ Y_g\\ Z_g\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{g}\textrm{R}_b & _{}^{g}\textrm{t}_b \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_b\\ Y_b\\ Z_b\\ 1 \end{bmatrix} \)
      • for each pose, the homogeneous transformation between the calibration target frame (the world frame) and the camera frame is recorded using for instance a pose estimation method (PnP) from 2D-3D point correspondences \( \begin{bmatrix} X_c\\ Y_c\\ Z_c\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{c}\textrm{R}_w & _{}^{c}\textrm{t}_w \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_w\\ Y_w\\ Z_w\\ 1 \end{bmatrix} \)
      The Robot-World/Hand-Eye calibration procedure returns the following homogeneous transformations \( \begin{bmatrix} X_w\\ Y_w\\ Z_w\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{w}\textrm{R}_b & _{}^{w}\textrm{t}_b \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_b\\ Y_b\\ Z_b\\ 1 \end{bmatrix} \) \( \begin{bmatrix} X_c\\ Y_c\\ Z_c\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{c}\textrm{R}_g & _{}^{c}\textrm{t}_g \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_g\\ Y_g\\ Z_g\\ 1 \end{bmatrix} \) This problem is also known as solving the \(\mathbf{A}\mathbf{X}=\mathbf{Z}\mathbf{B}\) equation, with:
      • \(\mathbf{A} \Leftrightarrow \hspace{0.1em} _{}^{c}\textrm{T}_w\)
      • \(\mathbf{X} \Leftrightarrow \hspace{0.1em} _{}^{w}\textrm{T}_b\)
      • \(\mathbf{Z} \Leftrightarrow \hspace{0.1em} _{}^{c}\textrm{T}_g\)
      • \(\mathbf{B} \Leftrightarrow \hspace{0.1em} _{}^{g}\textrm{T}_b\)
      \note At least 3 measurements are required (input vectors size must be greater or equal to 3).
    • convertPointsToHomogeneous

      public static void convertPointsToHomogeneous​(Mat src, Mat dst)
      Converts points from Euclidean to homogeneous space.
      Parameters:
      src - Input vector of N-dimensional points.
      dst - Output vector of N+1-dimensional points. The function converts points from Euclidean to homogeneous space by appending 1's to the tuple of point coordinates. That is, each point (x1, x2, ..., xn) is converted to (x1, x2, ..., xn, 1).
    • convertPointsFromHomogeneous

      public static void convertPointsFromHomogeneous​(Mat src, Mat dst)
      Converts points from homogeneous to Euclidean space.
      Parameters:
      src - Input vector of N-dimensional points.
      dst - Output vector of N-1-dimensional points. The function converts points homogeneous to Euclidean space using perspective projection. That is, each point (x1, x2, ... x(n-1), xn) is converted to (x1/xn, x2/xn, ..., x(n-1)/xn). When xn=0, the output point coordinates will be (0,0,0,...).
    • findFundamentalMat

      public static Mat findFundamentalMat​(MatOfPoint2f points1, MatOfPoint2f points2, int method, double ransacReprojThreshold, double confidence, int maxIters, Mat mask)
      Calculates a fundamental matrix from the corresponding points in two images.
      Parameters:
      points1 - Array of N points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      method - Method for computing a fundamental matrix.
      • REF: FM_7POINT for a 7-point algorithm. \(N = 7\)
      • REF: FM_8POINT for an 8-point algorithm. \(N \ge 8\)
      • REF: FM_RANSAC for the RANSAC algorithm. \(N \ge 8\)
      • REF: FM_LMEDS for the LMedS algorithm. \(N \ge 8\)
      ransacReprojThreshold - Parameter used only for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise.
      confidence - Parameter used for the RANSAC and LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
      mask - optional output mask
      maxIters - The maximum number of robust method iterations. The epipolar geometry is described by the following equation: \([p_2; 1]^T F [p_1; 1] = 0\) where \(F\) is a fundamental matrix, \(p_1\) and \(p_2\) are corresponding points in the first and the second images, respectively. The function calculates the fundamental matrix using one of four methods listed above and returns the found fundamental matrix. Normally just one matrix is found. But in case of the 7-point algorithm, the function may return up to 3 solutions ( \(9 \times 3\) matrix that stores all 3 matrices sequentially). The calculated fundamental matrix may be passed further to #computeCorrespondEpilines that finds the epipolar lines corresponding to the specified points. It can also be passed to #stereoRectifyUncalibrated to compute the rectification transformation. : // Example. Estimation of fundamental matrix using the RANSAC algorithm int point_count = 100; vector<Point2f> points1(point_count); vector<Point2f> points2(point_count); // initialize the points here ... for( int i = 0; i < point_count; i++ ) { points1[i] = ...; points2[i] = ...; } Mat fundamental_matrix = findFundamentalMat(points1, points2, FM_RANSAC, 3, 0.99);
      Returns:
      automatically generated
    • findFundamentalMat

      public static Mat findFundamentalMat​(MatOfPoint2f points1, MatOfPoint2f points2, int method, double ransacReprojThreshold, double confidence, int maxIters)
      Calculates a fundamental matrix from the corresponding points in two images.
      Parameters:
      points1 - Array of N points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      method - Method for computing a fundamental matrix.
      • REF: FM_7POINT for a 7-point algorithm. \(N = 7\)
      • REF: FM_8POINT for an 8-point algorithm. \(N \ge 8\)
      • REF: FM_RANSAC for the RANSAC algorithm. \(N \ge 8\)
      • REF: FM_LMEDS for the LMedS algorithm. \(N \ge 8\)
      ransacReprojThreshold - Parameter used only for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise.
      confidence - Parameter used for the RANSAC and LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
      maxIters - The maximum number of robust method iterations. The epipolar geometry is described by the following equation: \([p_2; 1]^T F [p_1; 1] = 0\) where \(F\) is a fundamental matrix, \(p_1\) and \(p_2\) are corresponding points in the first and the second images, respectively. The function calculates the fundamental matrix using one of four methods listed above and returns the found fundamental matrix. Normally just one matrix is found. But in case of the 7-point algorithm, the function may return up to 3 solutions ( \(9 \times 3\) matrix that stores all 3 matrices sequentially). The calculated fundamental matrix may be passed further to #computeCorrespondEpilines that finds the epipolar lines corresponding to the specified points. It can also be passed to #stereoRectifyUncalibrated to compute the rectification transformation. : // Example. Estimation of fundamental matrix using the RANSAC algorithm int point_count = 100; vector<Point2f> points1(point_count); vector<Point2f> points2(point_count); // initialize the points here ... for( int i = 0; i < point_count; i++ ) { points1[i] = ...; points2[i] = ...; } Mat fundamental_matrix = findFundamentalMat(points1, points2, FM_RANSAC, 3, 0.99);
      Returns:
      automatically generated
    • findFundamentalMat

      public static Mat findFundamentalMat​(MatOfPoint2f points1, MatOfPoint2f points2, int method, double ransacReprojThreshold, double confidence, Mat mask)
    • findFundamentalMat

      public static Mat findFundamentalMat​(MatOfPoint2f points1, MatOfPoint2f points2, int method, double ransacReprojThreshold, double confidence)
    • findFundamentalMat

      public static Mat findFundamentalMat​(MatOfPoint2f points1, MatOfPoint2f points2, int method, double ransacReprojThreshold)
    • findFundamentalMat

      public static Mat findFundamentalMat​(MatOfPoint2f points1, MatOfPoint2f points2, int method)
    • findFundamentalMat

      public static Mat findFundamentalMat​(MatOfPoint2f points1, MatOfPoint2f points2)
    • findFundamentalMat

      public static Mat findFundamentalMat​(MatOfPoint2f points1, MatOfPoint2f points2, Mat mask, UsacParams params)
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, Mat cameraMatrix, int method, double prob, double threshold, int maxIters, Mat mask)
      Calculates an essential matrix from the corresponding points in two images.
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix - Camera intrinsic matrix \(\cameramatrix{A}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera intrinsic matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera intrinsic matrix. When passing these coordinates, pass the identity matrix for this parameter.
      method - Method for computing an essential matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      prob - Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
      threshold - Parameter used for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise.
      mask - Output array of N elements, every element of which is set to 0 for outliers and to 1 for the other points. The array is computed only in the RANSAC and LMedS methods.
      maxIters - The maximum number of robust method iterations. This function estimates essential matrix based on the five-point algorithm solver in CITE: Nister03 . CITE: SteweniusCFS is also a related. The epipolar geometry is described by the following equation: \([p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\) where \(E\) is an essential matrix, \(p_1\) and \(p_2\) are corresponding points in the first and the second images, respectively. The result of this function may be passed further to #decomposeEssentialMat or #recoverPose to recover the relative pose between cameras.
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, Mat cameraMatrix, int method, double prob, double threshold, int maxIters)
      Calculates an essential matrix from the corresponding points in two images.
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix - Camera intrinsic matrix \(\cameramatrix{A}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera intrinsic matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera intrinsic matrix. When passing these coordinates, pass the identity matrix for this parameter.
      method - Method for computing an essential matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      prob - Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
      threshold - Parameter used for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. for the other points. The array is computed only in the RANSAC and LMedS methods.
      maxIters - The maximum number of robust method iterations. This function estimates essential matrix based on the five-point algorithm solver in CITE: Nister03 . CITE: SteweniusCFS is also a related. The epipolar geometry is described by the following equation: \([p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\) where \(E\) is an essential matrix, \(p_1\) and \(p_2\) are corresponding points in the first and the second images, respectively. The result of this function may be passed further to #decomposeEssentialMat or #recoverPose to recover the relative pose between cameras.
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, Mat cameraMatrix, int method, double prob, double threshold)
      Calculates an essential matrix from the corresponding points in two images.
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix - Camera intrinsic matrix \(\cameramatrix{A}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera intrinsic matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera intrinsic matrix. When passing these coordinates, pass the identity matrix for this parameter.
      method - Method for computing an essential matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      prob - Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
      threshold - Parameter used for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. for the other points. The array is computed only in the RANSAC and LMedS methods. This function estimates essential matrix based on the five-point algorithm solver in CITE: Nister03 . CITE: SteweniusCFS is also a related. The epipolar geometry is described by the following equation: \([p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\) where \(E\) is an essential matrix, \(p_1\) and \(p_2\) are corresponding points in the first and the second images, respectively. The result of this function may be passed further to #decomposeEssentialMat or #recoverPose to recover the relative pose between cameras.
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, Mat cameraMatrix, int method, double prob)
      Calculates an essential matrix from the corresponding points in two images.
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix - Camera intrinsic matrix \(\cameramatrix{A}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera intrinsic matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera intrinsic matrix. When passing these coordinates, pass the identity matrix for this parameter.
      method - Method for computing an essential matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      prob - Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct. line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. for the other points. The array is computed only in the RANSAC and LMedS methods. This function estimates essential matrix based on the five-point algorithm solver in CITE: Nister03 . CITE: SteweniusCFS is also a related. The epipolar geometry is described by the following equation: \([p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\) where \(E\) is an essential matrix, \(p_1\) and \(p_2\) are corresponding points in the first and the second images, respectively. The result of this function may be passed further to #decomposeEssentialMat or #recoverPose to recover the relative pose between cameras.
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, Mat cameraMatrix, int method)
      Calculates an essential matrix from the corresponding points in two images.
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix - Camera intrinsic matrix \(\cameramatrix{A}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera intrinsic matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera intrinsic matrix. When passing these coordinates, pass the identity matrix for this parameter.
      method - Method for computing an essential matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      confidence (probability) that the estimated matrix is correct. line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. for the other points. The array is computed only in the RANSAC and LMedS methods. This function estimates essential matrix based on the five-point algorithm solver in CITE: Nister03 . CITE: SteweniusCFS is also a related. The epipolar geometry is described by the following equation: \([p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\) where \(E\) is an essential matrix, \(p_1\) and \(p_2\) are corresponding points in the first and the second images, respectively. The result of this function may be passed further to #decomposeEssentialMat or #recoverPose to recover the relative pose between cameras.
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, Mat cameraMatrix)
      Calculates an essential matrix from the corresponding points in two images.
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix - Camera intrinsic matrix \(\cameramatrix{A}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera intrinsic matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera intrinsic matrix. When passing these coordinates, pass the identity matrix for this parameter.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      confidence (probability) that the estimated matrix is correct. line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. for the other points. The array is computed only in the RANSAC and LMedS methods. This function estimates essential matrix based on the five-point algorithm solver in CITE: Nister03 . CITE: SteweniusCFS is also a related. The epipolar geometry is described by the following equation: \([p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\) where \(E\) is an essential matrix, \(p_1\) and \(p_2\) are corresponding points in the first and the second images, respectively. The result of this function may be passed further to #decomposeEssentialMat or #recoverPose to recover the relative pose between cameras.
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, double focal, Point pp, int method, double prob, double threshold, int maxIters, Mat mask)
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      focal - focal length of the camera. Note that this function assumes that points1 and points2 are feature points from cameras with same focal length and principal point.
      pp - principal point of the camera.
      method - Method for computing a fundamental matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      threshold - Parameter used for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise.
      prob - Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
      mask - Output array of N elements, every element of which is set to 0 for outliers and to 1 for the other points. The array is computed only in the RANSAC and LMedS methods.
      maxIters - The maximum number of robust method iterations. This function differs from the one above that it computes camera intrinsic matrix from focal length and principal point: \(A = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\)
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, double focal, Point pp, int method, double prob, double threshold, int maxIters)
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      focal - focal length of the camera. Note that this function assumes that points1 and points2 are feature points from cameras with same focal length and principal point.
      pp - principal point of the camera.
      method - Method for computing a fundamental matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      threshold - Parameter used for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise.
      prob - Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct. for the other points. The array is computed only in the RANSAC and LMedS methods.
      maxIters - The maximum number of robust method iterations. This function differs from the one above that it computes camera intrinsic matrix from focal length and principal point: \(A = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\)
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, double focal, Point pp, int method, double prob, double threshold)
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      focal - focal length of the camera. Note that this function assumes that points1 and points2 are feature points from cameras with same focal length and principal point.
      pp - principal point of the camera.
      method - Method for computing a fundamental matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      threshold - Parameter used for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise.
      prob - Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct. for the other points. The array is computed only in the RANSAC and LMedS methods. This function differs from the one above that it computes camera intrinsic matrix from focal length and principal point: \(A = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\)
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, double focal, Point pp, int method, double prob)
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      focal - focal length of the camera. Note that this function assumes that points1 and points2 are feature points from cameras with same focal length and principal point.
      pp - principal point of the camera.
      method - Method for computing a fundamental matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise.
      prob - Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct. for the other points. The array is computed only in the RANSAC and LMedS methods. This function differs from the one above that it computes camera intrinsic matrix from focal length and principal point: \(A = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\)
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, double focal, Point pp, int method)
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      focal - focal length of the camera. Note that this function assumes that points1 and points2 are feature points from cameras with same focal length and principal point.
      pp - principal point of the camera.
      method - Method for computing a fundamental matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. confidence (probability) that the estimated matrix is correct. for the other points. The array is computed only in the RANSAC and LMedS methods. This function differs from the one above that it computes camera intrinsic matrix from focal length and principal point: \(A = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\)
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, double focal, Point pp)
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      focal - focal length of the camera. Note that this function assumes that points1 and points2 are feature points from cameras with same focal length and principal point.
      pp - principal point of the camera.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. confidence (probability) that the estimated matrix is correct. for the other points. The array is computed only in the RANSAC and LMedS methods. This function differs from the one above that it computes camera intrinsic matrix from focal length and principal point: \(A = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\)
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, double focal)
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      focal - focal length of the camera. Note that this function assumes that points1 and points2 are feature points from cameras with same focal length and principal point.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. confidence (probability) that the estimated matrix is correct. for the other points. The array is computed only in the RANSAC and LMedS methods. This function differs from the one above that it computes camera intrinsic matrix from focal length and principal point: \(A = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\)
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2)
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 . are feature points from cameras with same focal length and principal point.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. confidence (probability) that the estimated matrix is correct. for the other points. The array is computed only in the RANSAC and LMedS methods. This function differs from the one above that it computes camera intrinsic matrix from focal length and principal point: \(A = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\)
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, int method, double prob, double threshold, Mat mask)
      Calculates an essential matrix from the corresponding points in two images from potentially two different cameras.
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix1 - Camera matrix \(K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera matrix. When passing these coordinates, pass the identity matrix for this parameter.
      cameraMatrix2 - Camera matrix \(K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera matrix. When passing these coordinates, pass the identity matrix for this parameter.
      distCoeffs1 - Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
      distCoeffs2 - Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
      method - Method for computing an essential matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      prob - Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
      threshold - Parameter used for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise.
      mask - Output array of N elements, every element of which is set to 0 for outliers and to 1 for the other points. The array is computed only in the RANSAC and LMedS methods. This function estimates essential matrix based on the five-point algorithm solver in CITE: Nister03 . CITE: SteweniusCFS is also a related. The epipolar geometry is described by the following equation: \([p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\) where \(E\) is an essential matrix, \(p_1\) and \(p_2\) are corresponding points in the first and the second images, respectively. The result of this function may be passed further to #decomposeEssentialMat or #recoverPose to recover the relative pose between cameras.
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, int method, double prob, double threshold)
      Calculates an essential matrix from the corresponding points in two images from potentially two different cameras.
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix1 - Camera matrix \(K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera matrix. When passing these coordinates, pass the identity matrix for this parameter.
      cameraMatrix2 - Camera matrix \(K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera matrix. When passing these coordinates, pass the identity matrix for this parameter.
      distCoeffs1 - Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
      distCoeffs2 - Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
      method - Method for computing an essential matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      prob - Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
      threshold - Parameter used for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. for the other points. The array is computed only in the RANSAC and LMedS methods. This function estimates essential matrix based on the five-point algorithm solver in CITE: Nister03 . CITE: SteweniusCFS is also a related. The epipolar geometry is described by the following equation: \([p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\) where \(E\) is an essential matrix, \(p_1\) and \(p_2\) are corresponding points in the first and the second images, respectively. The result of this function may be passed further to #decomposeEssentialMat or #recoverPose to recover the relative pose between cameras.
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, int method, double prob)
      Calculates an essential matrix from the corresponding points in two images from potentially two different cameras.
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix1 - Camera matrix \(K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera matrix. When passing these coordinates, pass the identity matrix for this parameter.
      cameraMatrix2 - Camera matrix \(K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera matrix. When passing these coordinates, pass the identity matrix for this parameter.
      distCoeffs1 - Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
      distCoeffs2 - Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
      method - Method for computing an essential matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      prob - Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct. line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. for the other points. The array is computed only in the RANSAC and LMedS methods. This function estimates essential matrix based on the five-point algorithm solver in CITE: Nister03 . CITE: SteweniusCFS is also a related. The epipolar geometry is described by the following equation: \([p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\) where \(E\) is an essential matrix, \(p_1\) and \(p_2\) are corresponding points in the first and the second images, respectively. The result of this function may be passed further to #decomposeEssentialMat or #recoverPose to recover the relative pose between cameras.
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, int method)
      Calculates an essential matrix from the corresponding points in two images from potentially two different cameras.
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix1 - Camera matrix \(K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera matrix. When passing these coordinates, pass the identity matrix for this parameter.
      cameraMatrix2 - Camera matrix \(K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera matrix. When passing these coordinates, pass the identity matrix for this parameter.
      distCoeffs1 - Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
      distCoeffs2 - Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
      method - Method for computing an essential matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      confidence (probability) that the estimated matrix is correct. line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. for the other points. The array is computed only in the RANSAC and LMedS methods. This function estimates essential matrix based on the five-point algorithm solver in CITE: Nister03 . CITE: SteweniusCFS is also a related. The epipolar geometry is described by the following equation: \([p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\) where \(E\) is an essential matrix, \(p_1\) and \(p_2\) are corresponding points in the first and the second images, respectively. The result of this function may be passed further to #decomposeEssentialMat or #recoverPose to recover the relative pose between cameras.
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2)
      Calculates an essential matrix from the corresponding points in two images from potentially two different cameras.
      Parameters:
      points1 - Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix1 - Camera matrix \(K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera matrix. When passing these coordinates, pass the identity matrix for this parameter.
      cameraMatrix2 - Camera matrix \(K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera matrix. If this assumption does not hold for your use case, use #undistortPoints with P = cv::NoArray() for both cameras to transform image points to normalized image coordinates, which are valid for the identity camera matrix. When passing these coordinates, pass the identity matrix for this parameter.
      distCoeffs1 - Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
      distCoeffs2 - Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      confidence (probability) that the estimated matrix is correct. line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. for the other points. The array is computed only in the RANSAC and LMedS methods. This function estimates essential matrix based on the five-point algorithm solver in CITE: Nister03 . CITE: SteweniusCFS is also a related. The epipolar geometry is described by the following equation: \([p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\) where \(E\) is an essential matrix, \(p_1\) and \(p_2\) are corresponding points in the first and the second images, respectively. The result of this function may be passed further to #decomposeEssentialMat or #recoverPose to recover the relative pose between cameras.
      Returns:
      automatically generated
    • findEssentialMat

      public static Mat findEssentialMat​(Mat points1, Mat points2, Mat cameraMatrix1, Mat cameraMatrix2, Mat dist_coeff1, Mat dist_coeff2, Mat mask, UsacParams params)
    • decomposeEssentialMat

      public static void decomposeEssentialMat​(Mat E, Mat R1, Mat R2, Mat t)
      Decompose an essential matrix to possible rotations and translation.
      Parameters:
      E - The input essential matrix.
      R1 - One possible rotation matrix.
      R2 - Another possible rotation matrix.
      t - One possible translation. This function decomposes the essential matrix E using svd decomposition CITE: HartleyZ00. In general, four possible poses exist for the decomposition of E. They are \([R_1, t]\), \([R_1, -t]\), \([R_2, t]\), \([R_2, -t]\). If E gives the epipolar constraint \([p_2; 1]^T A^{-T} E A^{-1} [p_1; 1] = 0\) between the image points \(p_1\) in the first image and \(p_2\) in second image, then any of the tuples \([R_1, t]\), \([R_1, -t]\), \([R_2, t]\), \([R_2, -t]\) is a change of basis from the first camera's coordinate system to the second camera's coordinate system. However, by decomposing E, one can only get the direction of the translation. For this reason, the translation t is returned with unit length.
    • recoverPose

      public static int recoverPose​(Mat points1, Mat points2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Mat E, Mat R, Mat t, int method, double prob, double threshold, Mat mask)
      Recovers the relative camera rotation and the translation from corresponding points in two images from two different cameras, using cheirality check. Returns the number of inliers that pass the check.
      Parameters:
      points1 - Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix1 - Input/output camera matrix for the first camera, the same as in REF: calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
      distCoeffs1 - Input/output vector of distortion coefficients, the same as in REF: calibrateCamera.
      cameraMatrix2 - Input/output camera matrix for the first camera, the same as in REF: calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
      distCoeffs2 - Input/output vector of distortion coefficients, the same as in REF: calibrateCamera.
      E - The output essential matrix.
      R - Output rotation matrix. Together with the translation vector, this matrix makes up a tuple that performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Note that, in general, t can not be used for this tuple, see the parameter described below.
      t - Output translation vector. This vector is obtained by REF: decomposeEssentialMat and therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit length.
      method - Method for computing an essential matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      prob - Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
      threshold - Parameter used for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise.
      mask - Input/output mask for inliers in points1 and points2. If it is not empty, then it marks inliers in points1 and points2 for then given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the cheirality check. This function decomposes an essential matrix using REF: decomposeEssentialMat and then verifies possible pose hypotheses by doing cheirality check. The cheirality check means that the triangulated 3D points should have positive depth. Some details can be found in CITE: Nister03. This function can be used to process the output E and mask from REF: findEssentialMat. In this scenario, points1 and points2 are the same input for findEssentialMat.: // Example. Estimation of fundamental matrix using the RANSAC algorithm int point_count = 100; vector<Point2f> points1(point_count); vector<Point2f> points2(point_count); // initialize the points here ... for( int i = 0; i < point_count; i++ ) { points1[i] = ...; points2[i] = ...; } // Input: camera calibration of both cameras, for example using intrinsic chessboard calibration. Mat cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2; // Output: Essential matrix, relative rotation and relative translation. Mat E, R, t, mask; recoverPose(points1, points2, cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2, E, R, t, mask);
      Returns:
      automatically generated
    • recoverPose

      public static int recoverPose​(Mat points1, Mat points2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Mat E, Mat R, Mat t, int method, double prob, double threshold)
      Recovers the relative camera rotation and the translation from corresponding points in two images from two different cameras, using cheirality check. Returns the number of inliers that pass the check.
      Parameters:
      points1 - Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix1 - Input/output camera matrix for the first camera, the same as in REF: calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
      distCoeffs1 - Input/output vector of distortion coefficients, the same as in REF: calibrateCamera.
      cameraMatrix2 - Input/output camera matrix for the first camera, the same as in REF: calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
      distCoeffs2 - Input/output vector of distortion coefficients, the same as in REF: calibrateCamera.
      E - The output essential matrix.
      R - Output rotation matrix. Together with the translation vector, this matrix makes up a tuple that performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Note that, in general, t can not be used for this tuple, see the parameter described below.
      t - Output translation vector. This vector is obtained by REF: decomposeEssentialMat and therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit length.
      method - Method for computing an essential matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      prob - Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
      threshold - Parameter used for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. inliers in points1 and points2 for then given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the cheirality check. This function decomposes an essential matrix using REF: decomposeEssentialMat and then verifies possible pose hypotheses by doing cheirality check. The cheirality check means that the triangulated 3D points should have positive depth. Some details can be found in CITE: Nister03. This function can be used to process the output E and mask from REF: findEssentialMat. In this scenario, points1 and points2 are the same input for findEssentialMat.: // Example. Estimation of fundamental matrix using the RANSAC algorithm int point_count = 100; vector<Point2f> points1(point_count); vector<Point2f> points2(point_count); // initialize the points here ... for( int i = 0; i < point_count; i++ ) { points1[i] = ...; points2[i] = ...; } // Input: camera calibration of both cameras, for example using intrinsic chessboard calibration. Mat cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2; // Output: Essential matrix, relative rotation and relative translation. Mat E, R, t, mask; recoverPose(points1, points2, cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2, E, R, t, mask);
      Returns:
      automatically generated
    • recoverPose

      public static int recoverPose​(Mat points1, Mat points2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Mat E, Mat R, Mat t, int method, double prob)
      Recovers the relative camera rotation and the translation from corresponding points in two images from two different cameras, using cheirality check. Returns the number of inliers that pass the check.
      Parameters:
      points1 - Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix1 - Input/output camera matrix for the first camera, the same as in REF: calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
      distCoeffs1 - Input/output vector of distortion coefficients, the same as in REF: calibrateCamera.
      cameraMatrix2 - Input/output camera matrix for the first camera, the same as in REF: calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
      distCoeffs2 - Input/output vector of distortion coefficients, the same as in REF: calibrateCamera.
      E - The output essential matrix.
      R - Output rotation matrix. Together with the translation vector, this matrix makes up a tuple that performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Note that, in general, t can not be used for this tuple, see the parameter described below.
      t - Output translation vector. This vector is obtained by REF: decomposeEssentialMat and therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit length.
      method - Method for computing an essential matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      prob - Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct. line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. inliers in points1 and points2 for then given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the cheirality check. This function decomposes an essential matrix using REF: decomposeEssentialMat and then verifies possible pose hypotheses by doing cheirality check. The cheirality check means that the triangulated 3D points should have positive depth. Some details can be found in CITE: Nister03. This function can be used to process the output E and mask from REF: findEssentialMat. In this scenario, points1 and points2 are the same input for findEssentialMat.: // Example. Estimation of fundamental matrix using the RANSAC algorithm int point_count = 100; vector<Point2f> points1(point_count); vector<Point2f> points2(point_count); // initialize the points here ... for( int i = 0; i < point_count; i++ ) { points1[i] = ...; points2[i] = ...; } // Input: camera calibration of both cameras, for example using intrinsic chessboard calibration. Mat cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2; // Output: Essential matrix, relative rotation and relative translation. Mat E, R, t, mask; recoverPose(points1, points2, cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2, E, R, t, mask);
      Returns:
      automatically generated
    • recoverPose

      public static int recoverPose​(Mat points1, Mat points2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Mat E, Mat R, Mat t, int method)
      Recovers the relative camera rotation and the translation from corresponding points in two images from two different cameras, using cheirality check. Returns the number of inliers that pass the check.
      Parameters:
      points1 - Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix1 - Input/output camera matrix for the first camera, the same as in REF: calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
      distCoeffs1 - Input/output vector of distortion coefficients, the same as in REF: calibrateCamera.
      cameraMatrix2 - Input/output camera matrix for the first camera, the same as in REF: calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
      distCoeffs2 - Input/output vector of distortion coefficients, the same as in REF: calibrateCamera.
      E - The output essential matrix.
      R - Output rotation matrix. Together with the translation vector, this matrix makes up a tuple that performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Note that, in general, t can not be used for this tuple, see the parameter described below.
      t - Output translation vector. This vector is obtained by REF: decomposeEssentialMat and therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit length.
      method - Method for computing an essential matrix.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      confidence (probability) that the estimated matrix is correct. line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. inliers in points1 and points2 for then given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the cheirality check. This function decomposes an essential matrix using REF: decomposeEssentialMat and then verifies possible pose hypotheses by doing cheirality check. The cheirality check means that the triangulated 3D points should have positive depth. Some details can be found in CITE: Nister03. This function can be used to process the output E and mask from REF: findEssentialMat. In this scenario, points1 and points2 are the same input for findEssentialMat.: // Example. Estimation of fundamental matrix using the RANSAC algorithm int point_count = 100; vector<Point2f> points1(point_count); vector<Point2f> points2(point_count); // initialize the points here ... for( int i = 0; i < point_count; i++ ) { points1[i] = ...; points2[i] = ...; } // Input: camera calibration of both cameras, for example using intrinsic chessboard calibration. Mat cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2; // Output: Essential matrix, relative rotation and relative translation. Mat E, R, t, mask; recoverPose(points1, points2, cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2, E, R, t, mask);
      Returns:
      automatically generated
    • recoverPose

      public static int recoverPose​(Mat points1, Mat points2, Mat cameraMatrix1, Mat distCoeffs1, Mat cameraMatrix2, Mat distCoeffs2, Mat E, Mat R, Mat t)
      Recovers the relative camera rotation and the translation from corresponding points in two images from two different cameras, using cheirality check. Returns the number of inliers that pass the check.
      Parameters:
      points1 - Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix1 - Input/output camera matrix for the first camera, the same as in REF: calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
      distCoeffs1 - Input/output vector of distortion coefficients, the same as in REF: calibrateCamera.
      cameraMatrix2 - Input/output camera matrix for the first camera, the same as in REF: calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
      distCoeffs2 - Input/output vector of distortion coefficients, the same as in REF: calibrateCamera.
      E - The output essential matrix.
      R - Output rotation matrix. Together with the translation vector, this matrix makes up a tuple that performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Note that, in general, t can not be used for this tuple, see the parameter described below.
      t - Output translation vector. This vector is obtained by REF: decomposeEssentialMat and therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit length.
      • REF: RANSAC for the RANSAC algorithm.
      • REF: LMEDS for the LMedS algorithm.
      confidence (probability) that the estimated matrix is correct. line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. inliers in points1 and points2 for then given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the cheirality check. This function decomposes an essential matrix using REF: decomposeEssentialMat and then verifies possible pose hypotheses by doing cheirality check. The cheirality check means that the triangulated 3D points should have positive depth. Some details can be found in CITE: Nister03. This function can be used to process the output E and mask from REF: findEssentialMat. In this scenario, points1 and points2 are the same input for findEssentialMat.: // Example. Estimation of fundamental matrix using the RANSAC algorithm int point_count = 100; vector<Point2f> points1(point_count); vector<Point2f> points2(point_count); // initialize the points here ... for( int i = 0; i < point_count; i++ ) { points1[i] = ...; points2[i] = ...; } // Input: camera calibration of both cameras, for example using intrinsic chessboard calibration. Mat cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2; // Output: Essential matrix, relative rotation and relative translation. Mat E, R, t, mask; recoverPose(points1, points2, cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2, E, R, t, mask);
      Returns:
      automatically generated
    • recoverPose

      public static int recoverPose​(Mat E, Mat points1, Mat points2, Mat cameraMatrix, Mat R, Mat t, Mat mask)
      Recovers the relative camera rotation and the translation from an estimated essential matrix and the corresponding points in two images, using chirality check. Returns the number of inliers that pass the check.
      Parameters:
      E - The input essential matrix.
      points1 - Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix - Camera intrinsic matrix \(\cameramatrix{A}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera intrinsic matrix.
      R - Output rotation matrix. Together with the translation vector, this matrix makes up a tuple that performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Note that, in general, t can not be used for this tuple, see the parameter described below.
      t - Output translation vector. This vector is obtained by REF: decomposeEssentialMat and therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit length.
      mask - Input/output mask for inliers in points1 and points2. If it is not empty, then it marks inliers in points1 and points2 for the given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the chirality check. This function decomposes an essential matrix using REF: decomposeEssentialMat and then verifies possible pose hypotheses by doing chirality check. The chirality check means that the triangulated 3D points should have positive depth. Some details can be found in CITE: Nister03. This function can be used to process the output E and mask from REF: findEssentialMat. In this scenario, points1 and points2 are the same input for #findEssentialMat : // Example. Estimation of fundamental matrix using the RANSAC algorithm int point_count = 100; vector<Point2f> points1(point_count); vector<Point2f> points2(point_count); // initialize the points here ... for( int i = 0; i < point_count; i++ ) { points1[i] = ...; points2[i] = ...; } // cametra matrix with both focal lengths = 1, and principal point = (0, 0) Mat cameraMatrix = Mat::eye(3, 3, CV_64F); Mat E, R, t, mask; E = findEssentialMat(points1, points2, cameraMatrix, RANSAC, 0.999, 1.0, mask); recoverPose(E, points1, points2, cameraMatrix, R, t, mask);
      Returns:
      automatically generated
    • recoverPose

      public static int recoverPose​(Mat E, Mat points1, Mat points2, Mat cameraMatrix, Mat R, Mat t)
      Recovers the relative camera rotation and the translation from an estimated essential matrix and the corresponding points in two images, using chirality check. Returns the number of inliers that pass the check.
      Parameters:
      E - The input essential matrix.
      points1 - Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      cameraMatrix - Camera intrinsic matrix \(\cameramatrix{A}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera intrinsic matrix.
      R - Output rotation matrix. Together with the translation vector, this matrix makes up a tuple that performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Note that, in general, t can not be used for this tuple, see the parameter described below.
      t - Output translation vector. This vector is obtained by REF: decomposeEssentialMat and therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit length. inliers in points1 and points2 for the given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the chirality check. This function decomposes an essential matrix using REF: decomposeEssentialMat and then verifies possible pose hypotheses by doing chirality check. The chirality check means that the triangulated 3D points should have positive depth. Some details can be found in CITE: Nister03. This function can be used to process the output E and mask from REF: findEssentialMat. In this scenario, points1 and points2 are the same input for #findEssentialMat : // Example. Estimation of fundamental matrix using the RANSAC algorithm int point_count = 100; vector<Point2f> points1(point_count); vector<Point2f> points2(point_count); // initialize the points here ... for( int i = 0; i < point_count; i++ ) { points1[i] = ...; points2[i] = ...; } // cametra matrix with both focal lengths = 1, and principal point = (0, 0) Mat cameraMatrix = Mat::eye(3, 3, CV_64F); Mat E, R, t, mask; E = findEssentialMat(points1, points2, cameraMatrix, RANSAC, 0.999, 1.0, mask); recoverPose(E, points1, points2, cameraMatrix, R, t, mask);
      Returns:
      automatically generated
    • recoverPose

      public static int recoverPose​(Mat E, Mat points1, Mat points2, Mat R, Mat t, double focal, Point pp, Mat mask)
      Parameters:
      E - The input essential matrix.
      points1 - Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      R - Output rotation matrix. Together with the translation vector, this matrix makes up a tuple that performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Note that, in general, t can not be used for this tuple, see the parameter description below.
      t - Output translation vector. This vector is obtained by REF: decomposeEssentialMat and therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit length.
      focal - Focal length of the camera. Note that this function assumes that points1 and points2 are feature points from cameras with same focal length and principal point.
      pp - principal point of the camera.
      mask - Input/output mask for inliers in points1 and points2. If it is not empty, then it marks inliers in points1 and points2 for the given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the chirality check. This function differs from the one above that it computes camera intrinsic matrix from focal length and principal point: \(A = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\)
      Returns:
      automatically generated
    • recoverPose

      public static int recoverPose​(Mat E, Mat points1, Mat points2, Mat R, Mat t, double focal, Point pp)
      Parameters:
      E - The input essential matrix.
      points1 - Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      R - Output rotation matrix. Together with the translation vector, this matrix makes up a tuple that performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Note that, in general, t can not be used for this tuple, see the parameter description below.
      t - Output translation vector. This vector is obtained by REF: decomposeEssentialMat and therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit length.
      focal - Focal length of the camera. Note that this function assumes that points1 and points2 are feature points from cameras with same focal length and principal point.
      pp - principal point of the camera. inliers in points1 and points2 for the given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the chirality check. This function differs from the one above that it computes camera intrinsic matrix from focal length and principal point: \(A = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\)
      Returns:
      automatically generated
    • recoverPose

      public static int recoverPose​(Mat E, Mat points1, Mat points2, Mat R, Mat t, double focal)
      Parameters:
      E - The input essential matrix.
      points1 - Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      R - Output rotation matrix. Together with the translation vector, this matrix makes up a tuple that performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Note that, in general, t can not be used for this tuple, see the parameter description below.
      t - Output translation vector. This vector is obtained by REF: decomposeEssentialMat and therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit length.
      focal - Focal length of the camera. Note that this function assumes that points1 and points2 are feature points from cameras with same focal length and principal point. inliers in points1 and points2 for the given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the chirality check. This function differs from the one above that it computes camera intrinsic matrix from focal length and principal point: \(A = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\)
      Returns:
      automatically generated
    • recoverPose

      public static int recoverPose​(Mat E, Mat points1, Mat points2, Mat R, Mat t)
      Parameters:
      E - The input essential matrix.
      points1 - Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1 .
      R - Output rotation matrix. Together with the translation vector, this matrix makes up a tuple that performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Note that, in general, t can not be used for this tuple, see the parameter description below.
      t - Output translation vector. This vector is obtained by REF: decomposeEssentialMat and therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit length. are feature points from cameras with same focal length and principal point. inliers in points1 and points2 for the given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the chirality check. This function differs from the one above that it computes camera intrinsic matrix from focal length and principal point: \(A = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\)
      Returns:
      automatically generated
    • recoverPose

      public static int recoverPose​(Mat E, Mat points1, Mat points2, Mat cameraMatrix, Mat R, Mat t, double distanceThresh, Mat mask, Mat triangulatedPoints)
      Parameters:
      E - The input essential matrix.
      points1 - Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1.
      cameraMatrix - Camera intrinsic matrix \(\cameramatrix{A}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera intrinsic matrix.
      R - Output rotation matrix. Together with the translation vector, this matrix makes up a tuple that performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Note that, in general, t can not be used for this tuple, see the parameter description below.
      t - Output translation vector. This vector is obtained by REF: decomposeEssentialMat and therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit length.
      distanceThresh - threshold distance which is used to filter out far away points (i.e. infinite points).
      mask - Input/output mask for inliers in points1 and points2. If it is not empty, then it marks inliers in points1 and points2 for the given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the chirality check.
      triangulatedPoints - 3D points which were reconstructed by triangulation. This function differs from the one above that it outputs the triangulated 3D point that are used for the chirality check.
      Returns:
      automatically generated
    • recoverPose

      public static int recoverPose​(Mat E, Mat points1, Mat points2, Mat cameraMatrix, Mat R, Mat t, double distanceThresh, Mat mask)
      Parameters:
      E - The input essential matrix.
      points1 - Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1.
      cameraMatrix - Camera intrinsic matrix \(\cameramatrix{A}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera intrinsic matrix.
      R - Output rotation matrix. Together with the translation vector, this matrix makes up a tuple that performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Note that, in general, t can not be used for this tuple, see the parameter description below.
      t - Output translation vector. This vector is obtained by REF: decomposeEssentialMat and therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit length.
      distanceThresh - threshold distance which is used to filter out far away points (i.e. infinite points).
      mask - Input/output mask for inliers in points1 and points2. If it is not empty, then it marks inliers in points1 and points2 for the given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the chirality check. This function differs from the one above that it outputs the triangulated 3D point that are used for the chirality check.
      Returns:
      automatically generated
    • recoverPose

      public static int recoverPose​(Mat E, Mat points1, Mat points2, Mat cameraMatrix, Mat R, Mat t, double distanceThresh)
      Parameters:
      E - The input essential matrix.
      points1 - Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
      points2 - Array of the second image points of the same size and format as points1.
      cameraMatrix - Camera intrinsic matrix \(\cameramatrix{A}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera intrinsic matrix.
      R - Output rotation matrix. Together with the translation vector, this matrix makes up a tuple that performs a change of basis from the first camera's coordinate system to the second camera's coordinate system. Note that, in general, t can not be used for this tuple, see the parameter description below.
      t - Output translation vector. This vector is obtained by REF: decomposeEssentialMat and therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit length.
      distanceThresh - threshold distance which is used to filter out far away points (i.e. infinite points). inliers in points1 and points2 for the given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the chirality check. This function differs from the one above that it outputs the triangulated 3D point that are used for the chirality check.
      Returns:
      automatically generated
    • computeCorrespondEpilines

      public static void computeCorrespondEpilines​(Mat points, int whichImage, Mat F, Mat lines)
      For points in an image of a stereo pair, computes the corresponding epilines in the other image.
      Parameters:
      points - Input points. \(N \times 1\) or \(1 \times N\) matrix of type CV_32FC2 or vector<Point2f> .
      whichImage - Index of the image (1 or 2) that contains the points .
      F - Fundamental matrix that can be estimated using #findFundamentalMat or #stereoRectify .
      lines - Output vector of the epipolar lines corresponding to the points in the other image. Each line \(ax + by + c=0\) is encoded by 3 numbers \((a, b, c)\) . For every point in one of the two images of a stereo pair, the function finds the equation of the corresponding epipolar line in the other image. From the fundamental matrix definition (see #findFundamentalMat ), line \(l^{(2)}_i\) in the second image for the point \(p^{(1)}_i\) in the first image (when whichImage=1 ) is computed as: \(l^{(2)}_i = F p^{(1)}_i\) And vice versa, when whichImage=2, \(l^{(1)}_i\) is computed from \(p^{(2)}_i\) as: \(l^{(1)}_i = F^T p^{(2)}_i\) Line coefficients are defined up to a scale. They are normalized so that \(a_i^2+b_i^2=1\) .
    • triangulatePoints

      public static void triangulatePoints​(Mat projMatr1, Mat projMatr2, Mat projPoints1, Mat projPoints2, Mat points4D)
      This function reconstructs 3-dimensional points (in homogeneous coordinates) by using their observations with a stereo camera.
      Parameters:
      projMatr1 - 3x4 projection matrix of the first camera, i.e. this matrix projects 3D points given in the world's coordinate system into the first image.
      projMatr2 - 3x4 projection matrix of the second camera, i.e. this matrix projects 3D points given in the world's coordinate system into the second image.
      projPoints1 - 2xN array of feature points in the first image. In the case of the c++ version, it can be also a vector of feature points or two-channel matrix of size 1xN or Nx1.
      projPoints2 - 2xN array of corresponding points in the second image. In the case of the c++ version, it can be also a vector of feature points or two-channel matrix of size 1xN or Nx1.
      points4D - 4xN array of reconstructed points in homogeneous coordinates. These points are returned in the world's coordinate system. Note: Keep in mind that all input data should be of float type in order for this function to work. Note: If the projection matrices from REF: stereoRectify are used, then the returned points are represented in the first camera's rectified coordinate system. SEE: reprojectImageTo3D
    • correctMatches

      public static void correctMatches​(Mat F, Mat points1, Mat points2, Mat newPoints1, Mat newPoints2)
      Refines coordinates of corresponding points.
      Parameters:
      F - 3x3 fundamental matrix.
      points1 - 1xN array containing the first set of points.
      points2 - 1xN array containing the second set of points.
      newPoints1 - The optimized points1.
      newPoints2 - The optimized points2. The function implements the Optimal Triangulation Method (see Multiple View Geometry CITE: HartleyZ00 for details). For each given point correspondence points1[i] <-> points2[i], and a fundamental matrix F, it computes the corrected correspondences newPoints1[i] <-> newPoints2[i] that minimize the geometric error \(d(points1[i], newPoints1[i])^2 + d(points2[i],newPoints2[i])^2\) (where \(d(a,b)\) is the geometric distance between points \(a\) and \(b\) ) subject to the epipolar constraint \(newPoints2^T \cdot F \cdot newPoints1 = 0\) .
    • filterSpeckles

      public static void filterSpeckles​(Mat img, double newVal, int maxSpeckleSize, double maxDiff, Mat buf)
      Filters off small noise blobs (speckles) in the disparity map
      Parameters:
      img - The input 16-bit signed disparity image
      newVal - The disparity value used to paint-off the speckles
      maxSpeckleSize - The maximum speckle size to consider it a speckle. Larger blobs are not affected by the algorithm
      maxDiff - Maximum difference between neighbor disparity pixels to put them into the same blob. Note that since StereoBM, StereoSGBM and may be other algorithms return a fixed-point disparity map, where disparity values are multiplied by 16, this scale factor should be taken into account when specifying this parameter value.
      buf - The optional temporary buffer to avoid memory allocation within the function.
    • filterSpeckles

      public static void filterSpeckles​(Mat img, double newVal, int maxSpeckleSize, double maxDiff)
      Filters off small noise blobs (speckles) in the disparity map
      Parameters:
      img - The input 16-bit signed disparity image
      newVal - The disparity value used to paint-off the speckles
      maxSpeckleSize - The maximum speckle size to consider it a speckle. Larger blobs are not affected by the algorithm
      maxDiff - Maximum difference between neighbor disparity pixels to put them into the same blob. Note that since StereoBM, StereoSGBM and may be other algorithms return a fixed-point disparity map, where disparity values are multiplied by 16, this scale factor should be taken into account when specifying this parameter value.
    • getValidDisparityROI

      public static Rect getValidDisparityROI​(Rect roi1, Rect roi2, int minDisparity, int numberOfDisparities, int blockSize)
    • validateDisparity

      public static void validateDisparity​(Mat disparity, Mat cost, int minDisparity, int numberOfDisparities, int disp12MaxDisp)
    • validateDisparity

      public static void validateDisparity​(Mat disparity, Mat cost, int minDisparity, int numberOfDisparities)
    • reprojectImageTo3D

      public static void reprojectImageTo3D​(Mat disparity, Mat _3dImage, Mat Q, boolean handleMissingValues, int ddepth)
      Reprojects a disparity image to 3D space.
      Parameters:
      disparity - Input single-channel 8-bit unsigned, 16-bit signed, 32-bit signed or 32-bit floating-point disparity image. The values of 8-bit / 16-bit signed formats are assumed to have no fractional bits. If the disparity is 16-bit signed format, as computed by REF: StereoBM or REF: StereoSGBM and maybe other algorithms, it should be divided by 16 (and scaled to float) before being used here.
      _3dImage - Output 3-channel floating-point image of the same size as disparity. Each element of _3dImage(x,y) contains 3D coordinates of the point (x,y) computed from the disparity map. If one uses Q obtained by REF: stereoRectify, then the returned points are represented in the first camera's rectified coordinate system.
      Q - \(4 \times 4\) perspective transformation matrix that can be obtained with REF: stereoRectify.
      handleMissingValues - Indicates, whether the function should handle missing values (i.e. points where the disparity was not computed). If handleMissingValues=true, then pixels with the minimal disparity that corresponds to the outliers (see StereoMatcher::compute ) are transformed to 3D points with a very large Z value (currently set to 10000).
      ddepth - The optional output array depth. If it is -1, the output image will have CV_32F depth. ddepth can also be set to CV_16S, CV_32S or CV_32F. The function transforms a single-channel disparity map to a 3-channel image representing a 3D surface. That is, for each pixel (x,y) and the corresponding disparity d=disparity(x,y) , it computes: \(\begin{bmatrix} X \\ Y \\ Z \\ W \end{bmatrix} = Q \begin{bmatrix} x \\ y \\ \texttt{disparity} (x,y) \\ z \end{bmatrix}.\) SEE: To reproject a sparse set of points {(x,y,d),...} to 3D space, use perspectiveTransform.
    • reprojectImageTo3D

      public static void reprojectImageTo3D​(Mat disparity, Mat _3dImage, Mat Q, boolean handleMissingValues)
      Reprojects a disparity image to 3D space.
      Parameters:
      disparity - Input single-channel 8-bit unsigned, 16-bit signed, 32-bit signed or 32-bit floating-point disparity image. The values of 8-bit / 16-bit signed formats are assumed to have no fractional bits. If the disparity is 16-bit signed format, as computed by REF: StereoBM or REF: StereoSGBM and maybe other algorithms, it should be divided by 16 (and scaled to float) before being used here.
      _3dImage - Output 3-channel floating-point image of the same size as disparity. Each element of _3dImage(x,y) contains 3D coordinates of the point (x,y) computed from the disparity map. If one uses Q obtained by REF: stereoRectify, then the returned points are represented in the first camera's rectified coordinate system.
      Q - \(4 \times 4\) perspective transformation matrix that can be obtained with REF: stereoRectify.
      handleMissingValues - Indicates, whether the function should handle missing values (i.e. points where the disparity was not computed). If handleMissingValues=true, then pixels with the minimal disparity that corresponds to the outliers (see StereoMatcher::compute ) are transformed to 3D points with a very large Z value (currently set to 10000). depth. ddepth can also be set to CV_16S, CV_32S or CV_32F. The function transforms a single-channel disparity map to a 3-channel image representing a 3D surface. That is, for each pixel (x,y) and the corresponding disparity d=disparity(x,y) , it computes: \(\begin{bmatrix} X \\ Y \\ Z \\ W \end{bmatrix} = Q \begin{bmatrix} x \\ y \\ \texttt{disparity} (x,y) \\ z \end{bmatrix}.\) SEE: To reproject a sparse set of points {(x,y,d),...} to 3D space, use perspectiveTransform.
    • reprojectImageTo3D

      public static void reprojectImageTo3D​(Mat disparity, Mat _3dImage, Mat Q)
      Reprojects a disparity image to 3D space.
      Parameters:
      disparity - Input single-channel 8-bit unsigned, 16-bit signed, 32-bit signed or 32-bit floating-point disparity image. The values of 8-bit / 16-bit signed formats are assumed to have no fractional bits. If the disparity is 16-bit signed format, as computed by REF: StereoBM or REF: StereoSGBM and maybe other algorithms, it should be divided by 16 (and scaled to float) before being used here.
      _3dImage - Output 3-channel floating-point image of the same size as disparity. Each element of _3dImage(x,y) contains 3D coordinates of the point (x,y) computed from the disparity map. If one uses Q obtained by REF: stereoRectify, then the returned points are represented in the first camera's rectified coordinate system.
      Q - \(4 \times 4\) perspective transformation matrix that can be obtained with REF: stereoRectify. points where the disparity was not computed). If handleMissingValues=true, then pixels with the minimal disparity that corresponds to the outliers (see StereoMatcher::compute ) are transformed to 3D points with a very large Z value (currently set to 10000). depth. ddepth can also be set to CV_16S, CV_32S or CV_32F. The function transforms a single-channel disparity map to a 3-channel image representing a 3D surface. That is, for each pixel (x,y) and the corresponding disparity d=disparity(x,y) , it computes: \(\begin{bmatrix} X \\ Y \\ Z \\ W \end{bmatrix} = Q \begin{bmatrix} x \\ y \\ \texttt{disparity} (x,y) \\ z \end{bmatrix}.\) SEE: To reproject a sparse set of points {(x,y,d),...} to 3D space, use perspectiveTransform.
    • sampsonDistance

      public static double sampsonDistance​(Mat pt1, Mat pt2, Mat F)
      Calculates the Sampson Distance between two points. The function cv::sampsonDistance calculates and returns the first order approximation of the geometric error as: \( sd( \texttt{pt1} , \texttt{pt2} )= \frac{(\texttt{pt2}^t \cdot \texttt{F} \cdot \texttt{pt1})^2} {((\texttt{F} \cdot \texttt{pt1})(0))^2 + ((\texttt{F} \cdot \texttt{pt1})(1))^2 + ((\texttt{F}^t \cdot \texttt{pt2})(0))^2 + ((\texttt{F}^t \cdot \texttt{pt2})(1))^2} \) The fundamental matrix may be calculated using the #findFundamentalMat function. See CITE: HartleyZ00 11.4.3 for details.
      Parameters:
      pt1 - first homogeneous 2d point
      pt2 - second homogeneous 2d point
      F - fundamental matrix
      Returns:
      The computed Sampson distance.
    • estimateAffine3D

      public static int estimateAffine3D​(Mat src, Mat dst, Mat out, Mat inliers, double ransacThreshold, double confidence)
      Computes an optimal affine transformation between two 3D point sets. It computes \( \begin{bmatrix} x\\ y\\ z\\ \end{bmatrix} = \begin{bmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\\ \end{bmatrix} \begin{bmatrix} X\\ Y\\ Z\\ \end{bmatrix} + \begin{bmatrix} b_1\\ b_2\\ b_3\\ \end{bmatrix} \)
      Parameters:
      src - First input 3D point set containing \((X,Y,Z)\).
      dst - Second input 3D point set containing \((x,y,z)\).
      out - Output 3D affine transformation matrix \(3 \times 4\) of the form \( \begin{bmatrix} a_{11} & a_{12} & a_{13} & b_1\\ a_{21} & a_{22} & a_{23} & b_2\\ a_{31} & a_{32} & a_{33} & b_3\\ \end{bmatrix} \)
      inliers - Output vector indicating which points are inliers (1-inlier, 0-outlier).
      ransacThreshold - Maximum reprojection error in the RANSAC algorithm to consider a point as an inlier.
      confidence - Confidence level, between 0 and 1, for the estimated transformation. Anything between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation. The function estimates an optimal 3D affine transformation between two 3D point sets using the RANSAC algorithm.
      Returns:
      automatically generated
    • estimateAffine3D

      public static int estimateAffine3D​(Mat src, Mat dst, Mat out, Mat inliers, double ransacThreshold)
      Computes an optimal affine transformation between two 3D point sets. It computes \( \begin{bmatrix} x\\ y\\ z\\ \end{bmatrix} = \begin{bmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\\ \end{bmatrix} \begin{bmatrix} X\\ Y\\ Z\\ \end{bmatrix} + \begin{bmatrix} b_1\\ b_2\\ b_3\\ \end{bmatrix} \)
      Parameters:
      src - First input 3D point set containing \((X,Y,Z)\).
      dst - Second input 3D point set containing \((x,y,z)\).
      out - Output 3D affine transformation matrix \(3 \times 4\) of the form \( \begin{bmatrix} a_{11} & a_{12} & a_{13} & b_1\\ a_{21} & a_{22} & a_{23} & b_2\\ a_{31} & a_{32} & a_{33} & b_3\\ \end{bmatrix} \)
      inliers - Output vector indicating which points are inliers (1-inlier, 0-outlier).
      ransacThreshold - Maximum reprojection error in the RANSAC algorithm to consider a point as an inlier. between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation. The function estimates an optimal 3D affine transformation between two 3D point sets using the RANSAC algorithm.
      Returns:
      automatically generated
    • estimateAffine3D

      public static int estimateAffine3D​(Mat src, Mat dst, Mat out, Mat inliers)
      Computes an optimal affine transformation between two 3D point sets. It computes \( \begin{bmatrix} x\\ y\\ z\\ \end{bmatrix} = \begin{bmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\\ \end{bmatrix} \begin{bmatrix} X\\ Y\\ Z\\ \end{bmatrix} + \begin{bmatrix} b_1\\ b_2\\ b_3\\ \end{bmatrix} \)
      Parameters:
      src - First input 3D point set containing \((X,Y,Z)\).
      dst - Second input 3D point set containing \((x,y,z)\).
      out - Output 3D affine transformation matrix \(3 \times 4\) of the form \( \begin{bmatrix} a_{11} & a_{12} & a_{13} & b_1\\ a_{21} & a_{22} & a_{23} & b_2\\ a_{31} & a_{32} & a_{33} & b_3\\ \end{bmatrix} \)
      inliers - Output vector indicating which points are inliers (1-inlier, 0-outlier). an inlier. between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation. The function estimates an optimal 3D affine transformation between two 3D point sets using the RANSAC algorithm.
      Returns:
      automatically generated
    • estimateAffine3D

      public static Mat estimateAffine3D​(Mat src, Mat dst, double[] scale, boolean force_rotation)
      Computes an optimal affine transformation between two 3D point sets. It computes \(R,s,t\) minimizing \(\sum{i} dst_i - c \cdot R \cdot src_i \) where \(R\) is a 3x3 rotation matrix, \(t\) is a 3x1 translation vector and \(s\) is a scalar size value. This is an implementation of the algorithm by Umeyama \cite umeyama1991least . The estimated affine transform has a homogeneous scale which is a subclass of affine transformations with 7 degrees of freedom. The paired point sets need to comprise at least 3 points each.
      Parameters:
      src - First input 3D point set.
      dst - Second input 3D point set.
      scale - If null is passed, the scale parameter c will be assumed to be 1.0. Else the pointed-to variable will be set to the optimal scale.
      force_rotation - If true, the returned rotation will never be a reflection. This might be unwanted, e.g. when optimizing a transform between a right- and a left-handed coordinate system.
      Returns:
      3D affine transformation matrix \(3 \times 4\) of the form \(T = \begin{bmatrix} R & t\\ \end{bmatrix} \)
    • estimateAffine3D

      public static Mat estimateAffine3D​(Mat src, Mat dst, double[] scale)
      Computes an optimal affine transformation between two 3D point sets. It computes \(R,s,t\) minimizing \(\sum{i} dst_i - c \cdot R \cdot src_i \) where \(R\) is a 3x3 rotation matrix, \(t\) is a 3x1 translation vector and \(s\) is a scalar size value. This is an implementation of the algorithm by Umeyama \cite umeyama1991least . The estimated affine transform has a homogeneous scale which is a subclass of affine transformations with 7 degrees of freedom. The paired point sets need to comprise at least 3 points each.
      Parameters:
      src - First input 3D point set.
      dst - Second input 3D point set.
      scale - If null is passed, the scale parameter c will be assumed to be 1.0. Else the pointed-to variable will be set to the optimal scale. This might be unwanted, e.g. when optimizing a transform between a right- and a left-handed coordinate system.
      Returns:
      3D affine transformation matrix \(3 \times 4\) of the form \(T = \begin{bmatrix} R & t\\ \end{bmatrix} \)
    • estimateAffine3D

      public static Mat estimateAffine3D​(Mat src, Mat dst)
      Computes an optimal affine transformation between two 3D point sets. It computes \(R,s,t\) minimizing \(\sum{i} dst_i - c \cdot R \cdot src_i \) where \(R\) is a 3x3 rotation matrix, \(t\) is a 3x1 translation vector and \(s\) is a scalar size value. This is an implementation of the algorithm by Umeyama \cite umeyama1991least . The estimated affine transform has a homogeneous scale which is a subclass of affine transformations with 7 degrees of freedom. The paired point sets need to comprise at least 3 points each.
      Parameters:
      src - First input 3D point set.
      dst - Second input 3D point set. Else the pointed-to variable will be set to the optimal scale. This might be unwanted, e.g. when optimizing a transform between a right- and a left-handed coordinate system.
      Returns:
      3D affine transformation matrix \(3 \times 4\) of the form \(T = \begin{bmatrix} R & t\\ \end{bmatrix} \)
    • estimateTranslation3D

      public static int estimateTranslation3D​(Mat src, Mat dst, Mat out, Mat inliers, double ransacThreshold, double confidence)
      Computes an optimal translation between two 3D point sets. It computes \( \begin{bmatrix} x\\ y\\ z\\ \end{bmatrix} = \begin{bmatrix} X\\ Y\\ Z\\ \end{bmatrix} + \begin{bmatrix} b_1\\ b_2\\ b_3\\ \end{bmatrix} \)
      Parameters:
      src - First input 3D point set containing \((X,Y,Z)\).
      dst - Second input 3D point set containing \((x,y,z)\).
      out - Output 3D translation vector \(3 \times 1\) of the form \( \begin{bmatrix} b_1 \\ b_2 \\ b_3 \\ \end{bmatrix} \)
      inliers - Output vector indicating which points are inliers (1-inlier, 0-outlier).
      ransacThreshold - Maximum reprojection error in the RANSAC algorithm to consider a point as an inlier.
      confidence - Confidence level, between 0 and 1, for the estimated transformation. Anything between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation. The function estimates an optimal 3D translation between two 3D point sets using the RANSAC algorithm.
      Returns:
      automatically generated
    • estimateTranslation3D

      public static int estimateTranslation3D​(Mat src, Mat dst, Mat out, Mat inliers, double ransacThreshold)
      Computes an optimal translation between two 3D point sets. It computes \( \begin{bmatrix} x\\ y\\ z\\ \end{bmatrix} = \begin{bmatrix} X\\ Y\\ Z\\ \end{bmatrix} + \begin{bmatrix} b_1\\ b_2\\ b_3\\ \end{bmatrix} \)
      Parameters:
      src - First input 3D point set containing \((X,Y,Z)\).
      dst - Second input 3D point set containing \((x,y,z)\).
      out - Output 3D translation vector \(3 \times 1\) of the form \( \begin{bmatrix} b_1 \\ b_2 \\ b_3 \\ \end{bmatrix} \)
      inliers - Output vector indicating which points are inliers (1-inlier, 0-outlier).
      ransacThreshold - Maximum reprojection error in the RANSAC algorithm to consider a point as an inlier. between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation. The function estimates an optimal 3D translation between two 3D point sets using the RANSAC algorithm.
      Returns:
      automatically generated
    • estimateTranslation3D

      public static int estimateTranslation3D​(Mat src, Mat dst, Mat out, Mat inliers)
      Computes an optimal translation between two 3D point sets. It computes \( \begin{bmatrix} x\\ y\\ z\\ \end{bmatrix} = \begin{bmatrix} X\\ Y\\ Z\\ \end{bmatrix} + \begin{bmatrix} b_1\\ b_2\\ b_3\\ \end{bmatrix} \)
      Parameters:
      src - First input 3D point set containing \((X,Y,Z)\).
      dst - Second input 3D point set containing \((x,y,z)\).
      out - Output 3D translation vector \(3 \times 1\) of the form \( \begin{bmatrix} b_1 \\ b_2 \\ b_3 \\ \end{bmatrix} \)
      inliers - Output vector indicating which points are inliers (1-inlier, 0-outlier). an inlier. between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation. The function estimates an optimal 3D translation between two 3D point sets using the RANSAC algorithm.
      Returns:
      automatically generated
    • estimateAffine2D

      public static Mat estimateAffine2D​(Mat from, Mat to, Mat inliers, int method, double ransacReprojThreshold, long maxIters, double confidence, long refineIters)
      Computes an optimal affine transformation between two 2D point sets. It computes \( \begin{bmatrix} x\\ y\\ \end{bmatrix} = \begin{bmatrix} a_{11} & a_{12}\\ a_{21} & a_{22}\\ \end{bmatrix} \begin{bmatrix} X\\ Y\\ \end{bmatrix} + \begin{bmatrix} b_1\\ b_2\\ \end{bmatrix} \)
      Parameters:
      from - First input 2D point set containing \((X,Y)\).
      to - Second input 2D point set containing \((x,y)\).
      inliers - Output vector indicating which points are inliers (1-inlier, 0-outlier).
      method - Robust method used to compute transformation. The following methods are possible:
      • REF: RANSAC - RANSAC-based robust method
      • REF: LMEDS - Least-Median robust method RANSAC is the default method.
      ransacReprojThreshold - Maximum reprojection error in the RANSAC algorithm to consider a point as an inlier. Applies only to RANSAC.
      maxIters - The maximum number of robust method iterations.
      confidence - Confidence level, between 0 and 1, for the estimated transformation. Anything between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
      refineIters - Maximum number of iterations of refining algorithm (Levenberg-Marquardt). Passing 0 will disable refining, so the output matrix will be output of robust method.
      Returns:
      Output 2D affine transformation matrix \(2 \times 3\) or empty matrix if transformation could not be estimated. The returned matrix has the following form: \( \begin{bmatrix} a_{11} & a_{12} & b_1\\ a_{21} & a_{22} & b_2\\ \end{bmatrix} \) The function estimates an optimal 2D affine transformation between two 2D point sets using the selected robust algorithm. The computed transformation is then refined further (using only inliers) with the Levenberg-Marquardt method to reduce the re-projection error even more. Note: The RANSAC method can handle practically any ratio of outliers but needs a threshold to distinguish inliers from outliers. The method LMeDS does not need any threshold but it works correctly only when there are more than 50% of inliers. SEE: estimateAffinePartial2D, getAffineTransform
    • estimateAffine2D

      public static Mat estimateAffine2D​(Mat from, Mat to, Mat inliers, int method, double ransacReprojThreshold, long maxIters, double confidence)
      Computes an optimal affine transformation between two 2D point sets. It computes \( \begin{bmatrix} x\\ y\\ \end{bmatrix} = \begin{bmatrix} a_{11} & a_{12}\\ a_{21} & a_{22}\\ \end{bmatrix} \begin{bmatrix} X\\ Y\\ \end{bmatrix} + \begin{bmatrix} b_1\\ b_2\\ \end{bmatrix} \)
      Parameters:
      from - First input 2D point set containing \((X,Y)\).
      to - Second input 2D point set containing \((x,y)\).
      inliers - Output vector indicating which points are inliers (1-inlier, 0-outlier).
      method - Robust method used to compute transformation. The following methods are possible:
      • REF: RANSAC - RANSAC-based robust method
      • REF: LMEDS - Least-Median robust method RANSAC is the default method.
      ransacReprojThreshold - Maximum reprojection error in the RANSAC algorithm to consider a point as an inlier. Applies only to RANSAC.
      maxIters - The maximum number of robust method iterations.
      confidence - Confidence level, between 0 and 1, for the estimated transformation. Anything between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation. Passing 0 will disable refining, so the output matrix will be output of robust method.
      Returns:
      Output 2D affine transformation matrix \(2 \times 3\) or empty matrix if transformation could not be estimated. The returned matrix has the following form: \( \begin{bmatrix} a_{11} & a_{12} & b_1\\ a_{21} & a_{22} & b_2\\ \end{bmatrix} \) The function estimates an optimal 2D affine transformation between two 2D point sets using the selected robust algorithm. The computed transformation is then refined further (using only inliers) with the Levenberg-Marquardt method to reduce the re-projection error even more. Note: The RANSAC method can handle practically any ratio of outliers but needs a threshold to distinguish inliers from outliers. The method LMeDS does not need any threshold but it works correctly only when there are more than 50% of inliers. SEE: estimateAffinePartial2D, getAffineTransform
    • estimateAffine2D

      public static Mat estimateAffine2D​(Mat from, Mat to, Mat inliers, int method, double ransacReprojThreshold, long maxIters)
      Computes an optimal affine transformation between two 2D point sets. It computes \( \begin{bmatrix} x\\ y\\ \end{bmatrix} = \begin{bmatrix} a_{11} & a_{12}\\ a_{21} & a_{22}\\ \end{bmatrix} \begin{bmatrix} X\\ Y\\ \end{bmatrix} + \begin{bmatrix} b_1\\ b_2\\ \end{bmatrix} \)
      Parameters:
      from - First input 2D point set containing \((X,Y)\).
      to - Second input 2D point set containing \((x,y)\).
      inliers - Output vector indicating which points are inliers (1-inlier, 0-outlier).
      method - Robust method used to compute transformation. The following methods are possible:
      • REF: RANSAC - RANSAC-based robust method
      • REF: LMEDS - Least-Median robust method RANSAC is the default method.
      ransacReprojThreshold - Maximum reprojection error in the RANSAC algorithm to consider a point as an inlier. Applies only to RANSAC.
      maxIters - The maximum number of robust method iterations. between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation. Passing 0 will disable refining, so the output matrix will be output of robust method.
      Returns:
      Output 2D affine transformation matrix \(2 \times 3\) or empty matrix if transformation could not be estimated. The returned matrix has the following form: \( \begin{bmatrix} a_{11} & a_{12} & b_1\\ a_{21} & a_{22} & b_2\\ \end{bmatrix} \) The function estimates an optimal 2D affine transformation between two 2D point sets using the selected robust algorithm. The computed transformation is then refined further (using only inliers) with the Levenberg-Marquardt method to reduce the re-projection error even more. Note: The RANSAC method can handle practically any ratio of outliers but needs a threshold to distinguish inliers from outliers. The method LMeDS does not need any threshold but it works correctly only when there are more than 50% of inliers. SEE: estimateAffinePartial2D, getAffineTransform
    • estimateAffine2D

      public static Mat estimateAffine2D​(Mat from, Mat to, Mat inliers, int method, double ransacReprojThreshold)
      Computes an optimal affine transformation between two 2D point sets. It computes \( \begin{bmatrix} x\\ y\\ \end{bmatrix} = \begin{bmatrix} a_{11} & a_{12}\\ a_{21} & a_{22}\\ \end{bmatrix} \begin{bmatrix} X\\ Y\\ \end{bmatrix} + \begin{bmatrix} b_1\\ b_2\\ \end{bmatrix} \)
      Parameters:
      from - First input 2D point set containing \((X,Y)\).
      to - Second input 2D point set containing \((x,y)\).
      inliers - Output vector indicating which points are inliers (1-inlier, 0-outlier).
      method - Robust method used to compute transformation. The following methods are possible:
      • REF: RANSAC - RANSAC-based robust method
      • REF: LMEDS - Least-Median robust method RANSAC is the default method.
      ransacReprojThreshold - Maximum reprojection error in the RANSAC algorithm to consider a point as an inlier. Applies only to RANSAC. between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation. Passing 0 will disable refining, so the output matrix will be output of robust method.
      Returns:
      Output 2D affine transformation matrix \(2 \times 3\) or empty matrix if transformation could not be estimated. The returned matrix has the following form: \( \begin{bmatrix} a_{11} & a_{12} & b_1\\ a_{21} & a_{22} & b_2\\ \end{bmatrix} \) The function estimates an optimal 2D affine transformation between two 2D point sets using the selected robust algorithm. The computed transformation is then refined further (using only inliers) with the Levenberg-Marquardt method to reduce the re-projection error even more. Note: The RANSAC method can handle practically any ratio of outliers but needs a threshold to distinguish inliers from outliers. The method LMeDS does not need any threshold but it works correctly only when there are more than 50% of inliers. SEE: estimateAffinePartial2D, getAffineTransform
    • estimateAffine2D

      public static Mat estimateAffine2D​(Mat from, Mat to, Mat inliers, int method)
      Computes an optimal affine transformation between two 2D point sets. It computes \( \begin{bmatrix} x\\ y\\ \end{bmatrix} = \begin{bmatrix} a_{11} & a_{12}\\ a_{21} & a_{22}\\ \end{bmatrix} \begin{bmatrix} X\\ Y\\ \end{bmatrix} + \begin{bmatrix} b_1\\ b_2\\ \end{bmatrix} \)
      Parameters:
      from - First input 2D point set containing \((X,Y)\).
      to - Second input 2D point set containing \((x,y)\).
      inliers - Output vector indicating which points are inliers (1-inlier, 0-outlier).
      method - Robust method used to compute transformation. The following methods are possible:
      • REF: RANSAC - RANSAC-based robust method
      • REF: LMEDS - Least-Median robust method RANSAC is the default method.
      a point as an inlier. Applies only to RANSAC. between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation. Passing 0 will disable refining, so the output matrix will be output of robust method.
      Returns:
      Output 2D affine transformation matrix \(2 \times 3\) or empty matrix if transformation could not be estimated. The returned matrix has the following form: \( \begin{bmatrix} a_{11} & a_{12} & b_1\\ a_{21} & a_{22} & b_2\\ \end{bmatrix} \) The function estimates an optimal 2D affine transformation between two 2D point sets using the selected robust algorithm. The computed transformation is then refined further (using only inliers) with the Levenberg-Marquardt method to reduce the re-projection error even more. Note: The RANSAC method can handle practically any ratio of outliers but needs a threshold to distinguish inliers from outliers. The method LMeDS does not need any threshold but it works correctly only when there are more than 50% of inliers. SEE: estimateAffinePartial2D, getAffineTransform
    • estimateAffine2D

      public static Mat estimateAffine2D​(Mat from, Mat to, Mat inliers)
      Computes an optimal affine transformation between two 2D point sets. It computes \( \begin{bmatrix} x\\ y\\ \end{bmatrix} = \begin{bmatrix} a_{11} & a_{12}\\ a_{21} & a_{22}\\ \end{bmatrix} \begin{bmatrix} X\\ Y\\ \end{bmatrix} + \begin{bmatrix} b_1\\ b_2\\ \end{bmatrix} \)
      Parameters:
      from - First input 2D point set containing \((X,Y)\).
      to - Second input 2D point set containing \((x,y)\).
      inliers - Output vector indicating which points are inliers (1-inlier, 0-outlier).
      • REF: RANSAC - RANSAC-based robust method
      • REF: LMEDS - Least-Median robust method RANSAC is the default method.
      a point as an inlier. Applies only to RANSAC. between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation. Passing 0 will disable refining, so the output matrix will be output of robust method.
      Returns:
      Output 2D affine transformation matrix \(2 \times 3\) or empty matrix if transformation could not be estimated. The returned matrix has the following form: \( \begin{bmatrix} a_{11} & a_{12} & b_1\\ a_{21} & a_{22} & b_2\\ \end{bmatrix} \) The function estimates an optimal 2D affine transformation between two 2D point sets using the selected robust algorithm. The computed transformation is then refined further (using only inliers) with the Levenberg-Marquardt method to reduce the re-projection error even more. Note: The RANSAC method can handle practically any ratio of outliers but needs a threshold to distinguish inliers from outliers. The method LMeDS does not need any threshold but it works correctly only when there are more than 50% of inliers. SEE: estimateAffinePartial2D, getAffineTransform
    • estimateAffine2D

      public static Mat estimateAffine2D​(Mat from, Mat to)
      Computes an optimal affine transformation between two 2D point sets. It computes \( \begin{bmatrix} x\\ y\\ \end{bmatrix} = \begin{bmatrix} a_{11} & a_{12}\\ a_{21} & a_{22}\\ \end{bmatrix} \begin{bmatrix} X\\ Y\\ \end{bmatrix} + \begin{bmatrix} b_1\\ b_2\\ \end{bmatrix} \)
      Parameters:
      from - First input 2D point set containing \((X,Y)\).
      to - Second input 2D point set containing \((x,y)\).
      • REF: RANSAC - RANSAC-based robust method
      • REF: LMEDS - Least-Median robust method RANSAC is the default method.
      a point as an inlier. Applies only to RANSAC. between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation. Passing 0 will disable refining, so the output matrix will be output of robust method.
      Returns:
      Output 2D affine transformation matrix \(2 \times 3\) or empty matrix if transformation could not be estimated. The returned matrix has the following form: \( \begin{bmatrix} a_{11} & a_{12} & b_1\\ a_{21} & a_{22} & b_2\\ \end{bmatrix} \) The function estimates an optimal 2D affine transformation between two 2D point sets using the selected robust algorithm. The computed transformation is then refined further (using only inliers) with the Levenberg-Marquardt method to reduce the re-projection error even more. Note: The RANSAC method can handle practically any ratio of outliers but needs a threshold to distinguish inliers from outliers. The method LMeDS does not need any threshold but it works correctly only when there are more than 50% of inliers. SEE: estimateAffinePartial2D, getAffineTransform
    • estimateAffine2D

      public static Mat estimateAffine2D​(Mat pts1, Mat pts2, Mat inliers, UsacParams params)
    • estimateAffinePartial2D

      public static Mat estimateAffinePartial2D​(Mat from, Mat to, Mat inliers, int method, double ransacReprojThreshold, long maxIters, double confidence, long refineIters)
      Computes an optimal limited affine transformation with 4 degrees of freedom between two 2D point sets.
      Parameters:
      from - First input 2D point set.
      to - Second input 2D point set.
      inliers - Output vector indicating which points are inliers.
      method - Robust method used to compute transformation. The following methods are possible:
      • REF: RANSAC - RANSAC-based robust method
      • REF: LMEDS - Least-Median robust method RANSAC is the default method.
      ransacReprojThreshold - Maximum reprojection error in the RANSAC algorithm to consider a point as an inlier. Applies only to RANSAC.
      maxIters - The maximum number of robust method iterations.
      confidence - Confidence level, between 0 and 1, for the estimated transformation. Anything between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
      refineIters - Maximum number of iterations of refining algorithm (Levenberg-Marquardt). Passing 0 will disable refining, so the output matrix will be output of robust method.
      Returns:
      Output 2D affine transformation (4 degrees of freedom) matrix \(2 \times 3\) or empty matrix if transformation could not be estimated. The function estimates an optimal 2D affine transformation with 4 degrees of freedom limited to combinations of translation, rotation, and uniform scaling. Uses the selected algorithm for robust estimation. The computed transformation is then refined further (using only inliers) with the Levenberg-Marquardt method to reduce the re-projection error even more. Estimated transformation matrix is: \( \begin{bmatrix} \cos(\theta) \cdot s & -\sin(\theta) \cdot s & t_x \\ \sin(\theta) \cdot s & \cos(\theta) \cdot s & t_y \end{bmatrix} \) Where \( \theta \) is the rotation angle, \( s \) the scaling factor and \( t_x, t_y \) are translations in \( x, y \) axes respectively. Note: The RANSAC method can handle practically any ratio of outliers but need a threshold to distinguish inliers from outliers. The method LMeDS does not need any threshold but it works correctly only when there are more than 50% of inliers. SEE: estimateAffine2D, getAffineTransform
    • estimateAffinePartial2D

      public static Mat estimateAffinePartial2D​(Mat from, Mat to, Mat inliers, int method, double ransacReprojThreshold, long maxIters, double confidence)
      Computes an optimal limited affine transformation with 4 degrees of freedom between tw