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org.opencv.calib3d

Class Calib3d

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
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
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
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
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
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
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
This function differs from the one above that it computes camera matrix from focal length and principal point: \(K = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\)
Returns:
automatically generated
This function differs from the one above that it computes camera matrix from focal length and principal point: \(K = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\)
Returns:
automatically generated
This function differs from the one above that it computes camera matrix from focal length and principal point: \(K = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\)
Returns:
automatically generated
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
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
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
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
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
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
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
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
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
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
Returns:
automatically generated
Returns:
automatically generated
The function estimates the object pose given a set of object points, their corresponding image projections, as well as the camera matrix and the distortion coefficients, see the figure below (more precisely, the X-axis of the camera frame is pointing to the right, the Y-axis downward and the Z-axis forward). ![](pnp.jpg) Points expressed in the world frame \( \bf{X}_w \) are projected into the image plane \( \left[ u, v \right] \) using the perspective projection model \( \Pi \) and the camera intrinsic parameters matrix \( \bf{A} \): \( \begin{align*} \begin{bmatrix} u \\ v \\ 1 \end{bmatrix} &= \bf{A} \hspace{0.1em} \Pi \hspace{0.2em} ^{c}\bf{T}_w \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \\ \begin{bmatrix} u \\ v \\ 1 \end{bmatrix} &= \begin{bmatrix} f_x & 0 & c_x \\ 0 & f_y & c_y \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \end{align*} \) The estimated pose is thus the rotation (rvec) and the translation (tvec) vectors that allow transforming a 3D point expressed in the world frame into the camera frame: \( \begin{align*} \begin{bmatrix} X_c \\ Y_c \\ Z_c \\ 1 \end{bmatrix} &= \hspace{0.2em} ^{c}\bf{T}_w \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \\ \begin{bmatrix} X_c \\ Y_c \\ Z_c \\ 1 \end{bmatrix} &= \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \end{align*} \) Note:
Returns:
automatically generated
The function estimates the object pose given a set of object points, their corresponding image projections, as well as the camera matrix and the distortion coefficients, see the figure below (more precisely, the X-axis of the camera frame is pointing to the right, the Y-axis downward and the Z-axis forward). ![](pnp.jpg) Points expressed in the world frame \( \bf{X}_w \) are projected into the image plane \( \left[ u, v \right] \) using the perspective projection model \( \Pi \) and the camera intrinsic parameters matrix \( \bf{A} \): \( \begin{align*} \begin{bmatrix} u \\ v \\ 1 \end{bmatrix} &= \bf{A} \hspace{0.1em} \Pi \hspace{0.2em} ^{c}\bf{T}_w \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \\ \begin{bmatrix} u \\ v \\ 1 \end{bmatrix} &= \begin{bmatrix} f_x & 0 & c_x \\ 0 & f_y & c_y \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \end{align*} \) The estimated pose is thus the rotation (rvec) and the translation (tvec) vectors that allow transforming a 3D point expressed in the world frame into the camera frame: \( \begin{align*} \begin{bmatrix} X_c \\ Y_c \\ Z_c \\ 1 \end{bmatrix} &= \hspace{0.2em} ^{c}\bf{T}_w \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \\ \begin{bmatrix} X_c \\ Y_c \\ Z_c \\ 1 \end{bmatrix} &= \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \end{align*} \) Note:
Returns:
automatically generated
The function estimates the object pose given a set of object points, their corresponding image projections, as well as the camera matrix and the distortion coefficients, see the figure below (more precisely, the X-axis of the camera frame is pointing to the right, the Y-axis downward and the Z-axis forward). ![](pnp.jpg) Points expressed in the world frame \( \bf{X}_w \) are projected into the image plane \( \left[ u, v \right] \) using the perspective projection model \( \Pi \) and the camera intrinsic parameters matrix \( \bf{A} \): \( \begin{align*} \begin{bmatrix} u \\ v \\ 1 \end{bmatrix} &= \bf{A} \hspace{0.1em} \Pi \hspace{0.2em} ^{c}\bf{T}_w \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \\ \begin{bmatrix} u \\ v \\ 1 \end{bmatrix} &= \begin{bmatrix} f_x & 0 & c_x \\ 0 & f_y & c_y \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \end{align*} \) The estimated pose is thus the rotation (rvec) and the translation (tvec) vectors that allow transforming a 3D point expressed in the world frame into the camera frame: \( \begin{align*} \begin{bmatrix} X_c \\ Y_c \\ Z_c \\ 1 \end{bmatrix} &= \hspace{0.2em} ^{c}\bf{T}_w \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \\ \begin{bmatrix} X_c \\ Y_c \\ Z_c \\ 1 \end{bmatrix} &= \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \end{align*} \) Note:
Returns:
automatically generated
The function estimates transformation between two cameras making a stereo pair. If you have a stereo camera where the relative position and orientation of two cameras is fixed, and if you computed poses of an object relative to the first camera and to the second camera, (R1, T1) and (R2, T2), respectively (this can be done with solvePnP ), then those poses definitely relate to each other. This means that, given ( \(R_1\),\(T_1\) ), it should be possible to compute ( \(R_2\),\(T_2\) ). You only need to know the position and orientation of the second camera relative to the first camera. This is what the described function does. It computes ( \(R\),\(T\) ) so that: \(R_2=R*R_1\) \(T_2=R*T_1 + T,\) 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: \(F = cameraMatrix2^{-T} E cameraMatrix1^{-1}\) Besides the stereo-related information, the function can also perform a full calibration of each of 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 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 CALIB_SAME_FOCAL_LENGTH and 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
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Generated on 2019-12-20 14:24:32 / OpenCV 4.2.0