vector_to_essential_matrixT_vector_to_essential_matrixVectorToEssentialMatrixVectorToEssentialMatrixvector_to_essential_matrix (算子)

名称

vector_to_essential_matrixT_vector_to_essential_matrixVectorToEssentialMatrixVectorToEssentialMatrixvector_to_essential_matrix — 根据图像点对应关系和已知相机矩阵计算本质矩阵，并重建三维点。

签名

描述

For a stereo configuration with known camera matrices the geometric relation between the two images is defined by the essential matrix. The operator vector_to_essential_matrixvector_to_essential_matrixVectorToEssentialMatrixVectorToEssentialMatrixVectorToEssentialMatrixvector_to_essential_matrix determines the essential matrix EMatrixEMatrixEMatrixEMatrixEMatrixematrix from in general at least six given point correspondences, that fulfill the epipolar constraint:

算子 vector_to_essential_matrixvector_to_essential_matrixVectorToEssentialMatrixVectorToEssentialMatrixVectorToEssentialMatrixvector_to_essential_matrix is designed to deal only with a linear camera model. This is in contrast to the operator vector_to_rel_posevector_to_rel_poseVectorToRelPoseVectorToRelPoseVectorToRelPosevector_to_rel_pose, that encompasses lens distortions too. The internal camera parameters are passed by the arguments CamMat1CamMat1CamMat1CamMat1camMat1cam_mat_1 and CamMat2CamMat2CamMat2CamMat2camMat2cam_mat_2, which are 3x3 upper triangular matrices describing an affine transformation. The relation between the vector (X,Y,1), defining the direction from the camera to the viewed 3D point, and its (projective) 2D image coordinates (col,row,1) is:

The focal length is denoted by f, are scaling factors, s describes a skew factor and indicates the principal point. Mainly, these are the elements known from the camera parameters as used for example in calibrate_camerascalibrate_camerasCalibrateCamerasCalibrateCamerasCalibrateCamerascalibrate_cameras。Alternatively, the elements of the camera matrix can be described in a different way, see e.g. stationary_camera_self_calibrationstationary_camera_self_calibrationStationaryCameraSelfCalibrationStationaryCameraSelfCalibrationStationaryCameraSelfCalibrationstationary_camera_self_calibration。

The point correspondences (Rows1Rows1Rows1Rows1rows1rows_1,Cols1Cols1Cols1Cols1cols1cols_1) and (Rows2Rows2Rows2Rows2rows2rows_2,Cols2Cols2Cols2Cols2cols2cols_2) are typically found by applying the operator match_essential_matrix_ransacmatch_essential_matrix_ransacMatchEssentialMatrixRansacMatchEssentialMatrixRansacMatchEssentialMatrixRansacmatch_essential_matrix_ransac。Multiplying the image coordinates by the inverse of the camera matrices results in the 3D direction vectors, which can then be inserted in the epipolar constraint.

The parameter MethodMethodMethodMethodmethodmethod decides whether the relative orientation between the cameras is of a special type and which algorithm is to be applied for its computation. If MethodMethodMethodMethodmethodmethod is either 'normalized_dlt'"normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt" or 'gold_standard'"gold_standard""gold_standard""gold_standard""gold_standard""gold_standard" the relative orientation is arbitrary. Choosing 'trans_normalized_dlt'"trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt" or 'trans_gold_standard'"trans_gold_standard""trans_gold_standard""trans_gold_standard""trans_gold_standard""trans_gold_standard" means that the relative motion between the cameras is a pure translation. The typical application for this special motion case is the scenario of a single fixed camera looking onto a moving conveyor belt. In this case the minimum required number of corresponding points is just two instead of six in the general case.

The essential matrix is computed by a linear algorithm if 'normalized_dlt'"normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt" or 'trans_normalized_dlt'"trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt" is chosen. With 'gold_standard'"gold_standard""gold_standard""gold_standard""gold_standard""gold_standard" or 'trans_gold_standard'"trans_gold_standard""trans_gold_standard""trans_gold_standard""trans_gold_standard""trans_gold_standard" the algorithm gives a statistically optimal result. Here, 'normalized_dlt'"normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt" and 'gold_standard'"gold_standard""gold_standard""gold_standard""gold_standard""gold_standard" stand for direct-linear-transformation and gold-standard-algorithm respectively. All methods return the coordinates (XXXXxx,YYYYyy,ZZZZzz) of the reconstructed 3D points. The optimal methods also return the covariances of the 3D points in CovXYZCovXYZCovXYZCovXYZcovXYZcov_xyz. Let n be the number of points then the 3x3 covariance matrices are concatenated and stored in a tuple of length 9n. Additionally, the optimal methods return the covariance of the essential matrix CovEMatCovEMatCovEMatCovEMatcovEMatcov_emat。

If an optimal gold-standard-algorithm is chosen the covariances of the image points (CovRR1CovRR1CovRR1CovRR1covRR1cov_rr1, CovRC1CovRC1CovRC1CovRC1covRC1cov_rc1, CovCC1CovCC1CovCC1CovCC1covCC1cov_cc1, CovRR2CovRR2CovRR2CovRR2covRR2cov_rr2, CovRC2CovRC2CovRC2CovRC2covRC2cov_rc2, CovCC2CovCC2CovCC2CovCC2covCC2cov_cc2) can be incorporated in the computation. They can be provided for example by the operator points_foerstnerpoints_foerstnerPointsFoerstnerPointsFoerstnerPointsFoerstnerpoints_foerstner。If the point covariances are unknown, which is the default, empty tuples are input. In this case the optimization algorithm internally assumes uniform and equal covariances for all points.

The value ErrorErrorErrorErrorerrorerror indicates the overall quality of the optimization process and is the root-mean-square Euclidean distance in pixels between the points and their corresponding epipolar lines.

For the operator vector_to_essential_matrixvector_to_essential_matrixVectorToEssentialMatrixVectorToEssentialMatrixVectorToEssentialMatrixvector_to_essential_matrix a special configuration of scene points and cameras exists: if all 3D points lie in a single plane and additionally are all closer to one of the two cameras then the solution in the essential matrix is not unique but twofold. As a consequence both solutions are computed and returned by the operator. This means that all output parameters are of double length and the values of the second solution are simply concatenated behind the values of the first one.

执行信息

• 多线程类型：可重入（与非独占算子并行运行）。
• 多线程作用域：全局（可从任何线程调用）。
• 未采用并行化处理。

参数

可能的前趋

match_essential_matrix_ransacmatch_essential_matrix_ransacMatchEssentialMatrixRansacMatchEssentialMatrixRansacMatchEssentialMatrixRansacmatch_essential_matrix_ransac

可能的后继

essential_to_fundamental_matrixessential_to_fundamental_matrixEssentialToFundamentalMatrixEssentialToFundamentalMatrixEssentialToFundamentalMatrixessential_to_fundamental_matrix

替代

vector_to_rel_posevector_to_rel_poseVectorToRelPoseVectorToRelPoseVectorToRelPosevector_to_rel_pose, vector_to_fundamental_matrixvector_to_fundamental_matrixVectorToFundamentalMatrixVectorToFundamentalMatrixVectorToFundamentalMatrixvector_to_fundamental_matrix

另见

stationary_camera_self_calibrationstationary_camera_self_calibrationStationaryCameraSelfCalibrationStationaryCameraSelfCalibrationStationaryCameraSelfCalibrationstationary_camera_self_calibration

参考文献

Richard Hartley, Andrew Zisserman: “Multiple View Geometry in Computer Vision”; Cambridge University Press, Cambridge; 2003.
J.Chris McGlone (editor): “Manual of Photogrammetry”; American Society for Photogrammetry and Remote Sensing ; 2004.

模块

三维计量

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