ClassesClasses | | Operators

vector_to_rel_poseT_vector_to_rel_poseVectorToRelPoseVectorToRelPose (Operator)

Name

vector_to_rel_poseT_vector_to_rel_poseVectorToRelPoseVectorToRelPose — Compute the relative orientation between two cameras given image point correspondences and known camera parameters and reconstruct 3D space points.

Signature

vector_to_rel_pose( : : Rows1, Cols1, Rows2, Cols2, CovRR1, CovRC1, CovCC1, CovRR2, CovRC2, CovCC2, CamPar1, CamPar2, Method : RelPose, CovRelPose, Error, X, Y, Z, CovXYZ)

Herror T_vector_to_rel_pose(const Htuple Rows1, const Htuple Cols1, const Htuple Rows2, const Htuple Cols2, const Htuple CovRR1, const Htuple CovRC1, const Htuple CovCC1, const Htuple CovRR2, const Htuple CovRC2, const Htuple CovCC2, const Htuple CamPar1, const Htuple CamPar2, const Htuple Method, Htuple* RelPose, Htuple* CovRelPose, Htuple* Error, Htuple* X, Htuple* Y, Htuple* Z, Htuple* CovXYZ)

void VectorToRelPose(const HTuple& Rows1, const HTuple& Cols1, const HTuple& Rows2, const HTuple& Cols2, const HTuple& CovRR1, const HTuple& CovRC1, const HTuple& CovCC1, const HTuple& CovRR2, const HTuple& CovRC2, const HTuple& CovCC2, const HTuple& CamPar1, const HTuple& CamPar2, const HTuple& Method, HTuple* RelPose, HTuple* CovRelPose, HTuple* Error, HTuple* X, HTuple* Y, HTuple* Z, HTuple* CovXYZ)

HPose HCamPar::VectorToRelPose(const HTuple& Rows1, const HTuple& Cols1, const HTuple& Rows2, const HTuple& Cols2, const HTuple& CovRR1, const HTuple& CovRC1, const HTuple& CovCC1, const HTuple& CovRR2, const HTuple& CovRC2, const HTuple& CovCC2, const HCamPar& CamPar2, const HString& Method, HTuple* CovRelPose, HTuple* Error, HTuple* X, HTuple* Y, HTuple* Z, HTuple* CovXYZ) const

HPose HCamPar::VectorToRelPose(const HTuple& Rows1, const HTuple& Cols1, const HTuple& Rows2, const HTuple& Cols2, const HTuple& CovRR1, const HTuple& CovRC1, const HTuple& CovCC1, const HTuple& CovRR2, const HTuple& CovRC2, const HTuple& CovCC2, const HCamPar& CamPar2, const HString& Method, HTuple* CovRelPose, double* Error, HTuple* X, HTuple* Y, HTuple* Z, HTuple* CovXYZ) const

HPose HCamPar::VectorToRelPose(const HTuple& Rows1, const HTuple& Cols1, const HTuple& Rows2, const HTuple& Cols2, const HTuple& CovRR1, const HTuple& CovRC1, const HTuple& CovCC1, const HTuple& CovRR2, const HTuple& CovRC2, const HTuple& CovCC2, const HCamPar& CamPar2, const char* Method, HTuple* CovRelPose, double* Error, HTuple* X, HTuple* Y, HTuple* Z, HTuple* CovXYZ) const

HTuple HPose::VectorToRelPose(const HTuple& Rows1, const HTuple& Cols1, const HTuple& Rows2, const HTuple& Cols2, const HTuple& CovRR1, const HTuple& CovRC1, const HTuple& CovCC1, const HTuple& CovRR2, const HTuple& CovRC2, const HTuple& CovCC2, const HCamPar& CamPar1, const HCamPar& CamPar2, const HString& Method, HTuple* Error, HTuple* X, HTuple* Y, HTuple* Z, HTuple* CovXYZ)

HTuple HPose::VectorToRelPose(const HTuple& Rows1, const HTuple& Cols1, const HTuple& Rows2, const HTuple& Cols2, const HTuple& CovRR1, const HTuple& CovRC1, const HTuple& CovCC1, const HTuple& CovRR2, const HTuple& CovRC2, const HTuple& CovCC2, const HCamPar& CamPar1, const HCamPar& CamPar2, const HString& Method, double* Error, HTuple* X, HTuple* Y, HTuple* Z, HTuple* CovXYZ)

HTuple HPose::VectorToRelPose(const HTuple& Rows1, const HTuple& Cols1, const HTuple& Rows2, const HTuple& Cols2, const HTuple& CovRR1, const HTuple& CovRC1, const HTuple& CovCC1, const HTuple& CovRR2, const HTuple& CovRC2, const HTuple& CovCC2, const HCamPar& CamPar1, const HCamPar& CamPar2, const char* Method, double* Error, HTuple* X, HTuple* Y, HTuple* Z, HTuple* CovXYZ)

static void HOperatorSet.VectorToRelPose(HTuple rows1, HTuple cols1, HTuple rows2, HTuple cols2, HTuple covRR1, HTuple covRC1, HTuple covCC1, HTuple covRR2, HTuple covRC2, HTuple covCC2, HTuple camPar1, HTuple camPar2, HTuple method, out HTuple relPose, out HTuple covRelPose, out HTuple error, out HTuple x, out HTuple y, out HTuple z, out HTuple covXYZ)

HPose HCamPar.VectorToRelPose(HTuple rows1, HTuple cols1, HTuple rows2, HTuple cols2, HTuple covRR1, HTuple covRC1, HTuple covCC1, HTuple covRR2, HTuple covRC2, HTuple covCC2, HCamPar camPar2, string method, out HTuple covRelPose, out HTuple error, out HTuple x, out HTuple y, out HTuple z, out HTuple covXYZ)

HPose HCamPar.VectorToRelPose(HTuple rows1, HTuple cols1, HTuple rows2, HTuple cols2, HTuple covRR1, HTuple covRC1, HTuple covCC1, HTuple covRR2, HTuple covRC2, HTuple covCC2, HCamPar camPar2, string method, out HTuple covRelPose, out double error, out HTuple x, out HTuple y, out HTuple z, out HTuple covXYZ)

HTuple HPose.VectorToRelPose(HTuple rows1, HTuple cols1, HTuple rows2, HTuple cols2, HTuple covRR1, HTuple covRC1, HTuple covCC1, HTuple covRR2, HTuple covRC2, HTuple covCC2, HCamPar camPar1, HCamPar camPar2, string method, out HTuple error, out HTuple x, out HTuple y, out HTuple z, out HTuple covXYZ)

HTuple HPose.VectorToRelPose(HTuple rows1, HTuple cols1, HTuple rows2, HTuple cols2, HTuple covRR1, HTuple covRC1, HTuple covCC1, HTuple covRR2, HTuple covRC2, HTuple covCC2, HCamPar camPar1, HCamPar camPar2, string method, out double error, out HTuple x, out HTuple y, out HTuple z, out HTuple covXYZ)

Description

For a stereo configuration with known camera parameters the geometric relation between the two images is defined by the relative pose. The operator vector_to_rel_posevector_to_rel_poseVectorToRelPoseVectorToRelPoseVectorToRelPose computes the relative pose from in general at least six point correspondences in the image pair. RelPoseRelPoseRelPoseRelPoserelPose indicates the relative pose of camera 1 with respect to camera 2 (see create_posecreate_poseCreatePoseCreatePoseCreatePose for more information about poses and their representations.). This is in accordance with the explicit calibration of a stereo setup using the operator calibrate_camerascalibrate_camerasCalibrateCamerasCalibrateCamerasCalibrateCameras. Now, let R,t be the rotation and translation of the relative pose. Then, the essential matrix E is defined as , where denotes the 3x3 skew-symmetric matrix realising the cross product with the vector t. The pose can be determined from the epipolar constraint:

Note, that the essential matrix is a projective entity and thus is defined up to a scaling factor. From this follows that the translation vector of the relative pose can only be determined up to scale too. In fact, the computed translation vector will always be normalized to unit length. As a consequence, a threedimensional reconstruction of the scene, here in terms of points given by their coordinates (XXXXx,YYYYy,ZZZZz), can be carried out only up to a single global scaling factor. If the absolute 3D coordinates of the reconstruction are to be achieved the unknown scaling factor can be computed from a gauge, which has to be visible in both images. For example, a simple gauge can be given by any known distance between points in the scene.

The operator vector_to_rel_posevector_to_rel_poseVectorToRelPoseVectorToRelPoseVectorToRelPose is designed to deal with a camera model that includes lens distortions. This is in constrast to the operator vector_to_essential_matrixvector_to_essential_matrixVectorToEssentialMatrixVectorToEssentialMatrixVectorToEssentialMatrix, which encompasses only straight line preserving cameras. The camera parameters are passed by the arguments CamPar1CamPar1CamPar1CamPar1camPar1, CamPar2CamPar2CamPar2CamPar2camPar2. The 3D direction vectors and are calculated from the point coordinates (Rows1Rows1Rows1Rows1rows1,Cols1Cols1Cols1Cols1cols1) and (Rows2Rows2Rows2Rows2rows2,Cols2Cols2Cols2Cols2cols2) by inverting the process of projection (see calibrate_camerascalibrate_camerasCalibrateCamerasCalibrateCamerasCalibrateCameras). The point correspondences are typically determined by applying the operator match_rel_pose_ransacmatch_rel_pose_ransacMatchRelPoseRansacMatchRelPoseRansacMatchRelPoseRansac.

The parameter MethodMethodMethodMethodmethod decides whether the relative orientation between the cameras is of a special type and which algorithm is to be applied for its computation. If MethodMethodMethodMethodmethod is either 'normalized_dlt'"normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt" or '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" or '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 relative pose is computed by a linear algorithm if '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" is chosen. With '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" the algorithm gives a statistically optimal result. Here, 'normalized_dlt' and 'gold_standard' stand for direct-linear-transformation and gold-standard-algorithm respectively. All methods return the coordinates (XXXXx,YYYYy,ZZZZz) of the reconstructed 3D points. The optimal methods also return the covariances of the 3D points in CovXYZCovXYZCovXYZCovXYZcovXYZ. 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 6x6 covariance matrix of the pose CovRelPoseCovRelPoseCovRelPoseCovRelPosecovRelPose.

If an optimal gold-standard-algorithm is chosen the covariances of the image points (CovRR1CovRR1CovRR1CovRR1covRR1, CovRC1CovRC1CovRC1CovRC1covRC1, CovCC1CovCC1CovCC1CovCC1covCC1, CovRR2CovRR2CovRR2CovRR2covRR2, CovRC2CovRC2CovRC2CovRC2covRC2, CovCC2CovCC2CovCC2CovCC2covCC2) can be incorporated in the computation. They can be provided for example by the operator points_foerstnerpoints_foerstnerPointsFoerstnerPointsFoerstnerPointsFoerstner. 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 ErrorErrorErrorErrorerror indicates the overall quality of the optimization process and is the root-mean-square euclidian distance in pixels between the points and their corresponding epipolar lines.

For the operator vector_to_rel_posevector_to_rel_poseVectorToRelPoseVectorToRelPoseVectorToRelPose 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 relative pose 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.

Execution Information

Parameters

Rows1Rows1Rows1Rows1rows1 (input_control)  number-array HTupleHTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Input points in image 1 (row coordinate).

Restriction: length(Rows1) >= 6 || length(Rows1) >= 2

Cols1Cols1Cols1Cols1cols1 (input_control)  number-array HTupleHTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Input points in image 1 (column coordinate).

Restriction: length(Cols1) == length(Rows1)

Rows2Rows2Rows2Rows2rows2 (input_control)  number-array HTupleHTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Input points in image 2 (row coordinate).

Restriction: length(Rows2) == length(Rows1)

Cols2Cols2Cols2Cols2cols2 (input_control)  number-array HTupleHTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Input points in image 2 (column coordinate).

Restriction: length(Cols2) == length(Rows1)

CovRR1CovRR1CovRR1CovRR1covRR1 (input_control)  number-array HTupleHTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Row coordinate variance of the points in image 1.

Default value: []

CovRC1CovRC1CovRC1CovRC1covRC1 (input_control)  number-array HTupleHTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Covariance of the points in image 1.

Default value: []

CovCC1CovCC1CovCC1CovCC1covCC1 (input_control)  number-array HTupleHTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Column coordinate variance of the points in image 1.

Default value: []

CovRR2CovRR2CovRR2CovRR2covRR2 (input_control)  number-array HTupleHTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Row coordinate variance of the points in image 2.

Default value: []

CovRC2CovRC2CovRC2CovRC2covRC2 (input_control)  number-array HTupleHTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Covariance of the points in image 2.

Default value: []

CovCC2CovCC2CovCC2CovCC2covCC2 (input_control)  number-array HTupleHTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Column coordinate variance of the points in image 2.

Default value: []

CamPar1CamPar1CamPar1CamPar1camPar1 (input_control)  campar HCamPar, HTupleHTupleHtuple (real / integer / string) (double / int / long / string) (double / Hlong / HString) (double / Hlong / char*)

Camera parameters of the 1st camera.

CamPar2CamPar2CamPar2CamPar2camPar2 (input_control)  campar HCamPar, HTupleHTupleHtuple (real / integer / string) (double / int / long / string) (double / Hlong / HString) (double / Hlong / char*)

Camera parameters of the 2nd camera.

MethodMethodMethodMethodmethod (input_control)  string HTupleHTupleHtuple (string) (string) (HString) (char*)

Algorithm for the computation of the relative pose and for special pose types.

Default value: 'normalized_dlt' "normalized_dlt" "normalized_dlt" "normalized_dlt" "normalized_dlt"

List of values: 'gold_standard'"gold_standard""gold_standard""gold_standard""gold_standard", 'normalized_dlt'"normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt", 'trans_gold_standard'"trans_gold_standard""trans_gold_standard""trans_gold_standard""trans_gold_standard", 'trans_normalized_dlt'"trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt"

RelPoseRelPoseRelPoseRelPoserelPose (output_control)  pose HPose, HTupleHTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Computed relative orientation of the cameras (3D pose).

CovRelPoseCovRelPoseCovRelPoseCovRelPosecovRelPose (output_control)  real-array HTupleHTupleHtuple (real) (double) (double) (double)

6x6 covariance matrix of the relative camera orientation.

ErrorErrorErrorErrorerror (output_control)  real(-array) HTupleHTupleHtuple (real) (double) (double) (double)

Root-Mean-Square of the epipolar distance error.

XXXXx (output_control)  real-array HTupleHTupleHtuple (real) (double) (double) (double)

X coordinates of the reconstructed 3D points.

YYYYy (output_control)  real-array HTupleHTupleHtuple (real) (double) (double) (double)

Y coordinates of the reconstructed 3D points.

ZZZZz (output_control)  real-array HTupleHTupleHtuple (real) (double) (double) (double)

Z coordinates of the reconstructed 3D points.

CovXYZCovXYZCovXYZCovXYZcovXYZ (output_control)  real-array HTupleHTupleHtuple (real) (double) (double) (double)

Covariance matrices of the reconstructed 3D points.

Possible Predecessors

match_rel_pose_ransacmatch_rel_pose_ransacMatchRelPoseRansacMatchRelPoseRansacMatchRelPoseRansac

Possible Successors

gen_binocular_rectification_mapgen_binocular_rectification_mapGenBinocularRectificationMapGenBinocularRectificationMapGenBinocularRectificationMap, rel_pose_to_fundamental_matrixrel_pose_to_fundamental_matrixRelPoseToFundamentalMatrixRelPoseToFundamentalMatrixRelPoseToFundamentalMatrix

Alternatives

vector_to_essential_matrixvector_to_essential_matrixVectorToEssentialMatrixVectorToEssentialMatrixVectorToEssentialMatrix, vector_to_fundamental_matrixvector_to_fundamental_matrixVectorToFundamentalMatrixVectorToFundamentalMatrixVectorToFundamentalMatrix, binocular_calibrationbinocular_calibrationBinocularCalibrationBinocularCalibrationBinocularCalibration

See also

camera_calibrationcamera_calibrationCameraCalibrationCameraCalibrationCameraCalibration

References

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.

Module

3D Metrology


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