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match_essential_matrix_ransacT_match_essential_matrix_ransacMatchEssentialMatrixRansacMatchEssentialMatrixRansac (Operator)

Name

match_essential_matrix_ransacT_match_essential_matrix_ransacMatchEssentialMatrixRansacMatchEssentialMatrixRansac — Compute the essential matrix for a pair of stereo images by automatically finding correspondences between image points.

Signature

match_essential_matrix_ransac(Image1, Image2 : : Rows1, Cols1, Rows2, Cols2, CamMat1, CamMat2, GrayMatchMethod, MaskSize, RowMove, ColMove, RowTolerance, ColTolerance, Rotation, MatchThreshold, EstimationMethod, DistanceThreshold, RandSeed : EMatrix, CovEMat, Error, Points1, Points2)

Herror T_match_essential_matrix_ransac(const Hobject Image1, const Hobject Image2, const Htuple Rows1, const Htuple Cols1, const Htuple Rows2, const Htuple Cols2, const Htuple CamMat1, const Htuple CamMat2, const Htuple GrayMatchMethod, const Htuple MaskSize, const Htuple RowMove, const Htuple ColMove, const Htuple RowTolerance, const Htuple ColTolerance, const Htuple Rotation, const Htuple MatchThreshold, const Htuple EstimationMethod, const Htuple DistanceThreshold, const Htuple RandSeed, Htuple* EMatrix, Htuple* CovEMat, Htuple* Error, Htuple* Points1, Htuple* Points2)

void MatchEssentialMatrixRansac(const HObject& Image1, const HObject& Image2, const HTuple& Rows1, const HTuple& Cols1, const HTuple& Rows2, const HTuple& Cols2, const HTuple& CamMat1, const HTuple& CamMat2, const HTuple& GrayMatchMethod, const HTuple& MaskSize, const HTuple& RowMove, const HTuple& ColMove, const HTuple& RowTolerance, const HTuple& ColTolerance, const HTuple& Rotation, const HTuple& MatchThreshold, const HTuple& EstimationMethod, const HTuple& DistanceThreshold, const HTuple& RandSeed, HTuple* EMatrix, HTuple* CovEMat, HTuple* Error, HTuple* Points1, HTuple* Points2)

HHomMat2D HImage::MatchEssentialMatrixRansac(const HImage& Image2, const HTuple& Rows1, const HTuple& Cols1, const HTuple& Rows2, const HTuple& Cols2, const HHomMat2D& CamMat1, const HHomMat2D& CamMat2, const HString& GrayMatchMethod, Hlong MaskSize, Hlong RowMove, Hlong ColMove, Hlong RowTolerance, Hlong ColTolerance, const HTuple& Rotation, const HTuple& MatchThreshold, const HString& EstimationMethod, const HTuple& DistanceThreshold, Hlong RandSeed, HTuple* CovEMat, HTuple* Error, HTuple* Points1, HTuple* Points2) const

HHomMat2D HImage::MatchEssentialMatrixRansac(const HImage& Image2, const HTuple& Rows1, const HTuple& Cols1, const HTuple& Rows2, const HTuple& Cols2, const HHomMat2D& CamMat1, const HHomMat2D& CamMat2, const HString& GrayMatchMethod, Hlong MaskSize, Hlong RowMove, Hlong ColMove, Hlong RowTolerance, Hlong ColTolerance, double Rotation, Hlong MatchThreshold, const HString& EstimationMethod, double DistanceThreshold, Hlong RandSeed, HTuple* CovEMat, double* Error, HTuple* Points1, HTuple* Points2) const

HHomMat2D HImage::MatchEssentialMatrixRansac(const HImage& Image2, const HTuple& Rows1, const HTuple& Cols1, const HTuple& Rows2, const HTuple& Cols2, const HHomMat2D& CamMat1, const HHomMat2D& CamMat2, const char* GrayMatchMethod, Hlong MaskSize, Hlong RowMove, Hlong ColMove, Hlong RowTolerance, Hlong ColTolerance, double Rotation, Hlong MatchThreshold, const char* EstimationMethod, double DistanceThreshold, Hlong RandSeed, HTuple* CovEMat, double* Error, HTuple* Points1, HTuple* Points2) const

HHomMat2D HHomMat2D::MatchEssentialMatrixRansac(const HImage& Image1, const HImage& Image2, const HTuple& Rows1, const HTuple& Cols1, const HTuple& Rows2, const HTuple& Cols2, const HHomMat2D& CamMat2, const HString& GrayMatchMethod, Hlong MaskSize, Hlong RowMove, Hlong ColMove, Hlong RowTolerance, Hlong ColTolerance, const HTuple& Rotation, const HTuple& MatchThreshold, const HString& EstimationMethod, const HTuple& DistanceThreshold, Hlong RandSeed, HTuple* CovEMat, HTuple* Error, HTuple* Points1, HTuple* Points2) const

HHomMat2D HHomMat2D::MatchEssentialMatrixRansac(const HImage& Image1, const HImage& Image2, const HTuple& Rows1, const HTuple& Cols1, const HTuple& Rows2, const HTuple& Cols2, const HHomMat2D& CamMat2, const HString& GrayMatchMethod, Hlong MaskSize, Hlong RowMove, Hlong ColMove, Hlong RowTolerance, Hlong ColTolerance, double Rotation, Hlong MatchThreshold, const HString& EstimationMethod, double DistanceThreshold, Hlong RandSeed, HTuple* CovEMat, double* Error, HTuple* Points1, HTuple* Points2) const

HHomMat2D HHomMat2D::MatchEssentialMatrixRansac(const HImage& Image1, const HImage& Image2, const HTuple& Rows1, const HTuple& Cols1, const HTuple& Rows2, const HTuple& Cols2, const HHomMat2D& CamMat2, const char* GrayMatchMethod, Hlong MaskSize, Hlong RowMove, Hlong ColMove, Hlong RowTolerance, Hlong ColTolerance, double Rotation, Hlong MatchThreshold, const char* EstimationMethod, double DistanceThreshold, Hlong RandSeed, HTuple* CovEMat, double* Error, HTuple* Points1, HTuple* Points2) const

static void HOperatorSet.MatchEssentialMatrixRansac(HObject image1, HObject image2, HTuple rows1, HTuple cols1, HTuple rows2, HTuple cols2, HTuple camMat1, HTuple camMat2, HTuple grayMatchMethod, HTuple maskSize, HTuple rowMove, HTuple colMove, HTuple rowTolerance, HTuple colTolerance, HTuple rotation, HTuple matchThreshold, HTuple estimationMethod, HTuple distanceThreshold, HTuple randSeed, out HTuple EMatrix, out HTuple covEMat, out HTuple error, out HTuple points1, out HTuple points2)

HHomMat2D HImage.MatchEssentialMatrixRansac(HImage image2, HTuple rows1, HTuple cols1, HTuple rows2, HTuple cols2, HHomMat2D camMat1, HHomMat2D camMat2, string grayMatchMethod, int maskSize, int rowMove, int colMove, int rowTolerance, int colTolerance, HTuple rotation, HTuple matchThreshold, string estimationMethod, HTuple distanceThreshold, int randSeed, out HTuple covEMat, out HTuple error, out HTuple points1, out HTuple points2)

HHomMat2D HImage.MatchEssentialMatrixRansac(HImage image2, HTuple rows1, HTuple cols1, HTuple rows2, HTuple cols2, HHomMat2D camMat1, HHomMat2D camMat2, string grayMatchMethod, int maskSize, int rowMove, int colMove, int rowTolerance, int colTolerance, double rotation, int matchThreshold, string estimationMethod, double distanceThreshold, int randSeed, out HTuple covEMat, out double error, out HTuple points1, out HTuple points2)

HHomMat2D HHomMat2D.MatchEssentialMatrixRansac(HImage image1, HImage image2, HTuple rows1, HTuple cols1, HTuple rows2, HTuple cols2, HHomMat2D camMat2, string grayMatchMethod, int maskSize, int rowMove, int colMove, int rowTolerance, int colTolerance, HTuple rotation, HTuple matchThreshold, string estimationMethod, HTuple distanceThreshold, int randSeed, out HTuple covEMat, out HTuple error, out HTuple points1, out HTuple points2)

HHomMat2D HHomMat2D.MatchEssentialMatrixRansac(HImage image1, HImage image2, HTuple rows1, HTuple cols1, HTuple rows2, HTuple cols2, HHomMat2D camMat2, string grayMatchMethod, int maskSize, int rowMove, int colMove, int rowTolerance, int colTolerance, double rotation, int matchThreshold, string estimationMethod, double distanceThreshold, int randSeed, out HTuple covEMat, out double error, out HTuple points1, out HTuple points2)

Description

Given a set of coordinates of characteristic points (Rows1Rows1Rows1Rows1rows1,Cols1Cols1Cols1Cols1cols1) and (Rows2Rows2Rows2Rows2rows2,Cols2Cols2Cols2Cols2cols2) in the stereo images Image1Image1Image1Image1image1 and Image2Image2Image2Image2image2 along with known internal camera parameters, specified by the camera matrices CamMat1CamMat1CamMat1CamMat1camMat1 and CamMat2CamMat2CamMat2CamMat2camMat2, match_essential_matrix_ransacmatch_essential_matrix_ransacMatchEssentialMatrixRansacMatchEssentialMatrixRansacMatchEssentialMatrixRansac automatically determines the geometry of the stereo setup and finds the correspondences between the characteristic points. The geometry of the stereo setup is represented by the essential matrix EMatrixEMatrixEMatrixEMatrixEMatrix and all corresponding points have to fulfill the epipolar constraint.

The operator match_essential_matrix_ransacmatch_essential_matrix_ransacMatchEssentialMatrixRansacMatchEssentialMatrixRansacMatchEssentialMatrixRansac is designed to deal with a linear camera model. The internal camera parameters are passed by the arguments CamMat1CamMat1CamMat1CamMat1camMat1 and CamMat2CamMat2CamMat2CamMat2camMat2, which are 3x3 upper triangular matrices desribing an affine transformation. The relation between a vector (X,Y,1), representing the direction from the camera to the viewed 3D space point and its (projective) 2D image coordinates (col,row,1) is:

Note the column/row ordering in the point coordinates which has to be compliant with the x/y notation of the camera coordinate system. 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_camerasCalibrateCamerasCalibrateCamerasCalibrateCameras. Alternatively, the elements of the camera matrix can be described in a different way, see e.g. stationary_camera_self_calibrationstationary_camera_self_calibrationStationaryCameraSelfCalibrationStationaryCameraSelfCalibrationStationaryCameraSelfCalibration. Multiplied by the inverse of the camera matrices the direction vectors in 3D space are obtained from the (projective) image coordinates. For known camera matrices the epipolar constraint is given by:

The matching process is based on characteristic points, which can be extracted with point operators like points_foerstnerpoints_foerstnerPointsFoerstnerPointsFoerstnerPointsFoerstner or points_harrispoints_harrisPointsHarrisPointsHarrisPointsHarris. The matching itself is carried out in two steps: first, gray value correlations of mask windows around the input points in the first and the second image are determined and an initial matching between them is generated using the similarity of the windows in both images. Then, the RANSAC algorithm is applied to find the essential matrix that maximizes the number of correspondences under the epipolar constraint.

The size of the mask windows is MaskSizeMaskSizeMaskSizeMaskSizemaskSize x MaskSizeMaskSizeMaskSizeMaskSizemaskSize. Three metrics for the correlation can be selected. If GrayMatchMethodGrayMatchMethodGrayMatchMethodGrayMatchMethodgrayMatchMethod has the value 'ssd'"ssd""ssd""ssd""ssd", the sum of the squared gray value differences is used, 'sad'"sad""sad""sad""sad" means the sum of absolute differences, and 'ncc'"ncc""ncc""ncc""ncc" is the normalized cross correlation. For details please refer to binocular_disparitybinocular_disparityBinocularDisparityBinocularDisparityBinocularDisparity. The metric is minimized ('ssd'"ssd""ssd""ssd""ssd", 'sad'"sad""sad""sad""sad") or maximized ('ncc'"ncc""ncc""ncc""ncc") over all possible point pairs. A thus found matching is only accepted if the value of the metric is below the value of MatchThresholdMatchThresholdMatchThresholdMatchThresholdmatchThreshold ('ssd'"ssd""ssd""ssd""ssd", 'sad'"sad""sad""sad""sad") or above that value ('ncc'"ncc""ncc""ncc""ncc").

To increase the speed of the algorithm, the search area for the matchings can be limited. Only points within a window of points are considered. The offset of the center of the search window in the second image with respect to the position of the current point in the first image is given by RowMoveRowMoveRowMoveRowMoverowMove and ColMoveColMoveColMoveColMovecolMove.

If the second camera is rotated around the optical axis with respect to the first camera the parameter RotationRotationRotationRotationrotation may contain an estimate for the rotation angle or an angle interval in radians. A good guess will increase the quality of the gray value matching. If the actual rotation differs too much from the specified estimate the matching will typically fail. In this case, an angle interval should be specified, and RotationRotationRotationRotationrotation is a tuple with two elements. The larger the given interval the slower the operator is since the RANSAC algorithm is run over all angle increments within the interval.

After the initial matching is completed a randomized search algorithm (RANSAC) is used to determine the essential matrix EMatrixEMatrixEMatrixEMatrixEMatrix. It tries to find the essential matrix that is consistent with a maximum number of correspondences. For a point to be accepted, the distance to its corresponding epipolar line must not exceed the threshold DistanceThresholdDistanceThresholdDistanceThresholdDistanceThresholddistanceThreshold.

The parameter EstimationMethodEstimationMethodEstimationMethodEstimationMethodestimationMethod decides whether the relative orientation between the cameras is of a special type and which algorithm is to be applied for its computation. If EstimationMethodEstimationMethodEstimationMethodEstimationMethodestimationMethod 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 order to get a unique solution in the correspondence problem the minimum required number of corresponding points is six in the general case and three in the special, translational case.

The essential matrix 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, and returns the covariance of the essential matrix CovEMatCovEMatCovEMatCovEMatcovEMat as well. Here, 'normalized_dlt' and 'gold_standard' stand for direct-linear-transformation and gold-standard-algorithm respectively. Note, that in general the found correspondences differ depending on the deployed estimation method.

The value ErrorErrorErrorErrorerror indicates the overall quality of the estimation procedure and is the mean euclidian distance in pixels between the points and their corresponding epipolar lines.

Point pairs consistent with the mentioned constraints are considered to be in correspondences. Points1Points1Points1Points1points1 contains the indices of the matched input points from the first image and Points2Points2Points2Points2points2 contains the indices of the corresponding points in the second image.

For the operator match_essential_matrix_ransacmatch_essential_matrix_ransacMatchEssentialMatrixRansacMatchEssentialMatrixRansacMatchEssentialMatrixRansac 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 the output parameters EMatrixEMatrixEMatrixEMatrixEMatrix, CovEMatCovEMatCovEMatCovEMatcovEMat and ErrorErrorErrorErrorerror are of double length and the values of the second solution are simply concatenated behind the values of the first one.

The parameter RandSeedRandSeedRandSeedRandSeedrandSeed can be used to control the randomized nature of the RANSAC algorithm, and hence to obtain reproducible results. If RandSeedRandSeedRandSeedRandSeedrandSeed is set to a positive number the operator yields the same result on every call with the same parameters because the internally used random number generator is initialized with the RandSeedRandSeedRandSeedRandSeedrandSeed. If RandSeedRandSeedRandSeedRandSeedrandSeed = 0 the random number generator is initialized with the current time. In this case the results may not be reproducible.

Execution Information

Parameters

Image1Image1Image1Image1image1 (input_object)  singlechannelimage objectHImageHImageHobject (byte / uint2)

Input image 1.

Image2Image2Image2Image2image2 (input_object)  singlechannelimage objectHImageHImageHobject (byte / uint2)

Input image 2.

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

Row coordinates of characteristic points in image 1.

Restriction: length(Rows1) >= 6 || length(Rows1) >= 3

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

Column coordinates of characteristic points in image 1.

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

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

Row coordinates of characteristic points in image 2.

Restriction: length(Rows2) >= 6 || length(Rows2) >= 3

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

Column coordinates of characteristic points in image 2.

Restriction: length(Cols2) == length(Rows2)

CamMat1CamMat1CamMat1CamMat1camMat1 (input_control)  hom_mat2d HHomMat2D, HTupleHTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Camera matrix of the 1st camera.

CamMat2CamMat2CamMat2CamMat2camMat2 (input_control)  hom_mat2d HHomMat2D, HTupleHTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Camera matrix of the 2nd camera.

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

Gray value comparison metric.

Default value: 'ssd' "ssd" "ssd" "ssd" "ssd"

List of values: 'ncc'"ncc""ncc""ncc""ncc", 'sad'"sad""sad""sad""sad", 'ssd'"ssd""ssd""ssd""ssd"

MaskSizeMaskSizeMaskSizeMaskSizemaskSize (input_control)  integer HTupleHTupleHtuple (integer) (int / long) (Hlong) (Hlong)

Size of gray value masks.

Default value: 10

Typical range of values: 3 ≤ MaskSize MaskSize MaskSize MaskSize maskSize ≤ 15

Restriction: MaskSize >= 1

RowMoveRowMoveRowMoveRowMoverowMove (input_control)  integer HTupleHTupleHtuple (integer) (int / long) (Hlong) (Hlong)

Average row coordinate shift of corresponding points.

Default value: 0

Typical range of values: 0 ≤ RowMove RowMove RowMove RowMove rowMove ≤ 200

ColMoveColMoveColMoveColMovecolMove (input_control)  integer HTupleHTupleHtuple (integer) (int / long) (Hlong) (Hlong)

Average column coordinate shift of corresponding points.

Default value: 0

Typical range of values: 0 ≤ ColMove ColMove ColMove ColMove colMove ≤ 200

RowToleranceRowToleranceRowToleranceRowTolerancerowTolerance (input_control)  integer HTupleHTupleHtuple (integer) (int / long) (Hlong) (Hlong)

Half height of matching search window.

Default value: 200

Typical range of values: 50 ≤ RowTolerance RowTolerance RowTolerance RowTolerance rowTolerance ≤ 200

Restriction: RowTolerance >= 1

ColToleranceColToleranceColToleranceColTolerancecolTolerance (input_control)  integer HTupleHTupleHtuple (integer) (int / long) (Hlong) (Hlong)

Half width of matching search window.

Default value: 200

Typical range of values: 50 ≤ ColTolerance ColTolerance ColTolerance ColTolerance colTolerance ≤ 200

Restriction: ColTolerance >= 1

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

Estimate of the relative orientation of the right image with respect to the left image.

Default value: 0.0

Suggested values: 0.0, 0.1, -0.1, 0.7854, 1.571, 3.142

MatchThresholdMatchThresholdMatchThresholdMatchThresholdmatchThreshold (input_control)  number HTupleHTupleHtuple (integer / real) (int / long / double) (Hlong / double) (Hlong / double)

Threshold for gray value matching.

Default value: 10

Suggested values: 10, 20, 50, 100, 0.9, 0.7

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

Algorithm for the computation of the essential matrix and for special camera orientations.

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"

DistanceThresholdDistanceThresholdDistanceThresholdDistanceThresholddistanceThreshold (input_control)  number HTupleHTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Maximal deviation of a point from its epipolar line.

Default value: 1

Typical range of values: 0.5 ≤ DistanceThreshold DistanceThreshold DistanceThreshold DistanceThreshold distanceThreshold ≤ 5

Restriction: DistanceThreshold > 0

RandSeedRandSeedRandSeedRandSeedrandSeed (input_control)  integer HTupleHTupleHtuple (integer) (int / long) (Hlong) (Hlong)

Seed for the random number generator.

Default value: 0

EMatrixEMatrixEMatrixEMatrixEMatrix (output_control)  hom_mat2d HHomMat2D, HTupleHTupleHtuple (real) (double) (double) (double)

Computed essential matrix.

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

9x9 covariance matrix of the essential matrix.

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

Root-Mean-Square of the epipolar distance error.

Points1Points1Points1Points1points1 (output_control)  integer-array HTupleHTupleHtuple (integer) (int / long) (Hlong) (Hlong)

Indices of matched input points in image 1.

Points2Points2Points2Points2points2 (output_control)  integer-array HTupleHTupleHtuple (integer) (int / long) (Hlong) (Hlong)

Indices of matched input points in image 2.

Possible Predecessors

points_foerstnerpoints_foerstnerPointsFoerstnerPointsFoerstnerPointsFoerstner, points_harrispoints_harrisPointsHarrisPointsHarrisPointsHarris

Possible Successors

vector_to_essential_matrixvector_to_essential_matrixVectorToEssentialMatrixVectorToEssentialMatrixVectorToEssentialMatrix

See also

match_fundamental_matrix_ransacmatch_fundamental_matrix_ransacMatchFundamentalMatrixRansacMatchFundamentalMatrixRansacMatchFundamentalMatrixRansac, match_rel_pose_ransacmatch_rel_pose_ransacMatchRelPoseRansacMatchRelPoseRansacMatchRelPoseRansac, stationary_camera_self_calibrationstationary_camera_self_calibrationStationaryCameraSelfCalibrationStationaryCameraSelfCalibrationStationaryCameraSelfCalibration

References

Richard Hartley, Andrew Zisserman: “Multiple View Geometry in Computer Vision”; Cambridge University Press, Cambridge; 2003.
Olivier Faugeras, Quang-Tuan Luong: “The Geometry of Multiple Images: The Laws That Govern the Formation of Multiple Images of a Scene and Some of Their Applications”; MIT Press, Cambridge, MA; 2001.

Module

3D Metrology


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