essential_to_fundamental_matrixT_essential_to_fundamental_matrixEssentialToFundamentalMatrixEssentialToFundamentalMatrix (Operator)

Name

essential_to_fundamental_matrixT_essential_to_fundamental_matrixEssentialToFundamentalMatrixEssentialToFundamentalMatrix — Compute the fundamental matrix from an essential matrix.

Signature

essential_to_fundamental_matrix( : : EMatrix, CovEMat, CamMat1, CamMat2 : FMatrix, CovFMat)

Description

The fundamental matrix is the entity describing the epipolar constraint in image coordinates (C,R) and the essential matrix is its counterpart for 3D direction vectors (X,Y,1): Image coordinates result from 3D direction vectors by multiplication with the camera matrix CamMat: Therefore, the fundamental matrix FMatrixFMatrixFMatrixFMatrixFMatrix is calculated from the essential matrix EMatrixEMatrixEMatrixEMatrixEMatrix and the camera matrices CamMat1CamMat1CamMat1CamMat1camMat1, CamMat2CamMat2CamMat2CamMat2camMat2 by the following formula: The transformation of the essential matrix to the fundamental matrix goes along with the propagation of the covariance matrices CovEMatCovEMatCovEMatCovEMatcovEMat to CovFMatCovFMatCovFMatCovFMatcovFMat. If CovEMatCovEMatCovEMatCovEMatcovEMat is empty CovFMatCovFMatCovFMatCovFMatcovFMat will be empty too.

The conversion operator essential_to_fundamental_matrixessential_to_fundamental_matrixEssentialToFundamentalMatrixEssentialToFundamentalMatrixEssentialToFundamentalMatrix is used especially for a subsequent visualization of the epipolar line structure via the fundamental matrix, which depicts the underlying stereo geometry.

Execution Information

Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Processed without parallelization.

Parameters

EMatrixEMatrixEMatrixEMatrixEMatrix (input_control) hom_mat2d → (real / integer)

Essential matrix.

CovEMatCovEMatCovEMatCovEMatcovEMat (input_control) number-array → (real / integer)

9x9 covariance matrix of the essential matrix.

Default value: []

CamMat1CamMat1CamMat1CamMat1camMat1 (input_control) hom_mat2d → (real / integer)

Camera matrix of the 1. camera.

CamMat2CamMat2CamMat2CamMat2camMat2 (input_control) hom_mat2d → (real / integer)

Camera matrix of the 2. camera.

FMatrixFMatrixFMatrixFMatrixFMatrix (output_control) hom_mat2d → (real)

Computed fundamental matrix.

CovFMatCovFMatCovFMatCovFMatcovFMat (output_control) real-array → (real)

9x9 covariance matrix of the fundamental matrix.

Possible Predecessors

vector_to_essential_matrixvector_to_essential_matrixVectorToEssentialMatrixVectorToEssentialMatrixVectorToEssentialMatrix

Alternatives

rel_pose_to_fundamental_matrixrel_pose_to_fundamental_matrixRelPoseToFundamentalMatrixRelPoseToFundamentalMatrixRelPoseToFundamentalMatrix

Module

3D Metrology

Operators