rel_pose_to_fundamental_matrixT_rel_pose_to_fundamental_matrixRelPoseToFundamentalMatrixrel_pose_to_fundamental_matrixRelPoseToFundamentalMatrixRelPoseToFundamentalMatrix (Operator)

Name

rel_pose_to_fundamental_matrixT_rel_pose_to_fundamental_matrixRelPoseToFundamentalMatrixrel_pose_to_fundamental_matrixRelPoseToFundamentalMatrixRelPoseToFundamentalMatrix — Compute the fundamental matrix from the relative orientation of two cameras.

Signature

Description

Cameras including lens distortions can be modeled by the following set of parameters: the focal length f, two scaling factors Sx,Sy, the coordinates of the principal point (Cx,Cy) and the distortion coefficient kappa. For a more detailed description see the operator calibrate_camerascalibrate_camerasCalibrateCamerascalibrate_camerasCalibrateCamerasCalibrateCameras. Only cameras with a distortion coefficient equal to zero project straight lines in the world onto straight lines in the image. Then, image projection is a linear mapping and the camera, i.e. the set of internal parameters, can be described by the camera matrix CamMat:

                  /  f/Sx     0  Cx \
       CamMat  =  |     0  f/Sy  Cy |  .
                  \     0     0   1 /

Going from a nonlinear model to a linear model is an approximation of the real underlying camera. For a variety of camera lenses, especially lenses with long focal length, the error induced by this approximation can be neglected. Following the formula E=([t]_x R)^T, the essential matrix E is derived from the translation t and the rotation R of the relative pose RelPoseRelPoseRelPoseRelPoseRelPoserelPose (see also operator vector_to_rel_posevector_to_rel_poseVectorToRelPosevector_to_rel_poseVectorToRelPoseVectorToRelPose). In the linearized framework the fundamental matrix can be calculated from the relative pose and the camera matrices according to the formula presented under essential_to_fundamental_matrixessential_to_fundamental_matrixEssentialToFundamentalMatrixessential_to_fundamental_matrixEssentialToFundamentalMatrixEssentialToFundamentalMatrix:

                        -T            T         -1
     FMatrix  =  CamMat2   * ([t]_x R) * CamMat1    .

The transformation from a relative pose to a fundamental matrix goes along with the propagation of the covariance matrices CovRelPoseCovRelPoseCovRelPoseCovRelPoseCovRelPosecovRelPose to CovFMatCovFMatCovFMatCovFMatCovFMatcovFMat. If CovRelPoseCovRelPoseCovRelPoseCovRelPoseCovRelPosecovRelPose is empty CovFMatCovFMatCovFMatCovFMatCovFMatcovFMat will be empty too.

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

Parallelization

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

Parameters

Possible Predecessors

vector_to_rel_posevector_to_rel_poseVectorToRelPosevector_to_rel_poseVectorToRelPoseVectorToRelPose

Alternatives

essential_to_fundamental_matrixessential_to_fundamental_matrixEssentialToFundamentalMatrixessential_to_fundamental_matrixEssentialToFundamentalMatrixEssentialToFundamentalMatrix

See also

calibrate_camerascalibrate_camerasCalibrateCamerascalibrate_camerasCalibrateCamerasCalibrateCameras

Module

3D Metrology