rel_pose_to_fundamental

rel_pose_to_fundamental_matrix ( : : RelPose, CovRelPose, CamPar1, CamPar2 : FMatrix, CovFMat )

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

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 camera_calibration. 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 RelPose (see also operator vector_to_rel_pose). 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_matrix:

                        -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 CovRelPose to CovFMat. If CovRelPose is empty CovFMat will be empty too.

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

Parameters

`RelPose` (input_control)	pose-array `->` real / integer
Relative orientation of the cameras (3D pose).

`CovRelPose` (input_control)	number-array `->` real / integer
6x6 covariance matrix of relative pose.
Default value: '[]'

`CamPar1` (input_control)	number-array `->` real / integer
Parameters of the 1. camera.

`CamPar2` (input_control)	number-array `->` real / integer
Parameters of the 2. camera.

`FMatrix` (output_control)	hom_mat2d-array `->` real
Computed fundamental matrix.

`CovFMat` (output_control)	real-array `->` real
9x9 covariance matrix of the fundamental matrix.

Parallelization Information

rel_pose_to_fundamental_matrix is reentrant and processed without parallelization.

Possible Predecessors

vector_to_rel_pose

Alternatives

essential_to_fundamental_matrix

See also

camera_calibration

Module

3D Metrology