Epipolar Angular Factorisation of Essential Matrix for Camera Pose Calibration

A novel epipolar angular representation for camera pose is introduced. It leads to a factorisation of the pose rotation matrix into three canonical rotations: around the dual epipole for the second camera, around the z axis, and around the dual epipole for the first camera. If the rotation around the z axis is increased by 90 degrees and followed by the orthogonal projection on xy plane then the factorisation of essential matrix is produced. The proposed five parameter representation of the essential matrix is minimal. It exhibits the fast convergence in LMM optimization algorithm used for camera pose calibration. In such parametrisation the constraints based on the distance to the epipolar plane appeared slightly more accurate than constraints based on the distance to the epipolar line.