Spherical formulation of geometric motion segmentation constraints in fisheye cameras

We introduce a visual motion segmentation method employing spherical geometry for fisheye cameras and automoated driving. Three commonly used geometric constraints in pin-hole imagery (the positive height, positive depth and epipolar constraints) are reformulated to spherical coordinates, making them invariant to specific camera configurations as long as the camera calibration is known. A fourth constraint, known as the anti-parallel constraint, is added to resolve motion-parallax ambiguity, to support the detection of moving objects undergoing parallel or near-parallel motion with respect to the host vehicle. A final constraint constraint is described, known as the spherical three-view constraint, is described though not employed in our proposed algorithm. Results are presented and analyzed that demonstrate that the proposal is an effective motion segmentation approach for direct employment on fisheye imagery.