ESTABLISHING MOTION CORRESPONDENCE

Given n frames taken at different time instants and m points in each frame, the problem of motion correspondence is to map a point in one frame to another point in the next frame such that no two points map onto the same point. This problem is combinatorially explosive; one needs to introduce constraints to limit the search space. We propose a proximal uniformity constraint to solve the correspondence problem. According to this constraint, most objects in the real world follow smooth paths and cover a small distance in a small time. Therefore, given a location of a point in a frame, its location in the next frame lies in the proximity of its previous location. Further, resulting trajectories are smooth and uniform and do not show abrupt changes in velocity vector over time. An efficient, non-iterative polynomial time approximation algorithm which minimizes the proximal uniformity cost function and establishes correspondence over n frames is proposed. It is argued that any method using smoothness of motion alone cannot operate correctly without assuming correct initial correspondence, the correspondence in the first two frames. Therefore, we propose the use of gradient based optical flow for establishing the initial correspondence. This way the proposed approach combines the qualities of the gradient and token based methos for motion correspondence. The algorithm is then extended to take care of restricted cases of occlusion. A metric called distortion measure for measuring the goodness of solution to this n frame correspondence problem is also proposed. The experimental results for real and synthetic sequences are presented to support our claims. © 1991.