Contour point tracking by enforcement of rigidity constraints

The aperture problem is one of the omnipresent issues in computer vision. Its local character constrains point matching to high textured areas, so that points in gradient-oriented regions (such as straight lines) can not be reliably matched. We propose a new method to overcome this problem by devising a global matching strategy under the factorization framework. We solve the n-frame correspondence problem under this context by assuming the rigidity of the scene. To this end, a geometric constraint is used that selects the matching solution resulting in a rank-4 observation matrix. The rank of the observation matrix is a function of the matching solutions associated to each image and as such a simultaneous solution for all frames has to be found. An optimization procedure is used in this text in order to find the solution.