The Class of Stable Matchings for Computational Stereo

In this paper the notion of stability of a bipartite matching is introduced and studied. It is a strong but overlooked constraint very useful in computational stereo. The resulting algorithms require no prior continuity model, are parameter-free, very fast, and accurate in terms of mismatches. A whole class of stable matchings is presented. It is shown that some of the popular matching algorithms belong to this class and are subsets of stable complete matching. The existence and uniqueness theorem for stable complete matching is given in this paper. The main result of the paper deals with incorporating the ordering constraint into this framework. The corresponding existence theorem is given and a simple sub-optimal polynomial algorithm for maximum-cost stable monotonic matching is suggested. It is shown on standard stereo pairs that stable monotonic matching performs very well in the stereo matching task. It is also demonstrated that the algorithm is well suited for efficient disparity map fusion.