An Optimal Probabilistic Graphical Model for Point Set Matching

We present a probabilistic graphical model for point set matching. By using a result about the redundancy of the pairwise distances in a point set, we represent the binary relations over a simple triangulated graph that retains the same informational content as the complete graph. The maximal clique size of this resultant graph is independent of the point set sizes, what enables us to perform exact inference in polynomial time with a Junction Tree algorithm. The resulting technique is optimal in the Maximum a Posteriori sense. Experiments show that the algorithm significantly outperforms standard probabilistic relaxation labeling.