Faster graphical models for point-pattern matching

It has been shown that isometric matching problems can be solved exactly in polynomial time, by means of a Junction Tree with small maximal clique size. Recently, an iterative algorithm was presented which converges to the same solution an order of magnitude faster. Here, we build on both of these ideas to produce an algorithm with the same asymptotic running time as the iterative solution, but which requires only a single iteration of belief propagation. Thus our algorithm is much faster in practice, while maintaining similar error rates.