Fast Bayesian Shape Matching Using Geometric Algorithms

We present a Bayesian approach to comparison of geometric shapes with applications to classification of the molecular structures of proteins. Our approach involves the use of distributions defined on transformation invariant shape spaces and the specification of prior distributions on bipartite matchings. Here we emphasize the computational aspects of posterior inference arising from such models, and explore computationally efficient approximation algorithms based on a geometric hashing algorithm which is suitable for fully Bayesian shape matching against large databases. We demonstrate this approach on the problems of protein structure alignment, structural database searching, and structure classification. We discuss extensions to flexible shape spaces developed in previous work.