Bi-directional probabilistic hypergraph matching method using Bayes theorem

Abstract

Establishing correspondences between two hyper-graphs is a fundamental issue in computer vision, pattern recognition, and machine learning. A hyper-graph is modeled by feature set where the complex relations are represented by hyperedges. Hence, a match between two vertex sets determines a hyper-graph matching problem. We propose a new bidirectional probabilistic hyper-graph matching method using Bayesian inference principle. First, we formulate the corresponding hyper-graph matching problem as the maximization of a matching score function over all permutations of the vertexes. Second, we induce an algebraic relation between the hyper-edge weight matrixes and derive the desired vertex to vertex probabilistic matching algorithm using Bayes theorem. Third, we apply the well known convex relaxation procedure with probabilistic soft matching matrix to get a complete hard matching result. Finally, we have conducted the comparative experiments on synthetic data and real images. Experimental results show that the proposed method clearly outperforms existing algorithms especially in the presence of noise and outliers.