Layered graph matching by composite cluster sampling with collaborative and competitive interactions

This paper studies a framework for matching an unknown number of corresponding structures in two images (shapes), motivated by detecting objects in cluttered background and learning parts from articulated motion. Due to the large distortion between shapes and ambiguity caused by symmetric or cluttered structures, many inference algorithms often get stuck in local minimums and converge slowly. We propose a composite cluster sampling algorithm with a “candidacy graph” representation, where each vertex (candidate) is a possible match for a pair of source and target primitives (local structure or small curves), and the layered matching is then formulated as a multiple coloring problem. Each two vertices can be linked by either a competitive edge or a collaborative edge. These edges indicate the connected vertices should/shouldn't be assigned the same color. With this representation, the stochastic sampling contains two steps: (i) Sampling the competitive and collaborative edges to form a composite cluster, in which a few mutual-conflicting connected components are in different colors; (ii) Sampling the new colors to this cluster remaining consistency with Markov Chain Monte Carlo (MCMC) mechanism. The algorithm is applied to many applications on many public datasets and outperform the state of the art approaches.