Layered Graph Matching with Composite Cluster Sampling

This paper presents a framework of layered graph matching for integrating graph partition and matching. The objective is to find an unknown number of corresponding graph structures in two images. We extract discriminative local primitives from both images and construct a candidacy graph whose vertices are matching candidates (i.e., a pair of primitives) and whose edges are either negative for mutual exclusion or positive for mutual consistence. Then we pose layered graph matching as a multicoloring problem on the candidacy graph and solve it using a composite cluster sampling algorithm. This algorithm assigns some vertices into a number of colors, each being a matched layer, and turns off all the remaining candidates. The algorithm iterates two steps: 1) Sampling the positive and negative edges probabilistically to form a composite cluster, which consists of a few mutually conflicting connected components (CCPs) in different colors and 2) assigning new colors to these CCPs with consistence and exclusion relations maintained, and the assignments are accepted by the Markov Chain Monte Carlo (MCMC) mechanism to preserve detailed balance. This framework demonstrates state-of-the-art performance on several applications, such as multi-object matching with large motion, shape matching and retrieval, and object localization in cluttered background.