Graph partition by Swendsen-Wang cuts

Abstract

Vision tasks, such as segmentation, grouping, recognition, can be formulated as graph partition problems. The recent literature witnessed two popular graph cut algorithms: the Ncut using spectral graph analysis and the minimum-cut using the maximum flow algorithm. We present a third major approach by generalizing the Swendsen-Wang method - a well celebrated algorithm in statistical mechanics. Our algorithm simulates ergodic, reversible Markov chain jumps in the space of graph partitions to sample a posterior probability. At each step, the algorithm splits, merges, or regroups a sizable subgraph, and achieves fast mixing at low temperature enabling a fast annealing procedure. Experiments show it converges in 2-30 seconds on a PC for image segmentation. This is 400 times faster than the single-site update Gibbs sampler, and 20-40 times faster than the DDMCMC algorithm. The algorithm can optimize over the number of models and works for general forms of posterior probabilities, so it is more general than the existing graph cut approaches.