(BP)2: Beyond pairwise Belief Propagation labeling by approximating Kikuchi free energies

Belief Propagation (BP) can be very useful and efficient for performing approximate inference on graphs. But when the graph is very highly connected with strong conflicting interactions, BP tends to fail to converge. Generalized Belief Propagation (GBP) provides more accurate solutions on such graphs, by approximating Kikuchi free energies, but the clusters required for the Kikuchi approximations are hard to generate. We propose a new algorithmic way of generating such clusters from a graph without exponentially increasing the size of the graph during triangulation. In order to perform the statistical region labeling, we introduce the use of superpixels for the nodes of the graph, as it is a more natural representation of an image than the pixel grid. This results in a smaller but much more highly interconnected graph where BP consistently fails. We demonstrate how our version of the GBP algorithm outperforms BP on synthetic and natural images and in both cases, GBP converges after only a few iterations.