Understanding Belief Propagation and its Applications

“Inference” problem arise in computer vision, AI, statistical physics and coding theory. The rationale behind the belief propagation is an efficient way to solve inference problems by propagating local messages around neighborhoods [5]. Although researchers proved that the belief propagation (BP) converges to a unique fixed point (fixed probabilistic belief) on singly connected graphs [1], they also have shown that the BP is able to produce great results on graphs with loops, empirically [2]. However, a theoretical understanding and proof of this performance has not been achieved. Since images can be easily represented as the loopy graphs, where graph nodes are associated with pixels or image patches, many image processing researchers have experienced with BP, with promising results. In this report, we will focus on the principle of BP, and its applications in computer vision.