Application of the mean field methods to MRF optimization in computer vision

The mean field (MF) methods are an energy optimization method for Markov random fields (MRFs). These methods, which have their root in solid state physics, estimate the marginal density of each site of an MRF graph by iterative computation, similarly to loopy belief propagation (LBP). It appears that, being shadowed by LBP, the MF methods have not been seriously considered in the computer vision community. This study investigates whether these methods are useful for practical problems, particularly MPM (Maximum Posterior Marginal) inference, in computer vision. To be specific, we apply the naive MF equations and the TAP (Thouless-Anderson-Palmer) equations to interactive segmentation and stereo matching. In this paper, firstly, we show implementation of these methods for computer vision problems. Next, we discuss advantages of the MF methods to LBP. Finally, we present experimental results that the MF methods are well comparable to LBP in terms of accuracy and global convergence; furthermore, the 3rd-order TAP equation often outperforms LBP in terms of accuracy.