Multiscale Image Segmentation via Exact Inference of Hidden Markov Tree

Abstract

This paper addresses the problem of exact inference of probabilistic graphical models for multiscale segmentation of objects in the presence of dynamic backgrounds. Previous hidden Markov tree (HMT) based approaches have exploited the Expectation-Maximization (EM) algorithm to compute the optimal estimates of the multiscale parameters that maximize the likelihood function. However, the main problem with the EM algorithm is that it is a “greedy” method that converges to a local maxima on the log-likelihood surface. In this paper, we derive the Bethe free energy associated with the HMT which is a lower bound of cumulant energy function so as to recover multiscale posterior likelihoods exactly. This allows both inference and fusion of multiscale classification likelihoods to be computed through bottom-up likelihood estimation and up-bottom posterior inference of HMT. Experimental results on a frame of typical high-speed industrial inspection image demonstrate the correctness and robustness achieved by the proposed method.