The mean field theory in EM procedures for Markov random fields

In many signal processing and pattern recognition applications, the hidden data are modeled as Markov processes, and the main difficulty of using the maximisation (EM) algorithm for these applications is the calculation of the conditional expectations of the hidden Markov processes. It is shown how the mean field theory from statistical mechanics can be used to calculate the conditional expectations for these problems efficiently. The efficacy of the mean field theory approach is demonstrated on parameter estimation for one-dimensional mixture data and two-dimensional unsupervised stochastic model-based image segmentation. Experimental results indicate that in the 1-D case, the mean field theory approach provides results comparable to those obtained by Baum´s (1987) algorithm, which is known to be optimal. In the 2-D case, where Baum´s algorithm can no longer be used, the mean field theory provides good parameter estimates and image segmentation for both synthetic and real-world images