EM-based image segmentation using Potts models with external field

Image segmentation using Markov random fields involves parameter estimation in hidden Markov models for which the EM algorithm is widely used. In practice, a simple Markov model is often used to account for the spatial dependencies between pixels, namely the isotropic homogeneous Potts model with no external field. It has the advantage to involve only one interaction parameter and leads in a lot of cases to good results. The absence of an external field parameter implies that all colors have the same weight. In this paper, we investigate the use of additional parameters (external field) that would play the role of the weight terms in mixture distributions and would allow more flexibility for the segmentations. To deal with the difficulties that arise due to the dependence structure in the models, we use a class of EM-like algorithms based on the Mean Field approximation principle and presented in some previous work. We illustrate with numerical experiments the advantages of introducing an external field parameter in the basic Potts model