  This paper presents a Bayesian image segmentation model based on Potts prior
and loopy belief propagation. The proposed Bayesian model involves several
terms, including the pairwise interactions of Potts models, and the average
vectors and covariant matrices of Gauss distributions in color image modeling.
These terms are often referred to as hyperparameters in statistical machine
learning theory. In order to determine these hyperparameters, we propose a new
scheme for hyperparameter estimation based on conditional maximization of
entropy in the Potts prior. The algorithm is given based on loopy belief
propagation. In addition, we compare our conditional maximum entropy framework
with the conventional maximum likelihood framework, and also clarify how the
first order phase transitions in LBP's for Potts models influence our
hyperparameter estimation procedures.
