CLUSTER EXPANSIONS FOR THE DETERMINISTIC COMPUTATION OF BAYESIAN-ESTIMATORS BASED ON MARKOV RANDOM-FIELDS

We describe a family of approximations, denoted by ''cluster approxima tions,'' for the computation of the mean of a Markov random field (MRF ). This is a key computation in image processing when applied to the a posteriori MRF. The approximation is to, account exactly for only spa tially local interactions. Application of the approximation requires t he solution of a nonlinear multivariable fixed-point equation for whic h we prove several existence, uniqueness, and convergence-of-algorithm results. Four numerical examples are presented, including comparison with Monte Carlo calculations.