Ch. Wu et Pc. Doerschuk, CLUSTER EXPANSIONS FOR THE DETERMINISTIC COMPUTATION OF BAYESIAN-ESTIMATORS BASED ON MARKOV RANDOM-FIELDS, IEEE transactions on pattern analysis and machine intelligence, 17(3), 1995, pp. 275-293
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.