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<p><it>Abstract</it>—We describe a family of approximations, denoted by “cluster approximations,” 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 <it>posteriori</it> MRF. The approximation is to account exactly for only spatially local interactions. Application of the approximation requires the solution of a nonlinear multivariable fixed-point equation for which we prove several existence, uniqueness, and convergence-of-algorithm results. Four numerical examples are presented, including comparison with Monte Carlo calculations.</p>
Markov random fields, image restoration, Bayesian estimation, thresholded posterior mean estimator.
Peter C. Doerschuk, Chi-hsin Wu, "Cluster Expansions for the Deterministic Computation of Bayesian Estimators Based on Markov Random Fields", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 17, no. , pp. 275-293, March 1995, doi:10.1109/34.368192
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