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Cluster expansions for the deterministic computation of Bayesian estimators based on Markov random fields

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2 Author(s)
Chi-Hsin Wu ; Dept. of Image Process., Ind. Technol. Res. Inst., Hsinchu, Taiwan ; Doerschuk, P.C.

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 posteriori 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

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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:17 ,  Issue: 3 )