Tree Approximations to Markov Random Fields

Methods for approximately computing the marginal probability mass functions and means of a Markov random field (MRF) by approximating the lattice by a tree are described. Applied to the a posteriori MRF these methods solve Bayesian spatial pattern classification and image restoration problems. The methods are described, several theoretical results concerning fixed-point problems are proven, and four numerical examples are presented, including comparison with optimal estimators and the iterated conditional mode estimator and including two agricultural optical remote sensing problems. >

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