Computation of Bayesian estimators for Markov random field image models using the cluster approximation

Describes a family of approximations, denoted “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 a form of mean field theory and accounts exactly for only spatially local interactions. The implementation of the approximation requires the solution of a nonlinear multivariable fixed-point equation. Unlike many forms of mean field theory, the approximation is easy to apply even to nonquadratic Hamiltonians (e.g., it requires no analytical calculations), the structure of the gray level values in the original problem is retained, the resulting approximate mean field can be proven to lie in the same set which contains the true mean of the MRF, and there are existence, uniqueness, and convergence-of-algorithm results for the fixed-point equation. Two numerical examples are presented which emphasize nonlinear observation processes