Partition function estimation of Gibbs random field images using Monte Carlo simulations

A Monte Carlo simulation technique for estimating the partition function of a general Gibbs random field image is proposed. By expressing the partition function as an expectation, an importance sampling approach for estimating it using Monte Carlo simulations is developed. As expected, the resulting estimators are unbiased and consistent. Computations can be performed iteratively by using simple Monte Carlo algorithms with remarkable success, as demonstrated by simulations. The work concentrates on binary, second-order Gibbs random fields defined on a rectangular lattice. However, the proposed methods can be easily extended to more general Gibbs random fields. Their potential contribution to optimal parameter estimation and hypothesis testing problems for general Gibbs random field images using a likelihood approach is anticipated