Stochastic Simulation Techniques for Partition Function Approximation of GibbsRandom Field Images

摘要

A Monte Carlo simulation technique for the calculation of the partition functionof a general Gibbs random field is presented. We show that the partition function of a general Gibbs random field is equivalent to an expectation. This observation allows us to develop an importance sampling approach for estimating this expectation by using Monte-Carlo simulations. Two different methods are proposed for this task. We show that the resulting estimators are unbiased and consistent. Computations are performed iteratively, by using a simple, Metropolis-like, Monte-Carlo algorithm with remarkable success, as it is demonstrated by our simulations. Our work concentrates on binary, second-order Gibbs random fields defined on a rectangular lattice.