Monte Carlo simulation and statistical inference of morphologically constrained GRFs

This paper is about a new class of random spatial models, known as morphologically constrained Gibbs random fields, that are capable of modeling geometrical constraints in images by means of mathematical morphology. Two issues pertaining these models are considered in this paper: simulation and statistical inference. We first introduce a variant of the Metropolis algorithm, based on a multi-site updating strategy, for simulating morphologically constrained Gibbs random fields, that converges substantially faster than traditional single-site updating algorithms. We then consider the problem of optimally fitting morphologically constrained Gibbs random, fields to real data. We show that, under a natural condition, maximum likelihood parameter estimation can be approximately implemented by means of the pattern spectrum.