Unilateral approximation of Gibbs random field images

The relationship between a general Gibbs random field image and a mutually compatible Gibbs random field image is exploited. The possibility of approximating a general Gibbs random field by a mutually compatible Gibbs random field is investigated, and the consequences of such a representation are studied. It is shown that substantial computational savings can be obtained if a Monte Carlo algorithm is initialized, for the simulation of Gibbs random field images, with the resulting approximation. The fact that an efficient maximum-likelihood estimation procedure can be developed for the estimation of a general Gibbs random field, in the cases of reasonable unilateral approximation, is also demonstrated. Many problems related to the modeling of images with Gibbs random fields can be approximately solved by restricting interest to the class of mutually compatible Gibbs random fields