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Markov random fields are reviewed and investigated as models of texture. Results from the field of statistical physics are reformulated in a statistical setting. Standard Markov random fields do not have the ability to model morphological properties of textures, and this leads us to formulate an extension in the terms of mathematical morphology. The properties of morphological Markov random fields are illustrated. We go through the problem of Markov random field parameter estimation and suggest an extension of the asymptotic maximum likelihood estimator (Pickard, 1987) to the anisotropic first-order model.

Markov random field simulation is described and a new, fast, parallel algorithm for simulation conditional on the first-order statistics is presented. This algorithm and the morphological Markov random fields are then used for the simulation of the geometrical structure of oil reservoirs.

Markov random fields in a Bayesian setting are used successfully to analyze
hybridization filters automatically for the human genome project.

Last update 14-2-2001 by fkc