Estimation of Markov random field prior parameters using Markov chain Monte Carlo maximum likelihood

Recent developments in statistics now allow maximum likelihood estimators f or the parameters of Markov random fields (MRF's) to be constructed. We det ail the theory required, and present an algorithm that is easily implemente d and practical in terms of computation time. We demonstrate this algorithm on three MRF models-the standard Potts model, an inhomogeneous variation o f the Potts model, and a long-range interaction model, better adapted to mo deling real world images. We estimate the parameters from a synthetic and a real image, and then resynthesize the models to demonstrate which features of the image have been captured by the model. Segmentations are computed b ased on the estimated parameters and conclusions drawn.