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

摘要

Recent developments in statistics now allow maximum likelihood estimators for the parameters of Markov Random Fields to be constructed. We detail the theory required, and present an algorithm which is easily implemented and practical in terms of computation time. We demonstrate this algorithm on three MRF models -- the standard Potts model, an inhomogeneous variation of the Potts model, and a long-range interaction model, better adapted to modeling real-world images. We estimate the parameters from a synthetic and a real image, and then resynthesise the models to demonstrate which features of the image have been captured by the model. Segmentations are computed based on the estimated parameters and conclusions drawn.