1  Estimation of Markov Random Field prior parameters using Markov chain Monte Carlo Maximum Likelihood. X. Descombes and R. Morris and J. Zerubia and M. Berthod. IEEE Trans. Image Processing, 8(7): pages 954963, July 1999. Keywords : Markov processes, Monte Carlo methods, Potts model, Image segmentation, Maximum likelihood estimation .
@ARTICLE{xd99c,

author 
= 
{Descombes, X. and Morris, R. and Zerubia, J. and Berthod, M.}, 
title 
= 
{Estimation of Markov Random Field prior parameters using Markov chain Monte Carlo Maximum Likelihood}, 
year 
= 
{1999}, 
month 
= 
{July}, 
journal 
= 
{IEEE Trans. Image Processing}, 
volume 
= 
{8}, 
number 
= 
{7}, 
pages 
= 
{954963}, 
pdf 
= 
{http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=16772&arnumber=772239&count=14&index=6}, 
keyword 
= 
{Markov processes, Monte Carlo methods, Potts model, Image segmentation, Maximum likelihood estimation } 
} 
Abstract :
Developments in statistics now allow maximum likelihood estimators for the parameters of Markov random fields (MRFs) to be constructed. We detail the theory required, and present an algorithm that is easily implemented and practical in terms of computation time. We demonstrate this algorithm on three MRF modelsthe standard Potts model, an inhomogeneous variation of the Potts model, and a longrange interaction model, better adapted to modeling realworld 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 based on the estimated parameters and conclusions drawn. 
