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

Abstract

Recent 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 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 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.

Segmentation of Brain MRI

“…Generally, MRF model is assumed to be homogeneous, which means the parameter is constant. Plenty of previous researches have offered a series of methods to accurately estimate this parameter, which advance the effect of image segmentation (Deng & Clausi, 2004;Descombes et al, 1999). Due to its own features of medical image, homogeneous MRF model often leads to over-segmentation and induces higher misclassification rate.…”

“…A setting that is too high can result in an excessively smooth segmentation and a loss of important structural details. Some researchers have proposed several schemes for the estimation of MRF parameters (Descombes et al, 1999;Salzenstein & Pieczynski, 1997;R. Xu & Luo, 2009).…”

Semi-unsupervised Bayesian convex image restoration with location mixture of Gaussian

“…In the general case, K is dependant wrt. regularization parameters θ which is a major difficulty that blocks θ estimation [16], [21], [22]. For the well-posedness of the inverse problem we consider the energy E θ (x) = γ x c∈C φ (d t c x; θ) with the set C of cliques c and neighborhoods d c [7] and γ x > 0.…”

“…However, results on unsupervised method are sparser with some existing work [15], for instance based on marginal likelihood [16], quadratic prior [17], [18], per variables Metropolis-Hastings [19] or more recently Moreau approximation [20].…”

Unsupervised Image Segmentation Based on Bethe Approximation

“…See Refs. [10] and [11] for example, as for the Potts model in image processing. Here is the inverse temperature of the prior Gibbs distribution, and a;b is the Kronecker delta.…”