Markov random field

About: Markov random field is a research topic. Over the lifetime, 5669 publications have been published within this topic receiving 179568 citations. The topic is also known as: MRF.

On block updating in Markov random field models for disease mapping. (REVISED, May 2001)

Abstract: Gaussian Markov random field (GMRF) models are commonly used to model spatial correlation in disease mapping applications. For Bayesian inference by MCMC, so far mainly single-site updating algorithms have been considered. However, convergence and mixing properties of such algorithms can be extremely bad due to strong dependencies of parameters in the posterior distribution. In this paper, we propose various block sampling algorithms in order to improve the MCMC performance. The methodology is rather general, allows for non-standard full conditionals, and can be applied in a modular fashion in a large number of different scenarios. For illustration we consider three different models: two formulations for spatial modelling of a single disease (with and without additional unstructured parameters respectively), and one formulation for the joint analysis of two diseases. We apply the proposed algorithms to two datasets known from the literature. The results indicate that the largest benefits are obtained if parameters and the corresponding hyperparameter are updated jointly in one large block. In certain situations, even updating of all or nearly all parameters in one block may be necessary. Implementation of such block algorithms is surprisingly easy using methods for fast sampling of Gaussian Markov random fields (Rue, 2000). By comparison, estimates of the relative risk and related quantities, such as the posterior probability of an exceedence relative risk, based on single-site updating, can be rather misleading, even for very long runs. Our results may have wider relevance for efficient MCMC simulation in hierarchical models with Markov random field components.

Maximum a posteriori blind image deconvolution with Huber-Markov random-field regularization.

Abstract: We propose a maximum a posteriori blind deconvolution approach using a Huber-Markov random-field model. Compared with the conventional maximum-likelihood method, our algorithm not only suppresses noise effectively but also significantly alleviates the artifacts produced by the deconvolution process. The performance of this method is demonstrated by computer simulations.

Bayesian contextual classification based on modified M-estimates and Markov random fields

Abstract: A Bayesian contextual classification scheme is presented in connection with modified M-estimates and a discrete Markov random field model. The spatial dependence of adjacent class labels is characterized based on local transition probabilities in order to use contextual information. Due to the computational load required to estimate class labels in the final stage of optimization and the need to acquire robust spectral attributes derived from the training samples, modified M-estimates are implemented to characterize the joint class-conditional distribution. The experimental results show that the suggested scheme outperforms conventional noncontextual classifiers as well as contextual classifiers which are based on least squares estimates or other spatial interaction models.

Stereo integration, mean field theory and psychophysics

Abstract: We describe a theoretical formulation for stereo in terms of the Markov Random Field and Bayesian approach to vision. This formulation enables us to integrate the depth information from different types of matching primitives, or from different vision modules. We treat the correspondence problem and surface interpolation as different aspects of the same problem and solve them simultaneously, unlike most previous theories. We use techniques from statistical physics to compute properties of our theory and show how it relates to previous work. These techniques also suggest novel algorithms for stereo which are argued to be preferable to standard algorithms on theoretical and experimental grounds. It can be shown (Yuille, Geiger and Bulthoff 1989) that the theory is consistent with some psychophysical experiments which investigate the relative importance of different matching primitives.

Compact object recognition using energy-function-based optimization

Abstract: Describes a method of recognizing objects whose contours can be represented in smoothly varying polar coordinate form. Both low- and high-level information about the object (contour smoothness and edge sharpness at the low level and contour shape at the high level) are incorporated into a single energy function that defines a 1D, cyclic, Markov random field (1DCMRF). This 1DCMRF is based on a polar coordinate object representation whose center can be initialized at any location within the object. The recognition process is based on energy function minimization, which is implemented by simulated annealing. >