Showing papers on "Markov random field published in 1984"

Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images

Abstract: We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs distribution. Because of the Gibbs distribution, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mechanisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical system isolates low energy states (``annealing''), or what is the same thing, the most probable states under the Gibbs distribution. The analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations. The result is a highly parallel ``relaxation'' algorithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios.

Classification of textures using Markov random field models

Abstract: Two feature extraction methods for classification of textures are presented. It is assumed that the given M × M texture is generated by a Gaussian Markov random field (GMRF) model, in the first method, the least square estimates of model parameters are used as features. In the second method, using the notion of sufficient statistics, it is shown that the sample correlations over a symmetric window including the origin are optimal features for classification. Simple minimum distance classifiers using these two feature sets yield classification accuracies of over 99% and 92% respectively for a seven class problem.

Almost Sure Convergence of Multiparameter Martingales for Markov Random Fields

Abstract: We prove that bounded multiparameter martingales converge almost surely if the underlying $\sigma$-fields are generated by a Markov random field which satisfies Dobrushin's uniqueness condition. An example shows that it is not enough to assume that the Markov field is uniquely determined by its conditional probabilities.

Bayesian Estimation of One Dimensional Discrete Markov Random Fields.

Abstract: : This document presents two deterministic algorithms for the maximum a posteriori estimation of a one dimensional, binary Markov random field from noisy observations. Extensions to other related problems, such as one dimensional signal matching, and estimation of continuous valued Markov random fields are also discussed. Finally, the author presents an experimental comparison of the performance of optimal algorithms with a stochastic approximation scheme (simulated annealing). Additional keywords: Mathematical models, Dynamic programming, Gaussian noise, White noise, Army research. (Author)