Journal ArticleDOI
Generalized Ising models and their applications
S. Rabe,K. V. Mardia +1 more
TLDR
In this paper, three multilevel generalizations of the Ising model, including the general spin Ising Model, are described. But the normalizing constant is intractable.Abstract:
The Ising model has become more prominent in spatial statistics since its applications in image analysis, as pioneered by Besag. This paper describes three multilevel generalizations of the Ising model, including the general spin Ising model. We compare and contrast these three generalizations. In all three cases, the normalizing constant is intractable but, using the developments made by physicists, we give adequate approximations for the general spin model, together with complete expressions for the binary Ising model. We show that these approximations allow inference for the general spin model. An application to texture analysis is also given.read more
Citations
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Journal ArticleDOI
Thermodynamics of the 2-D Ising Model From a Random Path Sampling Method
TL;DR: In this article, the authors explore the thermodynamics of the 2-D Ising model from a random path sampling method and show how convergence of free energy and magnetization is obtained in a number of sweeps orders of magnitude below the number of total configurations.
Journal ArticleDOI
Modelling micro-texture
TL;DR: The paper models micro-texture using the general spin Ising model from statistical mechanics, which allows for any number of grey levels and any set of pair interactions, and estimates the correspomding parameter values.
References
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Journal ArticleDOI
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
Stuart Geman,Donald Geman +1 more
TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
Journal ArticleDOI
Crystal statistics. I. A two-dimensional model with an order-disorder transition
TL;DR: In this article, the eigenwert problem involved in the corresponding computation for a long strip crystal of finite width, joined straight to itself around a cylinder, is solved by direct product decomposition; in the special case $n=\ensuremath{\infty}$ an integral replaces a sum.
Journal ArticleDOI
On the statistical analysis of dirty pictures
TL;DR: In this paper, the authors proposed an iterative method for scene reconstruction based on a non-degenerate Markov Random Field (MRF) model, where the local characteristics of the original scene can be represented by a nondegenerate MRF and the reconstruction can be estimated according to standard criteria.
Journal ArticleDOI
The Potts model
TL;DR: In this paper, a tutorial review on the Potts model is presented aimed at bringing out the essential and important properties of the standard Potts models, focusing on exact and rigorous results, but other aspects of the problem are also described to achieve a unified perspective.