Statistical Mechanics of Image Restoration by the Plane Rotator Model

Abstract

On the basis of statistical mechanics formulation for problems of image restoration and errorcorrecting codes, we propose a new technique of image restoration for a binary image using the plane rotator model. In our formulation, the restored image is obtained from the equilibrium state of a ferromagnetic plane rotator model under a random field which consists of the corrupted image at finite temperature. The validity of our technique is evaluated by the dependence of overlap on the hyperparameters using the replica symmetric theory for the infinite-range model. The theory shows that our technique achieves the same optimal performance with that by the Ising spins. This statement is qualitatively confirmed by Monte Carlo simulations for two-dimensional images. Furthermore we estimate the dynamics of our technique by using Monte Carlo simulations. The simulations reveal that the convergence to the restored image is faster than that by the Ising model at low temperature.

Coupled Markov random field models with phases as line field and region field

“…When the summation with respect to the intensity is first taken in Eqs. (7) to (9) and ρ(u) = ∑ x ρ(x, u) is taken into account, it turns out that ρ(u) has a four-body interaction for line variables u ij , which implies that the interaction between line fields is indirectly included by the model. In spite of this situation, the results in the numerical experiments in the present paper indicate that the RCMRF model has better performance.…”

“…On the other hand, it is proposed to extend discrete states at each pixel to a continuous state in order to avoid local minima [5]. Saika and Nishimori [6,7] introduced a plane rotator model, as one © 2003 Wiley Periodicals, Inc.…”

Efficient and Scalable Approach to Equilibrium Conditional Simulation of Gibbs Markov Random Fields

“…Binary-valued Ising spin models, the q-state Potts model, and the continuous planar rotator are typical NGMRF examples. Widely studied in statistical physics, they have also found applications in areas such as image restoration [3][4][5] and spatial prediction [6].…”

Gibbs Markov random fields with continuous values based on the modified planar rotator model

“…This paper presents a novel Gibbs Markov random field for spatial processes that take continuous values in a closed subset of the real numbers. The NGMRF is based on the parametric planar rotator spin model from statistical physics, which has successfully been applied to binary image restoration [36]. The spatial prediction method proposed herein was prompted by our recent study which revealed that a suitably modified planar rotator model changes its low-temperature quasi-critical behavior (which is characterized by power-law decaying correlation function) to a regime characterized by a flexible short-range spatial correlation function [37].…”