Probabilistic inference to the problem of inverse-halftoning based on statistical mechanics of the Q-Ising model

2007 ◽  
Vol 1301 ◽  
pp. 136-139
Author(s):  
Yohei Saika
Keyword(s):  
Ising Model ◽  
Statistical Mechanics ◽  
Probabilistic Inference ◽  
Inverse Halftoning

scholarly journals Bayes-optimal solution to inverse halftoning based on statistical mechanics of the Q-Ising model

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Yohei Saika ◽  
Jun-ichi Inoue ◽  
Hiroyuki Tanaka ◽  
Masato Okada
Keyword(s):  
Ising Model ◽  
Statistical Mechanics ◽  
Optimal Solution ◽  
Grayscale Image ◽  
Inverse Process ◽  
Black And White ◽  
Numerical Result ◽  
Inverse Halftoning ◽  
The Mean ◽  
Infinite Range

AbstractOn the basis of statistical mechanics of the Q-Ising model, we formulate the Bayesian inference to the problem of inverse halftoning, which is the inverse process of representing gray-scales in images by means of black and white dots. Using Monte Carlo simulations, we investigate statistical properties of the inverse process, especially, we reveal the condition of the Bayes-optimal solution for which the mean-square error takes its minimum. The numerical result is qualitatively confirmed by analysis of the infinite-range model. As demonstrations of our approach, we apply the method to retrieve a grayscale image, such as standard image Lena, from the halftoned version. We find that the Bayes-optimal solution gives a fine restored grayscale image which is very close to the original. In addition, based on statistical mechanics of the Q-Ising model, we are sucessful in constructing a practically useful method of inverse halftoning using the Bethe approximation.

Statistical Mechanics of a Compressible Ising Model with Application to β Brass

1971 ◽  
Vol 55 (2) ◽  
pp. 861-879 ◽  
Author(s):  
George A. Baker ◽  
John W. Essam
Keyword(s):  
Ising Model ◽  
Statistical Mechanics

scholarly journals Order-disorder statistics. I

1949 ◽  
Vol 196 (1044) ◽  
pp. 36-50 ◽  
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Three Dimensional ◽  
Infinite Matrix ◽  
Characteristic Structure ◽  
Single Function ◽  
Simple Characteristic ◽  
Distant Neighbour ◽  
Function Of Two Variables

In 1941 Kramers & Wannier discussed the statistical mechanics of a two-dimensional Ising model of a ferromagnetic. By making use of a ‘screw transformation’ they showed that the partition function was the largest eigenvalue of an infinite matrix of simple characteristic structure. In the present paper an alternative method is used for deriving the partition function, and this enables the ‘screw transformation’ to be generalized to apply to a number of problems of classical statistical mechanics, including the three-dimensional Ising model. Distant neighbour interactions can also be taken into account. The relation between the ferromagnetic and order-disorder problems is discussed, and it is shown that the partition function in both cases can be derived from a single function of two variables. Since distant neighbour interactions can be taken into account the theory can be formally applied to the statistical mechanics of a system of identical particles.

Sign in / Sign up

Export Citation Format

Share Document