Statistical-mechanical algorithm in MRF model based on variational principle

The Markov random field (MRF) model, which is a method in the image restoration, is reformulated, based on the variational principle of the difference minimum between the original and damaged image datas, under the constraints for the area of black faces, the boundary length between the different darkness and the number of corners in the edge. Moreover, a new method is proposed for the estimation of the areas of black faces, the boundary length between the different darkness and the number of corners in the edge from only the damaged image