Monte Carlo methods for optimizing the piecewise constant Mumford-Shah segmentation model

Abstract

Natural images are depicted in a computer as pixels on a square grid and neighboring pixels are generally highly correlated. This representation can be mapped naturally to a statistical physics framework on a square lattice. In this paper, we developed an effective use of statistical mechanics to solve the image segmentation problem, which is an outstanding problem in image processing. Our Monte Carlo method using several advanced techniques, including blockspin transformation, Eden clustering and simulated annealing, seeks the solution of the celebrated Mumford-Shah image segmentation model. In particular, the advantage of our method is prominent for the case of multiphase segmentation. Our results verify that statistical physics can be a very efficient approach for image processing.