The Decision of the Optimal Parameters in Markov Random Fields of Images by Genetic Algorithm

This paper introduces the principle of genetic algorithm and the basic method for solving Markov random field parameters.The study in the past twenty years showed that Markov random field (MRF) is a powerful tool to discribe image features.Now MRF is often used in image texture classification.This is because image feature can be described quantificationally by a group of MRF parameters, and different MRF parameters represent different image textures.So the key problem of applying MRF to image texture classification is how to decide the optimal MRF parameters.Many Scientists have been studying the problem.They attempt to configure two or three pixels around a central pixel as group, which is called cliques.They think that image textures are configurations of these cliques, and each clique corresponds to a parameter.The value of the parameter reflects the attribute of the cliques corresponding to the parameter.The larger the value is, the more cliques an image texture contains.If the value is negative, it means that the cliques will restrain image textures.Virtually, the decision of the optimal parameters is to decide the optimal configuration of cliques.For a 256 level gray image, the number of configures may be 256 8(two-order MRF).The number is so large that it is difficult to find the optimal configuration.In addition, the textures of aerial images are too complex to be described by simple cliques.According to our study, they should be described by five-order MRF.In this case, the number of neighbors is 24, and each neighbor pixel corresponds to a parameter whose value reflects the relation between the neighbor and its central pixel.The relation can be expressed as a relation function about central pixels and their neighbors.Theoretically, parameter can be computed from the function by the least square method.But, for a 256 level gray image, because the gray values corresponding to two or three parameters in the function may be same or close, the function may have no solution.In order to solve the problem, this paper presents the genetic algorithm to decide optimal neighbors.Genetic algorithm is a global optimal algorithm.It has robust, fast and parallel features.This paper regards the sum of square of residuals as fitting function and discusses the detailed produce to solve MRF parameters by genetic algorithm, which includes encoding, decoding, crossover and mutation, etc.Experimental results are given to show the classification effectiveness of the method proposed in the paper.