Zhaobao Zheng 
  
THE DECISION OF THE OPTIMAL PARAMETERS IN MARKOV RANDOM FIELDS OF 
IMAGES BY GENETIC ALGORITHM 
Zhaobao Zheng , Hong Zheng 
School of Information Engineering 
Wuhan Technical University of Surveying and Mapping 
129 Ruoyu Road, 430079, Wuhan, P.R.China 
zbzheng ? wtusm.edu.cn 
Working Group WG  /3 
KEY WORDS: Genetic algorithm, Markov Random Field, Parameter optimum, Texture classification 
ABSTRACT 
This paper introduces the principle of genetic algorithm and the basic method of solving Markov Random Field 
parameters. Focusing on the shortcoming in present methods, a new method based on genetic algorithms is proposed to 
solve the parameters in the Markov Random Field. The detail procedure is discussed in this paper. On the basis of the 
parameters solved by genetic algorithm, some experiments on classification of aerial images are given in this paper. 
Experiment results show that the proposed method is effective and the classification results are satisfied. 
1 INTRODUCTION 
Image texture is an important feature for image processing and analysis .The study in the past twenty years shows that 
Markov Random Field (MRF) is a powerful tool to describe image features. Now MRF is often used in image texture 
classification. This is because image features can be described quantificationally by a group of MRF parameters, and 
different MRF parameters represents different image textures(Zhaobao Zheng/1996, Hong Zheng/1997). So the key 
problem applying MRF in image texture classification is how to decide the optimal MRF parameters. A lot of scholars 
have been studying the problem .They attempt to configure two or three pixels around a central pixel as a group, which 
is called cliques . They think that image textures are the configurations of these cliques, and each cliques corresponds to 
a parameter . The value of the parameter reflects the attribute of the c/iques corresponding to the parameter .The larger 
the value is , the more the cliques a image texture contains. If the value is negative ,it means 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° (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 the 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 pixek 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 to decide optimal neighbors 
by genetic algorithm . Genetic algorithmis 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 detail produce to solve MRF 
parameters by genetic algorithm ,which includes encoding, decoding, crossover and mutation etc.. Experiment results 
are given to show the classification effectiveness of the method proposed in the paper . 
2 THE DECISION OF THE OPTIMAL PARAMETERS IN MRF BY GENETIC ALGORITHMS 
2.1 Overview of Genetic Algorithm 
The genetic algorithm proposed by John Holland has been recently exploited in pattern recognition problems involving 
optimization processes that provide a suitable solution in handling uncertainty in pattern analysis(D.E. Goldberg/1989). 
The genetic algorithm (GA) is an adaptive procedure that searches for good solutions by using a collection of search 
  
1048 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
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