Abstract：It’s difficult to estimate the parameters in Markov Random Field (MRF) due to the computationally intractable partition function when using Markov random field as the prior model of image in Bayesian method. So a new method based on Evolutionary Programming (EP) is presented to estimate these parameters in this paper. This method employs evolutionary programming to search for the suited parameters, from which the most similar simulated image of the original 〗image can be obtained. Using this method, the calculation of the computationally intractable partition function can be avoided. Moreover, the most similar (even the entirely identical) simulated image of the original image can be obtained, which makes this method better than other traditional methods based on the likelihood function. Finally, this method is verified by experimental results.
[1] Besag J. Spatial Interactions and the Statistical Analysis of Lattice Systems. Journal of the Royal Statistical Society (Series B), 1974, 36(2): 192-236 [2] Derin H, Elliott H. Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields. IEEE Trans on Pattern Analysis and Machine Intelligence, 1987, 9(1): 39-55 [3] Lu M J, Wang R S. Reliable Image Segmentation Based on Markov Random Field Model. Acta Electronica Sinica, 1999, 27(2): 87-89 (in Chinese) (陆明俊, 王润生. 基于MRF模型的可靠的图像分割. 电子学报, 1999, 27(2): 87-89) [4] Liu W Q, Chen H, Xia D S. Markov Random Field Based Fast Segmentation. Journal of Image and Graphics, 2001, 6(3): 228-233 (in Chinese) (刘伟强, 陈 鸿, 夏德深. 基于马尔可夫随机场的快速图像分割. 中国图像图形学报, 2001, 6(3): 228-233) [5] Rmillard B, Beaudoin C. Statistical Comparison of Images Using Gibbs Random Fields. In: Proc of the Conference on Vision Interface. Trois-Rivires, Canada, 1999, 424-431 [6] Geman S, Geman D. Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images. IEEE Trans on Pattern Analysis and Machine Intelligence, 1984, 6(6): 721-741 [7] Figueiredo M, Leito J. Unsupervised Image Restoration and Edge Location Using Compound Gauss Markov Random Fields and the MDL Principle. IEEE Trans on Image Processing, 1997, 6(8): 1089-1102 [8] Yang W J, Liu H X, Wang Z M, Qin L. The Application of Markov Random Fields Method to Restoration of Gray-Scale Image. Signal Processing, 1998, 14(3): 255-264 (in Chinese) (杨文杰, 刘浩学, 王子美, 秦 炼. Markov随机场方法在灰度图像恢复中的应用. 信号处理, 1998, 14(3): 255-264) [9] Saquib S S, Bouman C A, Sauer K. ML Parameter Estimation for Markov Random Fields with Applications to Bayesian Tomography. IEEE Trans on Image Processing, 1998, 7(7): 1029-1044 [10] Besag J. Statistical Analysis of Non-Lattice Data. The Statistician, 1975, 24(3): 179-195 [11] Forbes F, Peyrard N. Hidden Markov Random Field Model Selection Criteria Based on Mean Field-Like Approximations. IEEE Trans on Pattern Analysis and Machine Intelligence, 2003, 25(9): 1089-1101 [12] Zhou Z Y, Leahy R M, Qi J Y. Approximate Maximum Likelihood Hyperparameter Estimation for Gibbs Priors. IEEE Trans on Image Processing, 1997, 6(6): 844-861 [13] Descombes X, Morris R, Zerubia J, Berthod M. Estimation of Markov Random Field Prior Parameters Using Markov Chain Monte Carlo Maximum Likelihood. IEEE Trans on Image Processing, 1999, 8(7): 954-963 [14] Moller J. Aspects of Spatial Statistics Stochastic Geometry and Markov Chain Monte Carlo Methods. Ph.D Dissertation. Faculty of Engineering and Science, Aalborg University, Aalborg, Denmark, 1998 [15] El-Baz A, Farag A A. Parameter Estimation in Gibbs-Markov Image Models. In: Proc of the 6th International Conference on Information Fusion. Queensland, Australia, 2003, 934-942 [16] Bouman C, Sauer K. A Generalized Gaussian Image Model for Edge-Preserving MAP Estimation. IEEE Trans on Image Processing, 1993, 2(3): 296-310 [17] Mao S S, Wang J L, Pu X L. Advanced Mathematical Statistics. Beijing, China: Higher Education Press, 1998 (in Chinese) (茆诗松, 王静龙, 濮晓龙. 高等数理统计. 北京: 高等教育出版社, 1998) [18] Yun Q X. Evolution Algorithm. Beijing, China: Metallurgical Industry Press, 2000 (in Chinese) (云庆夏. 进化算法. 北京: 冶金工业出版社, 2000)
2006, Vol. 19 
