This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Unsupervised Segmentation of Markov Random Field Modeled Textured Images Using Selectionist Relaxation
March 1998 (vol. 20 no. 3)
pp. 252-262

Abstract—Among the existing texture segmentation methods, those relying on Markov random fields have retained substantial interest and have proved to be very efficient in supervised mode. The use of Markov random fields in unsupervised mode is, however, hampered by the parameter estimation problem. The recent solutions proposed to overcome this difficulty rely on assumptions about the shapes of the textured regions or about the number of textures in the input image that may not be satisfied in practice. In this paper, an evolutionary approach, selectionist relaxation, is proposed as a solution to the problem of segmenting Markov random field modeled textures in unsupervised mode. In selectionist relaxation, the computation is distributed among a population of units that iteratively evolves according to simple and local evolutionary rules. A unit is an association between a label and a texture parameter vector. The units whose likelihood is high are allowed to spread over the image and to replace the units that receive lower support from the data. Consequently, some labels are growing while others are eliminated. Starting with an initial random population, this evolutionary process eventually results in a stable labelization of the image, which is taken as the segmentation. In this work, the generalized Ising model is used to represent textured data. Because of the awkward nature of the partition function in this model, a high-temperature approximation is introduced to allow the evaluation of unit likelihoods. Experimental results on images containing various synthetic and natural textures are reported.

[1] T.R. Reed and H.J.M. du Buf, "A Review of Recent Texture Segmentation and Feature Extraction Techniques," CVGIP: Image Understanding, vol. 57, no. 3, pp. 359-372, 1993.
[2] R. Kindermann and J.L. Snell, "Markov Random Fields and Their Applications," Contemporary Mathematics, vol. 1. Providence, R.I.: Am. Math. Soc., 1980.
[3] R.C. Dubes and A.K. Jain, "Random Field Models in Image Analysis," J. Applied Statistics, vol. 16, no. 2, pp. 131-164, 1989.
[4] G.R. Cross and A.K. Jain, "Markov Random Field Texture Models," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 5, no. 1, pp. 25-39, Jan. 1983.
[5] R. Chellappa, S. Chatterjee, and R. Bagdazian, "Texture Synthesis and Compression Using Gaussian-Markov Random Field Models," IEEE Trans. Systems, Man, and Cybernetics, vol. 15, no. 2, pp. 298-303, 1985.
[6] R. Chellappa and S. Chatterjee, "Classification of Textures Using Gaussian Markov Random Fields," IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 33, pp. 959-963, 1985.
[7] F.S. Cohen and D.B. Cooper, "Simple Parallel Hierarchical and Relaxation Algorithms for Segmenting Noncausal Markovian Random Fields," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, no. 2, pp. 195-219, 1987.
[8] H. Derin and W.S. Cole, "Segmentation of Textured Images Using Gibbs Random Fields," Computer Vision, Graphics, and Image Processing, vol. 35, pp. 72-98, 1986.
[9] H. Derin and H. Elliott, "Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, no. 1, pp. 39-55, Jan. 1987.
[10] B.S. Manjunath, T. Simchony, and R. Chellappa, "Stochastic and Deterministic Networks for Texture Segmentation," IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 38, no. 6, pp. 1,039-1,049, 1990.
[11] S. Geman and D. Geman, "Stochastic Relaxation, Gibbs Distributions, and theBayesian Restoration of Images," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 6, pp. 721-741, Nov. 1984.
[12] B.S. Manjunath and R. Chellappa, “Unsupervised Texture Segmentation Using Markov Random Field Models,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, pp. 478-482, 1991.
[13] R. Hu and M.M. Fahmy, "Texture Segmentation Based on a Hierarchical Markov Random Field Model," Signal Processing, vol. 26, pp. 285-305, 1992.
[14] F.S. Cohen and Z. Fan, "Maximum Likelihood Unsupervised Textured Image Segmentation," CVGIP: Graphical Models and Image Processing, vol. 54, no. 3, pp. 239-251, 1992.
[15] H.H. Nguyen and P. Cohen, "Gibbs Random Fields, Fuzzy Clustering, and the Unsupervised Segmentation of Textured Images," CVGIP: Graphical Models and Image Processing, vol. 55, no. 1, pp. 1-19, 1993.
[16] S. Lakshmanan and H. Derin, “Simultaneous Parameter Estimation and Segmentation of Gibbs Random Fields Using Simulated Annealing,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, pp. 799-813, 1989.
[17] C.S. Won and H. Derin, "Unsupervised Segmentation of Noisy and Textured Images Using Markov Random Fields," CVGIP: Graphical Models and Image Processing, vol. 54, no. 4, pp. 308-328, 1992.
[18] J.H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis With Applications to Biology, Control, and Artificial Intelligence.Cambridge, Mass.: MIT Press/A Bradford Book, 1992.
[19] D.E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning.Reading, Mass.: Addison Wesley, 1989.
[20] R. Tanese, "Distributed Genetic Algorithms," Proc. Third Int'l Conf. Genetic Algorithms, J.D. Schaffer, ed., pp. 434-439.San Mateo, Calif.: Morgan Kaufmann, 1989.
[21] J.P. Cohoon, S.U. Hegde, W.N. Martin, and D.S. Richards, "Distributed Genetic Algorithms for the Floorplan Design Problem," IEEE Trans. Computer-Aided Design, vol. 10, no. 4, pp. 483-491, Apr. 1991.
[22] H. Mühlenbein, "Parallel Genetic Algorithms, Population Genetics and Combinatorial Optimization," Proc. Third Int'l Conf. Genetic Algorithms, J.D. Schaffer, ed., pp. 416-421.San Mateo, Calif.: Morgan Kaufmann, 1989.
[23] B. Manderick and P. Spiessens, "Fine-Grained Parallel Genetic Algorithms," Proc. Third Int'l Conf. Genetic Algorithms, J.D. Schaffer, ed., pp. 428-433.San Mateo, Calif.: Morgan Kaufmann, 1989.
[24] P. Spiessens and B. Manderick, "A Massively Parallel Genetic Algorithm. Implementation and First Analysis," Proc. Fourth Int'l Conf. Genetic Algorithms, R.K. Belew and L.B. Booker, eds., pp. 279-286.San Mateo, Calif.: Morgan Kaufmann, 1991.
[25] R.J. Collins, "Studies in Artificial Evolution," PhD thesis, Univ. of California, Los Angeles, 1992.
[26] P. Andrey and P. Tarroux, "Unsupervised Image Segmentation Using a Distributed Genetic Algorithm," Pattern Recognition, vol. 27, no. 5, pp. 659-673, 1994.
[27] M. Hassner and J. Sklansky, "The Use of Markov Random Fields as Models of Texture," Computer Graphics and Image Processing, vol. 12, pp. 357-370, 1980.
[28] R. Chellappa, "Two-Dimensional Discrete Gaussian Markov Random Field Models for Image Processing," Progress in Pattern Recognition 2. L.N. Kanal and A. Rosenfeld, eds., pp. 79-112.New York: North-Holland,Elsevier Science Publishers, 1985.
[29] G.L. Gimel'farb and A.V. Zalesny, "Probabilistic Models of Digital Region Maps Based on Markov Random Fields With Short- and Long-Range Interaction," Pattern Recognition Letters, vol. 14, pp. 789-797, 1993.
[30] J. Besag, "Spatial Interaction and the Statistical Analysis of Lattice Systems," J. Royal Statistical Soc., Series B, vol. 36, pp. 192-236, 1974.
[31] D.E. Goldberg and K. Deb, "A Comparative Analysis of Selection Schemes Used in Genetic Algorithms," Foundations of Genetic Algorithms, G.J. Rawlins, ed., pp. 69-93.San Mateo, Calif.: Morgan Kaufmann, 1991.
[32] G. Syswerda, "Uniform Crossover in Genetic Algorithms," Proc. Third Int'l Conf. Genetic Algorithms, J.D. Schaffer, ed., pp. 2-9.San Mateo, Calif.: Morgan Kaufmann, 1989.
[33] J. Besag, "On the Statistical Analysis of Dirty Pictures," J. Royal Statistical Soc., Series B, vol. 48, no. 3, pp. 259-302, 1986.
[34] C.-C. Chen and C.-L. Huang, "Markov Random Fields for Texture Classification," Pattern Recognition Letters, vol. 14, pp. 907-914, 1993.

Index Terms:
Unsupervised texture segmentation, Markov/Gibbs random fields, partition function approximation, genetic algorithms, selectionist relaxation.
Citation:
Philippe Andrey, Philippe Tarroux, "Unsupervised Segmentation of Markov Random Field Modeled Textured Images Using Selectionist Relaxation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 3, pp. 252-262, March 1998, doi:10.1109/34.667883
Usage of this product signifies your acceptance of the Terms of Use.