A fuzzy clustering approach toward Hidden Markov random field models for enhanced spatially constrained image segmentation

IEEE Transactions on Fuzzy Systems

Volumn 16, Issue 5, 2008, Pages 1351-1361

  Chatzis, Sotirios P ^a   Varvarigou, Theodora A ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Fuzzy clustering; Hidden Markov models; Image segmentation; Mean field approximation

Indexed keywords

APPLICATIONS; DIGITAL IMAGE STORAGE; FLOW OF SOLIDS; FUZZY RULES; FUZZY SETS; FUZZY SYSTEMS; HIDDEN MARKOV MODELS; IMAGE PROCESSING; IMAGE SEGMENTATION; MARKOV PROCESSES; POLYNOMIAL APPROXIMATION; SPEECH RECOGNITION;

CLUSTERING; CLUSTERING APPROACHES; CLUSTERING PROBLEMS; CLUSTERING PROCEDURES; CONSTRAINED CLUSTERING; FUZZY C-MEANS; FUZZY OBJECTIVE FUNCTIONS; HIDDEN MARKOV RANDOM FIELD MODELS; HMRF MODELS; MEAN-FIELD APPROXIMATION;

FUZZY CLUSTERING;

EID: 54349092861     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2008.2005008     Document Type: Article

References (43)

1. G. Winkler, Image Analysis, Random Fields, and Markov Chain Monte Carlo Methods, 2nd ed. (Stochastic Modeling and Applied Probability Series). Berlin, Germany: Springer-Verlag, 2006.
2. W. Qian and D. Titterington, "Parameters estimation for hidden Gibbs chains," Stat. Probab. Lett., vol. 10, pp. 49-58, 1990.
3. J. Besag, "On the statistical analysis of dirty pictures," J. Roy. Stat. Soc. B, vol. 48, pp. 259-302, 1986.
4. S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images," IEEE Trans. Pattern Anal. Mach. Intell., vol. PAMI-6, no. 6, pp. 721-741, Nov. 1984.
5. J. Besag, "Statistical analysis of nonlattice data," Statistician vol. 24, pp. 179-195, 1975.
6. W. Qian and D. Titterington, "Estimation of parameters in hidden Markov models," Philos. Trans. Roy. Soc. London A, vol. 337, pp. 407-428, 1991.
7. N. Hjort, E. Mohn, and G. Storvik, "A simulation study of some contextual classification methods for remotely sensed data," IEEE Trans. Geosci. Electron., vol. GE-25, no. 6, pp. 796-804, Nov. 1987.
8. A. P. Dunmur and D. Titterington, "Parameter estimation in latent profile models," Comput. Stat. Data Anal., pp. 371-388, 2007.
9. G. Celeux, F. Forbes, and N. Peyrard, "EM procedures using mean field-like approximations for Markov model-based image segmentation," Pattern Recognit., vol. 36, no. 1, pp. 131-144, 2003.
10. L. Zadeh, "Fuzzy sets," Inf. Control, vol. 8, pp. 338-353, 1965.
11. J. Bezdek, Pattern Recognition With Fuzzy Objective Function Algorithms. New York: Plenum, 1981.
12. J. C. Bezdek, N. R. Pal, J. Keller, and R. Krishnapuram, Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Norwell, MA: Kluwer, 1999.
13. S. Chen and D. Zhang, "Robust image segmentation using FCM with spatial constraints based on new Kernel-induced distance measure," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 34, no. 4, pp. 1907-1916, Aug. 2004.
14. D. Pham and J. L. Prince, "An adaptive fuzzy c-means algorithm for image segmentation in the presence of intensity inhomogeneities," Pattern Recognit. Lett., vol. 20, pp. 57-68, 1999.
15. J. Leski, "Toward a robust fuzzy clustering," Fuzzy Sets Syst., vol. 137, no. 2, pp. 215-233, 2003.
16. p norm distances," IEEE Trans. Fuzzy Syst., vol. 8, no. 5, pp. 576-582, Oct. 2000.
17. J. Leski, "An ε-insensitive approach to fuzzy clustering," Int. J. Appl. Math. Comput. Sci., vol. 11, no. 4, pp. 993-1007, 2001.
18. S. Chatzis and T. Varvarigou, "Factor analysis latent subspace modeling and robust fuzzy clustering using t distributions," IEEE Trans. Fuzzy Syst., to be published.
19. N. R. Pal, K. Pal, J. M. Keller, and J. Bezdek, "A possibilistic fuzzy c-means clustering algorithm," IEEE Trans. Fuzzy Syst., vol. 13, no. 4, pp. 517-530, Aug. 2005.
20. F. Masulli and S. Rovetta, "Soft transition from probabilistic to possibilistic fuzzy clustering," IEEE Trans. Fuzzy Syst., vol. 14, no. 4, pp. 516-527, Aug. 2006.
21. J. Yu and M. S. Yang, "A generalized fuzzy clustering regularization model with optimality tests and model complexity analysis," IEEE Trans. Fuzzy Syst., vol. 15, no. 5, pp. 904-915, Oct. 2007.
22. S. Nefti, M. Oussalah, and U. Kaymak, "A new fuzzy set merging technique using inclusion-based fuzzy clustering," IEEE Trans. Fuzzy Syst., vol. 16, no. 1, pp. 145-161, Feb. 2008.
23. M. N. Ahmed, S. M. Yamany, N. Mohamed, A. A. Farag, and T. Moriarty, "A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data," IEEE Trans. Med. Imag., vol. 21, no. 3, pp. 193-199, Mar. 2002.
24. Y. A. Tolias and S. M. Panas, "Image segmentation by a fuzzy clustering algorithm using adaptive spatially constrained membership functions," IEEE Trans. Syst., Man, Cybern. A, Syst. Humans, vol. 28, no. 3, pp. 359-369, May 1998.
25. D. L. Pham, "Fuzzy clustering with spatial constraints," in Proc. IEEE Int. Conf. Image Process., 2002, vol. 2, pp. 65-68.
26. A.-C. Liew, H. Yan, and N. F. Law, "Image segmentation based on adaptive cluster prototype estimation," IEEE Trans. Fuzzy Syst., vol. 13, no. 4, pp. 444-453, Aug. 2005.
27. J. Maroquin, S. Mitte, and T. Poggio, "Probabilistic solution of ill-posed problems in computational vision," J. Amer. Stat. Assoc. vol. 82, pp. 76-89, 1987.
28. P. Clifford, "Markov random fields in statistics," in Disorder in Physical Systems. A Volume in Honour of John M. Hammersley on the Occasion of his 70th Birthday, G. Grimmett and D. Welsh, Eds. Oxford, U.K.: Clarendon, 1990.
29. G. McLachlan and D. Peel, Finite Mixture Models (Probability and Statistics Series). New York: Wiley, 2000.
30. Y. Zhang, M. Brady, and S. Smith, "Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm," IEEE Trans. Med. Imag., vol. 20, no. 1, pp. 45-57, Jan. 2001.
31. S. Geman and C. Graffigne, "Markov random field image models and their applications to computer vision," in Proc. Int. Conf. Math. Providence, RI: Amer. Math. Soc., 1987, pp. 1498-1517.
32. B. Chalmond, "An iterative Gibbsian technique for reconstruction of m-ary images," Pattern Recognit., vol. 22, no. 6, pp. 747-761, 1989.
33. J. Zhang, "The mean field theory in EM procedures for Markov random fields," IEEE Trans. Image Process., vol. 2, no. 1, pp. 27-40, Jan. 1993.
34. D. Chandler, Introduction to Modern Statistical Mechanics. New York: Oxford Univ. Press, 1987.
35. F. Forbes and N. Peyrard, "Hidden Markov random field model selection criteria based on mean field-like approximations," IEEE Trans. Pattern Anal. Mach. Intell., vol. 25, no. 9, pp. 1089-1101, Sep. 2003.
36. S. Miyamoto and M. Mukaidono, "Fuzzy c-means as a regularization and maximum entropy approach," in Proc. 7th Int. Fuzzy Syst. Assoc. World Congr., 1997, vol. 2, pp. 86-92.
37. H. Ichihashi, K. Miyagishi, and K. Honda, "Fuzzy c-means clustering with regularization by K-L information," in Proc. 10th IEEE Int. Conf. Fuzzy Syst., 2001, pp. 924-927.
38. E. Ruspini, "A new approach to clustering," Inf. Control, vol. 15, pp. 22-32, 1969.
39. C. Nikou, N. Galatsanos, and A. Likas, "A class-adaptive spatially variant mixture model for image segmentation," IEEE Trans. Image Process., vol. 16, no. 4, pp. 1121-1130, Apr. 2007.
40. D. C. Stanford, "Fast automatic unsupervised image segmentation and curve detection in spatial point pattern," Ph.D. dissertation, Dept. Stat., Univ. Washington, Seattle, 1999.
41. D. Martin, C. Fowlkes, D. Tal, and J. Malik, "A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics," in Proc. 8th IEEE Int. Conf. Comput. Vis., Vancouver, BC, Canada, 2001, vol. 2, pp. 416-423.
42. R. Unnikrishnan, C. Pantofaru, and M. Hebert, "A measure for objective evaluation of image segmentation algorithms," in Proc. IEEE Conf. Comput. Vis. Pattern Recognit. Jun. 20-26, 2005, vol. 3, pp. 34-41.
43. R. Unnikrishnan and M. Hebert, "Measures of similarity," in Proc. IEEE Workshop Comput. Vis. Appl., Jan. 2005, pp. 394-400.