The Mean Field Theory in EM Procedures for Markov Random Fields

IEEE Transactions on Signal Processing

Volumn 40, Issue 10, 1992, Pages 2570-2583

  Zhang, Jun ^a  

^a UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

PARAMETER ESTIMATION; PATTERN RECOGNITION; RANDOM PROCESSES; SIGNAL PROCESSING;

BAUM'S ALGORITHM; CONDITIONAL EXPECTATIONS; EXPECTATION MAXIMIZATION; HIDDEN DATA; IMAGE SEGMENTATION; MARKOV RANDOM FIELDS; MEAN FIELD THEORY;

IMAGE PROCESSING;

EID: 0026938712     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.157297     Document Type: Article

References (29)

1. A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. Row Soc. Stat., ser. B., no. 1, pp. 1-38, 1977.
2. R. A. Redner and H. F. Walker, “Mixture densities, maximum-likelihood and the EM algorithm,” SIAM Rev., vol. 26, pp. 195-239, 1984.
3. C. W. Therrien, T. F. Quatieri, and D. E. Dudgeon, “Statistical model-based algorithms for image analysis,” Proc. IEEE, vol. 74, Apr. 1986.
4. J. Zhang and J. W. Modestino, “Markov random fields with applications to texture classification and discrimination,” in Proc. 20th Annu. Conf. Inform. Sci. Syst. (Princeton University, NJ), Mar. 1986.
5. H. Derin and H. Elliott, “Modeling and segmentation of noisy and textured images using Gibbs random fields,” IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-9, pp. 39-55, Jan. 1987.
6. F. S. Cohen and D. B. Cooper, “Simple, parallel, hierarchical, and relaxation algorithms for segmenting noncasual Markovian random field models,” Trans. IEEE Patt. Anal. Machine Intell., vol. PAMI-9, pp. 195-219, Mar. 1987.
7. P. A. Kelly. H. Derin, and K. D. Hart, “Adaptive segmentation of speckled images using a hierarchical random field model,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 36. pp. 1626-1641, Oct. 1988.
8. J. Zhang, “Two-dimensional stochastic model-based image analysis,” Ph.D. dissertation, Rensselaer Polytechnic Institute, Troy, NY, Aug. 1988.
9. J. F. Silverman and D. B. Cooper, “Bayesian clustering for unsupervised estimation of surface and texture models,” IEEE Trans. Patt. Anal. Machine Intell., vol. 10, pp. 482-485, 1988.
10. Y. Shen, “A statistical model-based approach for cluster validation with applications to image segmentation,” M.S. thesis, EECS Dep. Univ. Wisconsin-Milwaukee, Sept. 1990.
11. L. R. Rabiner, “A tutorial on hidden Markov models and selected applications in speech recognition,” Proc. IEEE, vol. 77, pp. 257-286, Feb. 1989.
12. J. Marroquin, S. Mitter, and T. Poggio, “Computer vision,” J. Amer. Stat., ASS., vol. 82, pp. 76-89, Mar. 1987.
13. L. Baum, T. Petrie, G. Soules, and N. Weiss, “A maximization technique occurring in the statistical analysis of probablistic functions of Markov chains,” Ann. Math. Stat., vol. 41, no. 1, pp. 164-171, 1970.
14. D. Geiger and F. Girosi, “Parallel and deterministic algorithms for MRF's: Surface reconstruction and integration,” AI Memo 1114, M.I.T., June 1989; also
15. IEEE Trans. Patt. Anal. Machine Intell., vol. 12, pp. 401-412, May 1991.
16. J. Zerubia and R. Chellappa, “Mean field approximation using compound Gauss-Markov random field for edge detection and image restoration,” in ICASSP'90, pp. 2193-2196.
17. A. L. Yuille, “Generalized deformable models, statistical physics, and matching problems,” Neural Comptuation, vol. 2, pp. 1-24, 1990.
18. D. Chandler, Introduction to Modern Statistical Mechanics. Oxford University Press, 1987.
19. W. Kuepper and J. Zhang, “Image interpretation using Markov random fields,” Memo. IT-1, ICSI, June 1990.
20. J. Besag, “Spatial interaction and the statistical analysis of lattice systems,” J. Roy. Stat. Soc., ser. B, vol. 36, pp. 192-226, 1974.
21. R. Kindermann and J. L. Snell, Markov Random Field and Their Applications. Providence, RI: American Mathematical Society, 1980.
22. J. Besag, “On the statistical analysis of dirty pictures,” J. Roy. Stat. Soc., ser. B, vol. 48, pp. 259-302, 1986.
23. S. Geman and D. Geman, “Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images,” IEEE Trans. Patt. Anal. Machine Intell., vol. 6, pp. 721-741, Nov. 1984.
24. S. Lakshmanan and H. Derin, “Simultaneous parameter estimation and segmentation of Gibbs random fields using simulated annealing,” IEEE Trans. Patt. Anal. Machine Intell., vol. 11, pp. 799-813, Aug. 1989.
25. J. Tou and R. Gonzalez, Pattern Recognition Principle. Reading, MA: Addison-Wesley, 1979.
26. Math/Library™, IMSL Inc., 1989.
27. J. Zhang and J. W. Modestino, “A statistical model-fitting approach to cluster validation with applications to image segmentation,” IEEE Trans. Patt. Anal. Machine Intell., pp. 1009-1016, Oct. 1990.
28. J. Zerubia and F. Ploytette, “Parallel algorithms for low level vision on a connection machine CM2,” in 13th IMACS Conf. (Dublin, Ireland), July 1991, pp. 763-765.
29. T. Simochony, R. Chellappa, and Z. Lichtenstein, “The graduated nonconvexity algorithm for image estimation using compound Gauss-Markov fields models,” in Proc. ICASSP (Glasgow, U.K.), May 1989, pp. 1417-1420.