Cluster validation for unsupervised stochastic model-based image segmentation

IEEE Transactions on Image Processing

Volumn 7, Issue 2, 1998, Pages 180-195

  Langan, David A ^b   Modestino, James W ^a,c   Zhang, Jun ^a,d  

^a IEEE

^b GENERAL ELECTRIC COMPANY   (United States)

^c RENSSELAER POLYTECHNIC INSTITUTE   (United States)

^d University of Wisconsin Milwaukee   (United States)

Author keywords

Clustering methods; Image analysis; Image classification; Image processing; Image segmentation; Markov processes; Maximum likelihood estimation; Stochastic fields

Indexed keywords

ALGORITHMS; FUNCTIONS; IMAGE ANALYSIS; INFORMATION THEORY; MARKOV PROCESSES; MATHEMATICAL MODELS; PROBLEM SOLVING; VECTORS;

CLUSTER VALIDATION PROBLEM; EXPECTATION MAXIMIZATION (EM) ALGORITHM; MAXIMUM LIKELIHOOD ESTIMATION (MLE);

IMAGE SEGMENTATION;

EID: 0031996422     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.660995     Document Type: Article

References (39)

1. R. M. Haralick, "Statistical and structural approaches to texture," Proc. IEEE, vol. 67, pp. 786-804, May 1979.
2. J. W. Modestino, R. W. Fries, and A. L. Vickers, "Texture discrimination based upon an assumed stochastic texture model," IEEE Trans. Pattern Anal. Machine Intell., vol. 3, pp. 557-580, Sept. 1981.
3. C. W. Therrien, T. F. Quatieri, and D. E. Dudgeon, "Statistical model-based algorithms for image analysis," in Proc. IEEE, Apr. 1986, vol. 74, pp. 532-551.
4. H. Derin and H. Elliott, "Modeling and segmentation of noisy and textured images using gibbs random fields," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, no. 1, pp. 39-55, Jan. 1987.
5. F. S. Cohen and D. B. Cooper, "Simple, parallel, hierarchical, and relaxation algorithms for segmenting noncausal Markovian random field models," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, pp. 195-219, Mar. 1987.
6. 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. 1628-1641, Oct. 1988.
7. J. Zhang, "Two-dimensional stochastic model-based image analysis," Ph.D. dissertation, Electr., Comput., Syst. Eng. Dept., Rensselaer Polytech. Inst., Troy, NY, Aug. 1988.
8. J. F. Silverman and D. B. Cooper, "Bayesian clustering for unsupervised estimation of surface and texture models," IEEE Trans. Pattern Anal. Machine Intell., vol. 10, pp. 482-485, July 1988.
9. Y. Shen, "Cluster validation with applications to image segmentation," Masters thesis, Electr. Eng. Comput. Sci. Dept., Univ. Wisconsin, Milwaukee, WI, Aug. 1990.
10. D. A. Langan, "Application of the EM algorithn to unsupervised stochastic model-based image segmentation and validation," Ph.D. dissertation, Rensselaer Polytechnic Inst., Troy, NY, Aug. 1993.
11. J. Zhang, J. W. Modestino, and D. A. Langan, "Maximum-likelihood parameter estimation for unsupervised stochastic model-based image segmentation," IEEE Trans. Image Processing, vol. 3, pp. 403-419, July 1994.
12. C. S. Won and H. Derin, "Unsupervised segmentation of noisy and textured images using markov random fields," CVGIP: Graph. Models Image Processing, vol. 54, pp. 308-328, July 1992.
13. G. R. Cross and A. K. Jain, "Markov random field texture models," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-5, pp. 25-39, Jan. 1983.
14. R. Chellapa, "Two-dimensional discrete Gaussian Markov random field models for image processing," in Progress in Pattern Recognition, L. Kanal and A. Rosenfeld, Eds. Amsterdam, The Netherlands: North-Holland, 1985, vol. 2, pp. 79-112.
15. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," J. Roy. Stat., vol. 39, pp. 1-38, 1977.
16. D. A. Langan, K. J. Molnar, J. W. Modestino, and J. Zhang, "Use of the mean-field approximation in an em-based approach to unsupervised stochastic model-based image segmentation," in IEEE Int. Conf. Acoustics, Speech, and Signal Processing, Mar. 1992, vol. III, pp. 57-60.
17. R. O. Duda and P. E. Hart, Classification and Scene Analysis. New York: Wiley, 1973.
18. D. M. Titterington, A. F. M. Smith, and U. E. Makov, Statistical Analysis of Finite Mixture Distributions. New York: Wiley, 1985.
19. C. W. Therrien, Decision Estimation and Classification. New York: Wiley, 1989.
20. H. Akaike, "A new look at the statistical model identification," IEEE Trans. Automat. Contr., vol. AC-19, Dec. 1974.
21. J. Rissanen, "Modeling by shortest data description," Automatica, vol. 14, pp. 465-471, 1978.
22. N. Merhav, "The estimation of the model order in exponential families," IEEE Trans. Inform. Theory, vol. 35, Sept. 1989.
23. D. A. Langan, K. J. Molnar, J. W. Modestino, and J. Zhang, "Application of mean-field MRF state estimation and a divergence-based stopping criterion to an EM-based approach for unsupervised stochastic model-based image segmentation," Tech. Rep., Ctr. Image Proc. Res. (CIPR), Rensselaer Polytech. Inst., Aug. 1993.
24. D. Geiger and F. Girosi, "Parallel and deterministic algorithms for MRFS: Surface reconstruction and integration," A. I. Memo 1114, Mass. Inst. Technol. Artific. Intell. Lab. and Ctr. Biol. Inform. Processing, Whitaker College, June 1989.
25. S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 721-741, Nov. 1984.
26. S. Lakshmanan and H. Derin, "Simultaneous parameter estimation and segmentation of Gibbs random fields using simulated annealing," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-11, no. 8, pp. 799-813, 1989.
27. R. A. Redner and H. F. Walker, "Mixture densities, maximum likelihood, and the EM algorithm," SIAM Rev., vol. 26, pp. 195-239, Apr. 1984.
28. H. Stark and J. W. Woods, Probability, Random Processes, and Estimation Theory for Engineers. Englewood Cliffs, NJ: Prentice-Hall, 1986.
29. M. Aitkin and D. B. Rubin, "Estimation and hypothesis testing in finite mixture models," J. R. Stat. Soc. B., pp. 67-75, 1985.
30. J. Zhang and J. W. Modestino, "A model-fitting approach to cluster validation with application to stochastic model-based image segmentation," IEEE Trans. Pattern Recognit. Machine Intell., vol. 12, pp. 1009-1017, Oct. 1990.
31. S. L. Sclove, "Application of model-selection criteria to some problems in multivariate analysis," Psychometrika, vol. 52, pp. 333-343, 1987.
32. H. Akaike, "On entropy maximization principle," in Applications of Statistics, P. R. Krishnaiah, Ed. Amsterdam, The Netherlands: North-Holland, 1977.
33. R. J. Bhansali, "A derivation of the information criteria for selecting autoregressive models," Adv. Appl. Prob., vol. 18, pp. 360-387, 1986.
34. R. L. Kashyap, "Inconsistency of the AIC rule for estimating the order of autoregressive models," IEEE Trans. Automat. Contr., vol. AC-25, no. 5, 1980.
35. S. L. Sclove, "Application of the conditional population-mixture model to image segmentation," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-5, pp. 428-433, July 1983.
36. G. Schwarz, "Estimating the dimension of a model," Ann. Stat., vol. 6, pp. 461-464, 1978.
37. N. Merhav, M. Gutman, and J. Ziv, "On the estimation of the model order of a Markov chain and universal data compression," IEEE Trans. Inform. Theory, vol. 35, pp. 1014-1019, Sept. 1989.
38. H. L. Van Trees, Detection, Estimation and Modulation Theory. New York: Wiley, 1968, vol. 1.
39. J. Besag, "On the statistical analysis of dirty pictures," J. R. Stat Soc. B, vol. 48, pp. 259-302, 1986.