Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn PAMI-6, Issue 6, 1984, Pages 721-741

  Geman, Stuart ^a   Geman, Donald ^b  

^a BROWN UNIVERSITY   (United States)

^b UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

Annealing; Gibbs distribution; image restoration; line process; MAP estimate; Markov random field; relaxation scene modeling; spatial degradation

Indexed keywords

BAYESIAN RESTORATION; GIBBS DISTRIBUTIONS; STOCHASTIC RELAXATION;

IMAGE PROCESSING;

EID: 0021518209     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.1984.4767596     Document Type: Article

References (31)

1. K. Abend, T. J. Harley, and L. N. Kanal, “Classification of binary random patterns,” IEEE Trans. Inform. Theory, vol. IT-11, pp. 538–544, 1965.
2. H. C. Andrews and B. R. Hunt, Digital Image Restoration. Englewood Cliffs, NJ, Prentice-Hall, 1977.
3. M. S. Bartlett, The Statistical Analysis of Spatial Pattern. London: Chapman and Hall, 1976.
4. T. Berger and F. Bonomi, “Parallel updating of certain Markov random fields,” preprint.
5. J. Besag, “Nearest-neighbor systems and the auto-logistic model for binary data,” J. Royal Statist. Soc., series B, vol. 34, pp. 75-83,1972.
6. J. Besag, “Spatial interaction and the statistical analysis of lattice systems (with discussion),” J. Royal Statist. Soc., series B, vol. 36, pp.192-326,1974.
7. A. B. Bortz, M. H. Kalos, and J. L. Lebowitz, “A new algorithm for Monte Carlo simulation of Ising spin systems,” J. Comp. Phys., vol. 17, pp. 10-18,1975.
8. V. Cerny, “A thermodynamical approach to the travelling salesman problem: an efficient simulation algorithm,” preprint, Inst. Phys. & Biophys., Comenius Univ., Bratislava, 1982.
9. P. Cheeseman, “A method of computing maximum entropy probability values for expert systems,” preprint.
10. R. Chellappa and R. L. Kashyap, “Digital image restoration using spatial interaction models,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-30, 461–472, 1982.
11. D. B. Cooper and F. P. Sung, “Multiple-window parallel adaptive boundary finding in computer vision,” IEEE Trans. Pattern Anal. Machine Intell. vol. PAMI-5, pp. 299-316,1983.
12. G. C. Cross and A. K. Jain, “Markov random field texture models” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-5
13. L. S. Davis and A. Rosenfeld, “Cooperating processes for low-level vision: A survey,” 1980.
14. H. Derin, H. Elliott, R. Christi, and D. Geman, “Bayes smoothing algorithms for segmentation of images modelled by Markov random fields,” Univ. Massachusetts Tech. Rep., Aug. 1983.
15. R. L. Dobrushin, “The description of a random field by means of conditional probabilities and conditions of its regularity,” Theory Prob. App!,vol. 13, pp. 197-224,1968.
16. H. Elliott, H. Derin, R. Christi, and D. Geman, “Application of the Gibbs distribution to image segmentation,” Univ. Massachusetts Tech. Rep., Aug. 1983.
17. H. Elliott, F. R. Hansen, L. Srinivasan, and M. F. Tenorio, “Application of MAP estimation techniques to image segmentation,” Univ. Massachusetts Tech. Rep., 1982.
18. P. A. Flinn, “Monte Carlo calculation of phase separation in a 2-dimensional Ising system,” J. Statist. Phys., vol. 10, pp. 89–97, 1974.
19. B. R. Frieden, “Restoring with maximum likelihood and maximum entropy,”J. Opt. Soc. Amer., vol. 62, pp. 511–518, 1972.
20. D. Geman and S. Geman, “Parameter estimation for some Markov random fields,” Brown Univ. Tech. Rep., Aug. 1983.
21. S. Geman, “Stochastic relaxation methods for image restoration and expert systems,” in Proc. ARO Workshop: Unsupervised Image Analysis, Brown Univ., 1983; to appear in Automated Image Analysis: Theory and Experiments, D. B. Cooper, R. L. Launer, and D. E. McClure, Eds. New York: Academic, 1984.
22. U. Grenander, Lectures in Pattern Theory, Vols. I-III. New York: Springer-Verlag, 1981.
23. D. Griffeath, “Introduction to random fields,” in Denumerable Markov Chains, Kemeny, Knapp and Snell, Eds. New York: Springer-Verlag, 1976.
24. A. Habibi, “Two-dimensional Bayesian estimate of images,” Proc. IEEE, vol. 60, pp. 878–883, 1972.
25. F. R. Hansen and H. Elliott, “Image segmentation using simple Markov field models,” Comput. Graphics Image Processing, vol. 20, pp. 101-132,1982.
26. A. R. Hanson and E. M. Riseman, “Segmentation of natural scenes,” in Computer Visions Systems. New York: Academic, 1978.
27. J. M. Harnmersley and D. C. Handscomb, Monte Carlo Methods. London: Methuen, 1964.
28. M. Hassner and J. Sklansky, “The use of Markov random fields as models of texture,” Comput. Graphics Image Processing, vol. 12, pp. 357-370,1980.
29. G. E. Hinton and T. J. Sejnowski, “Optimal perceptual inference,” in Proc. IEEE Conf. Comput. Vision Pattern Recognition
30. R. A. Hummel and S. W. Zucker, “On the foundations of relaxation labeling processes,” IEEE Trans. Pattern Anal. Machine Intel!, vol. PAMI-5, pp. 267-287,1983.
31. B. R. Hunt, “Bayesian methods in nonlinear digital image restoration,” IEEE Trans. Comput., vol. C-23, pp. 219-229,1977.