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Simulated Annealing: A Proof of Convergence

Published: 01 June 1994 Publication History

Abstract

We prove the convergence of the simulated annealing procedure when the decision to change the current configuration is blind of the cost of the new configuration. In case of filtering binary images, the proof easily generalizes to other procedures, including that of Metropolis. We show that a function Q associated with the algorithm must be chosen as large as possible to provide a fast rate of convergence. The worst case (Q constant) is associated with the "blind" algorithm. On the other hand, an appropriate Q taking sufficiently high values yields a better rate of convergence than that of Metropolis procedure.

References

[1]
{1} J. Besag, "On the statistical analysis of dirty pictures," JRSS B, vol. 48, pp. 259-302, 1986.
[2]
{2} M. E. Johnson, Ed., Simulated Annealing and Optimization: Modern Algorithms With VLSI, Optimal Design and Missile Defense Applications. New York: American Science Press, 1989.
[3]
{3} G. R. Cross and A. K. Jain, "Markov random field texture models," IEEE Trans. Pattern Anal. Machine Intell., vol. 5, no. 1, pp. 25-39, 1983.
[4]
{4} S. B. Gelfand and S. K. Mitter, "Simulated annealing," in Proc. Advanced school CISM, Udine, Italy, 1987, pp. 1-51.
[5]
{5} D. Geman, "Random fields and inverse problems in imaging," Lectures Notes in Mathematics, vol. 1427, pp. 117-196, 1988.
[6]
{6} S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, no. 6, 721-741, June 1984.
[7]
{7} B. Gidas, "Non stationary Markov chains and convergence of simulated annealing algorithms," J. Statist. Phys., vol. 39, pp. 73-131, 1985.
[8]
{8} V. Granville and J. P. Rasson, "A new modelisation of noise in image remote sensing," Statist. and Probab. Lett. vol. 14, pp. 61-65, 1992.
[9]
{9} V. Granville and J. P. Rasson, "A Bayesian filter for a mixture model of noise in image remote sensing," Comput. Statist. Data Anal. vol. 15, pp. 297-308, 1993.
[10]
{10} V. Granville, J. P. Rasson, and F. Orban-Ferauge, "Un modèle Bayesien de segmentation d'images," in Proc. 4th Journées Scientifiques du Réseau de Télédétection de L'UREF, Montréal, Oct. 1991 (to appear).
[11]
{11} X. Guyon, "Champs stationnaires sur Z<sup>2</sup>: Modéles, statistique et simulations," Université Paris I., 1985.
[12]
{12} B. Hajek, Cooling schedules for optimal annealing, Math. Oper. Res. vol. 13, pp. 311-329, 1988.
[13]
{13} J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods. London: Methuen, 1964.
[14]
{14} S. Lakshmanan and H. Derin, "Simultaneous parameter estimation and segmentation of Gibbs random fields using simulated annealing," IEEE Trans. Pattern Anal. Machine Intell., vol. 11, no. 8, 799-813, Aug. 1989.
[15]
{15} V. Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Applications. Dordrecht, D. Reidel, 1987.
[16]
{16} R. S. Varga, Matrix Iterative Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1962.

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Published In

cover image IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence  Volume 16, Issue 6
June 1994
115 pages

Publisher

IEEE Computer Society

United States

Publication History

Published: 01 June 1994

Author Tags

  1. Metropolis procedure
  2. binary image filtering
  3. convergence
  4. image processing
  5. simulated annealing

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