Skip to main content

Self annealing: Unifying deterministic annealing and relaxation labeling

  • Deterministic Methods
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1223))

Abstract

Deterministic annealing and relaxation labeling algorithms for classification and matching are presented and discussed. A new approach —self annealing—is introduced to bring deterministic annealing and relaxation labeling into accord. Self annealing results in an emergent linear schedule for winner-take-all and assignment problems. Also, the relaxation labeling algorithm can be seen as an approximation to the self annealing algorithm for matching and labeling problems.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. S. Bridle. Training stochastic model recognition algorithms as networks can lead to maximum mutual information estimation of parameters. In D. S. Touretzky, editor, Advances in Neural Information Processing Systems 2, pages 211–217, San Mateo, CA, 1990. Morgan Kaufmann.

    Google Scholar 

  2. J. Buhmann and T. Hofmann. Central and pairwise data clustering by competitive neural networks. In J. Cowan, G. Tesauro, and J. Alspector, editors, Advances in Neural Information Processing Systems 6, pages 104–111. Morgan Kaufmann, San Francisco, CA, 1994.

    Google Scholar 

  3. W. J. Christmas, J. Kittler, and M. Petrou. Structural matching in computer vision using probabilistic relaxation. IEEE Trans. Patt. Anal. Mach. Intell., 17(5):749–764, Aug. 1995.

    Google Scholar 

  4. R. Duda and P. Hart. Pattern Classification and Scene Analysis. Wiley, New York, NY, 1973.

    Google Scholar 

  5. O. Faugeras and M. Berthod. Improving consistency and reducing ambiguity in stochastic labeling: an optimization approach. IEEE Trans. Patt. Anal. Mach. Intell., 3(4):412–424, Jul. 1981.

    Google Scholar 

  6. A. H. Gee and R. W. Prager. Polyhedral combinatorics and neural networks. Neural Computation, 6(1):161–180, Jan. 1994.

    Google Scholar 

  7. D. Geiger and A. L. Yuille. A common framework for image segmentation. Intl. Journal of Computer Vision, 6(3):227–243, Aug. 1991.

    Google Scholar 

  8. S. Gold and A. Rangarajan. A graduated assignment algorithm for graph matching. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(4):377–388, 1996.

    Google Scholar 

  9. E. R. Hancock and J. Kittler. Discrete relaxation. Pattern Recognition, 23(7):711–733, 1990.

    Article  Google Scholar 

  10. J. J. Hopfield and D. Tank. 'Neural’ computation of decisions in optimization problems. Biological Cybernetics, 52:141–152, 1985.

    PubMed  Google Scholar 

  11. R. Hummel and S. Zucker. On the foundations of relaxation labeling processes. IEEE Trans. Patt. Anal. Mach. Intell., 5(3):267–287, May 1983.

    Google Scholar 

  12. A. K. Jain and R. C. Dubes. Algorithms for Clustering Data. Prentice Hall, Englewood Cliffs, NJ, 1988.

    Google Scholar 

  13. B. Kamgar-Parsi and B. Kamgar-Parsi. On problem solving with Hopfield networks. Biological Cybernetics, 62:415–423, 1990.

    MathSciNet  Google Scholar 

  14. J. Kivinen and M. K. Warmuth. Exponentiated gradient versus gradient descent for linear predictors. Technical Report UCSC-CRL-94-16, Univ. Calif. Santa Cruz, June 1994.

    Google Scholar 

  15. J. J. Kosowsky and A. L. Yuille. The invisible hand algorithm: Solving the assignment problem with statistical physics. Neural Networks, 7(3):477–490, 1994.

    Article  Google Scholar 

  16. M.Pelillo. On the dynamics of relaxation labeling processes. In IEEE Intl. Conf. on Neural Networks (ICNN), volume 2, pages 606–1294. IEEE Press, 1994.

    Google Scholar 

  17. M. Pelillo. Learning compatibility coefficients for relaxation labeling processes. IEEE Trans. Patt. Anal. Mach. Intell, 16(9):933–945, Sept. 1994.

    Google Scholar 

  18. C. Peterson and B. Söderberg. A new method for mapping optimization problems onto neural networks. Intl. Journal of Neural Systems, 1(1):3–22, 1989.

    Google Scholar 

  19. A. Rangarajan, S. Gold, and E. Mjolsness. A novel optimizing network architecture with applications. Neural Computation, 8(5):1041–1060, 1996.

    Google Scholar 

  20. A. Rangarajan, A. L. Yuille, S. Gold, and E. Mjolsness. A convergence proof for the softassign quadratic assignment algorithm. In Advances in Neural Information Processing Systems (NIPS) 9. MIT Press, 1997. (in press).

    Google Scholar 

  21. A. Rosenfeld, R. Hummel, and S. Zucker. Scene labeling by relaxation operations. IEEE Trans. Syst. Man, Cybern., 6(6):420–433, Jun. 1976.

    Google Scholar 

  22. R. Sinkhorn. A relationship between arbitrary positive matrices and doubly stochastic matrices. Ann. Math. Statist., 35:876–879, 1964.

    Google Scholar 

  23. F. R. Waugh and R. M. Westervelt. Analog neural networks with local competition. I. Dynamics and stability. Physical Review E, 47(6):4524–4536, June 1993.

    Article  MathSciNet  Google Scholar 

  24. A. L. Yuille and J. J. Kosowsky. Statistical physics algorithms that converge. Neural Computation, 6(3):341–356, May 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Marcello Pelillo Edwin R. Hancock

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rangarajan, A. (1997). Self annealing: Unifying deterministic annealing and relaxation labeling. In: Pelillo, M., Hancock, E.R. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 1997. Lecture Notes in Computer Science, vol 1223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62909-2_83

Download citation

  • DOI: https://doi.org/10.1007/3-540-62909-2_83

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62909-2

  • Online ISBN: 978-3-540-69042-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics