Relaxation Labelling

  • Josef Kittler
Part of the NATO ASI Series book series (volume 30)


This paper attempts to provide a theoretical basis for probabilistic relaxation. First the problem of a formal specification is addressed. An approach to determining support functions is developed based on a formula for combining contextual evidence derived in the paper. A method of developing relaxation labelling schemes using these support functions is briefly described.


Contextual Information Support Function Interaction Relation Labelling Problem Global Criterion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Rosenfeld, A., R.A. Hummel and S.W. Zucker, “Scene labeling by relaxation operations,”IEEE SMC, SMC-6, pp. 420–433, 1976.Google Scholar
  2. [2]
    Waltz, D.L., “Understanding line drawings of scenes with shadows” in The Psychology of Computer Vision, ed. P.H. Winston, McGraw-Hill, New York, 1975.Google Scholar
  3. [3]
    Kittler, J. and J. Hlingworth, “A review of relaxation labelling algorithms,” Image and Vision Computing, 3, pp. 206–216, 1985.CrossRefGoogle Scholar
  4. [4]
    []Kittler, J., “Compatibility and support functions in probabilistic relaxation,” Proc. 8th ICPR, Paris, xxx 1986.Google Scholar
  5. [5]
    Haralick, R.M., “An interpretation for probabilistic relaxation,” CGVIP, 22, pp. 388–395, 1983.Google Scholar
  6. [6]
    Peleg, S., “A new probabilistic relaxation scheme,” IEEE PAMI, PAMI-2, pp. 362–369, 1980.Google Scholar
  7. [7]
    Kittler, J. and J. Föglein, “On compatibility and support functions in probabilistic relaxation,” CVGIP, 1986.Google Scholar
  8. [8]
    Kirby, R.L., “A product rule relaxation method,” CGIP, 13, pp. 158–189, 1980.Google Scholar
  9. [9]
    Zucker, S.W. and J.L. Mohammed, “Analysis of probabilistic labeling processes,” Proc. IEEE PRIP Conf, Chicago, pp. 307–312, 1978.Google Scholar
  10. [10]
    Brayer, J.M., P.H. Swain and K.S. Fu, “Modelling of earth resources satellite data,” in Applications of Syntactic Pattern Recognition, K.S. Fu, ed., New York, Springer, 1982.Google Scholar
  11. [11]
    Kittler, J. and J. Föglein, “Contextual classification of multispectral pixel data,” Image and Vision Computing, 2, pp. 13–29, 1984.CrossRefGoogle Scholar
  12. [12]
    Faugeras, O.D. and M. Berthod, “Improving consistency and reducing ambiguity in stochastic labeling: an optimization approach,” IEEE PA MI, PAMI—3, pp. 412–424, 1981.Google Scholar
  13. [13]
    Hummel, R.A. and S.W. Zucker, “On the foundations of relaxation labeling processes,” IEEE PAMI, PAMI-5, pp. 267–287, 1983.Google Scholar
  14. [14]
    Illingworth, J. and J. Kittler, “Optimisation algorithms in probabilistic relaxation labelling” (in this volume).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Josef Kittler
    • 1
  1. 1.Department of Electronic and Electrical EngineeringUniversity of SurreyGuildfordUK

Personalised recommendations