An Algorithm for Binary Image Segmentation Using Polygonal Markov Fields

  • Rafał Kluszczyński
  • Marie-Colette van Lieshout
  • Tomasz Schreiber
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3617)


We present a novel algorithm for binary image segmentation based on polygonal Markov fields. We recall and adapt the dynamic representation of these fields, and formulate image segmentation as a statistical estimation problem for a Gibbsian modification of an underlying polygonal Markov field. We discuss briefly the choice of Hamiltonian, and develop Monte Carlo techniques for finding the optimal partition of the image. The approach is illustrated by a range of examples.


Image Segmentation Image Domain Statistical Estimation Problem Total Edge Length Homogeneous Poisson Point Process 
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.


  1. 1.
    Arak, T.: On Markovian random fields with finite number of values. In: 4th USSR-Japan Symposium on Probability Theory and Mathematical Statistics, Abstracts of Communications, Tbilisi (1982)Google Scholar
  2. 2.
    Arak, T., Surgailis, D.: Markov fields with polygonal realisations. Probability Theory and Related Fields 80, 543–579 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Arak, T., Surgailis, D.: Consistent polygonal fields. Probability Theory and Related Fields 89, 319–346 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Arak, T., Clifford, P., Surgailis, D.: Point-based polygonal models for random graphs. Advances in Applied Probability 25, 348–372 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Baddeley, A.J., van Lieshout, M.N.M.: ICM for object recognition. In: Dodge, Y., Whittaker, J. (eds.) Computational Statistics, vol. 2, pp. 271–286. Physica/Springer, Heidelberg (1992)Google Scholar
  6. 6.
    Clifford, P., Middleton, R.D.: Reconstruction of polygonal images. Journal of Applied Statistics 16, 409–422 (1989)CrossRefGoogle Scholar
  7. 7.
    Clifford, P., Nicholls, G.K.: A Metropolis sampler for polygonal image reconstruction. Electronic version (1994), available at
  8. 8.
    Hurn, M.A., Husby, O., Rue, H.: Advances in Bayesian image analysis. In: Green, P.J., Richardson, S., Hjort, N.L. (eds.) Highly Structured Stochastic Systems. Oxford Statistical Science Series, vol. 27, pp. 323–325. Oxford University Press, Oxford (2003)Google Scholar
  9. 9.
    Kluszczyński, R., van Lieshout, M.N.M., Schreiber, T.: Image segmentation by polygonal Markov fields (2004), Electronic version available as CWI Research Report PNA-R0409 at:
  10. 10.
    Rosenfeld, A., Kak, A.C.: Digital picture processing, 2nd edn., vol. 2. Academic Press, Orlando (1982)Google Scholar
  11. 11.
    Schreiber, T.: Mixing properties of polygonal Markov fields in the plane, 18 (2003), Electronic version available at
  12. 12.
    Schreiber, T.: Random dynamics and thermodynamic limits for polygonal Markov fields in the plane, 17 (2004), Electronic version available at

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Rafał Kluszczyński
    • 1
  • Marie-Colette van Lieshout
    • 2
  • Tomasz Schreiber
    • 1
  1. 1.Nicolaus Copernicus UniversityToruńPoland
  2. 2.CWIAmsterdamThe Netherlands

Personalised recommendations