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Disagreement Loop and Path Creation/Annihilation Algorithms for Binary Planar Markov Fields with Applications to Image Segmentation

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  • TOMASZ SCHREIBER
  • MARIE‐COLETTE VAN LIESHOUT

Abstract

. We introduce a class of Gibbs–Markov random fields built on regular tessellations that can be understood as discrete counterparts of Arak–Surgailis polygonal fields. We focus first on consistent polygonal fields, for which we show consistency, Markovianity and solvability by means of dynamic representations. Next, we develop disagreement loop as well as path creation and annihilation dynamics for their general Gibbsian modifications, which cover most lattice‐based Gibbs–Markov random fields subject to certain mild conditions. Applications to foreground–background image segmentation problems are discussed.

Suggested Citation

  • Tomasz Schreiber & Marie‐Colette Van Lieshout, 2010. "Disagreement Loop and Path Creation/Annihilation Algorithms for Binary Planar Markov Fields with Applications to Image Segmentation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 264-285, June.
    • Handle: RePEc:bla:scjsta:v:37:y:2010:i:2:p:264-285
    DOI: 10.1111/j.1467-9469.2009.00678.x
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    References listed on IDEAS

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    1. G. K. Nicholls, 1998. "Bayesian image analysis with Markov chain Monte Carlo and coloured continuum triangulation models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 643-659.
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    Cited by:

    1. M.N.M. Lieshout, 2013. "Discrete Multicolour Random Mosaics with an Application to Network Extraction," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 734-751, December.

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