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Bayesian image analysis with Markov chain Monte Carlo and coloured continuum triangulation models

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  • G. K. Nicholls

Abstract

It is now possible to carry out Bayesian image segmentation from a continuum parametric model with an unknown number of regions. However, few suitable parametric models exist. We set out to model processes which have realizations that are naturally described by coloured planar triangulations. Triangulations are already used, to represent image structure in machine vision, and in finite element analysis, for domain decomposition. However, no normalizable parametric model, with realizations that are coloured triangulations, has been specified to date. We show how this must be done, and in particular we prove that a normalizable measure on the space of triangulations in the interior of a fixed simple polygon derives from a Poisson point process of vertices. We show how such models may be analysed by using Markov chain Monte Carlo methods and we present two case‐studies, including convergence analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:60:y:1998:i:3:p:643-659
    DOI: 10.1111/1467-9868.00145
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    Cited by:

    1. Ghislaine Gayraud & Judith Rousseau, 2002. "Nonparametric Bayesian Estimation of Level Sets," Working Papers 2002-03, Center for Research in Economics and Statistics.
    2. 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.

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