Image segmentation by polygonal Markov Fields

Annals of the Institute of Statistical Mathematics

Volumn 59, Issue 3, 2007, Pages 465-486

  Kluszczynski R ^a   Van Lieshout, M N M ^b   Schreiber, T ^a  

^a NICOLAUS COPERNICUS UNIVERSITY   (Poland)

^b CWI   (Netherlands)

Author keywords

Arak process; Dynamic representation; Gibbs sampler; Gibbsian modification; Image segmentation; L p misclassification rate; Multi coloured polygonal Markov field

Indexed keywords

HAMILTONIANS; MARKOV PROCESSES; MATHEMATICAL MODELS; MONTE CARLO METHODS; PARAMETER ESTIMATION;

ARAK PROCESS; DYNAMIC REPRESENTATIONS; GIBBS SAMPLERS; GIBBSIAN MODIFICATIONS; MISCLASSIFICATION RATES; MULTI COLORED POLYGONAL MARKOV FIELDS;

IMAGE SEGMENTATION;

EID: 34548591360     PISSN: 00203157     EISSN: 15729052     Source Type: Journal    
DOI: 10.1007/s10463-006-0062-8     Document Type: Article

References (26)

1. Arak, T. (1982). On Markovian random fields with finite number of values. In: 4th USSR-Japan symposium on probability theory and mathematical statistics, Abstracts of Communications. Tbilisi
2. Arak T., Surgailis D. (1989). Markov fields with polygonal realisations. Probabability Theory and Related Fields, 80, 543-579
3. Arak T., Surgailis D. (1991). Consistent polygonal fields. Probabability Theory and Related Fields, 89, 319-346
4. Arak T., Clifford P., Surgailis D. (1993). Point-based polygonal models for random graphs. Advances in Applied Probability, 25, 348-372
5. Baddeley A.J., van Lieshout M.N.M. (1992). ICM for object recognition. In: Dodge Y., Whittaker J. (Eds) Computational Statistics, Vol 2. Heidelberg, Physica/Springer, pp. 271-286
6. Borkar, V., Mitter, S. K. (1993). Stochastic processes that generate polygonal and related random fields, Research Report LIDS-P2216, MIT
7. Clifford P., Middleton R.D. (1989). Reconstruction of polygonal images. Journal of Applied Statistics, 16, 409-422
8. Clifford, P., Nicholls, G. K. (1994). A Metropolis sampler for polygonal image reconstruction, Electronic version available at: http://www.stats.ox.ac. uk/~ clifford/ papers/met_poly.html
9. Gimel'farb G.L. (1999). Image textures and Gibbs random fields. Dordrecht, Kluwer
10. Green P.J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711-732
11. Green P.J., Richardson S., Hjort N.L. (Eds) (2003). Highly structured stochastic systems, Oxford Statistical Science Series Vol 27. Oxford, Oxford University Press
12. Haario H., Saksman E. (1991). Simulated annealing process in general state space. Advances in Applied Probability, 23, 886-893
13. Heikkinen J., Arjas E. (1998). Non-parametric Bayesian estimation of a spatial Poisson intensity. Scandinavian Journal of Statistics, 25, 435-450
14. Hurn M.A., Husby O., Rue H. (2003). 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. Oxford, Oxford University Press, pp. 323-325
15. Liggett T. (1985). Interacting particle systems. New York, Springer
16. Møller J., Skare ∅. (2001). Bayesian image analysis with coloured Voronoi tessellations and a view to applications in reservoir modelling. Statistical Modelling, 1, 213-232
17. Møller J., Waagepetersen R.P. (1998). Markov connected component fields. Advances in Applied Probability (SGSA), 30, 1-35
18. Nicholls G.K. (1998). Bayesian image analysis with Markov chain Monte Carlo and coloured continuum triangulation models. Journal of the Royal Statistical Society, Series B, 60, 643-659
19. Ortner M. (2004). Processus ponctuels marqués pour l'extraction automatique de caricatures de bâtiments à partir de modèles numériques d'elévation. PhD Thesis, University of Nice-Sophia Antipolis.
20. Osher S., Paragios N. (Eds) (2003). Geometric level set methods in imaging, vision, and graphics. New York, Springer
21. Paskin M.A., Thrun S. (2005). Robotic mapping with polygonal random fields. In: Proceedings in Artificial Intelligence UAI-05
22. Rosenfeld A., Kak A.C. (1982). Digital picture processing, 2nd edn, Vol 2. Orlando, Academic Press
23. Schreiber, T. (2005). Random dynamics and thermodynamic limits for polygonal Markov fields in the plane. Advances in Applied Probability, 37 (4) (in press).
24. Tjelmeland H., Besag J. (1998). Markov random fields with higher order interactions. Scandinavian Journal of Statistics, 25, 415-433
25. Vincent, L. (1999). Mathematical morphology. In: O. Barndorff-Nielsen, W. S. Kendall, M. N. M. van Lieshout (Eds.) Stochastic geometry, likelihood and computation. Boca Raton: CRC Press/Chapman and Hall
26. Winkler G. (2003). Image analysis, random fields and Markov chain Monte Carlo methods, A mathematical introduction, 2nd edn, Applications of Mathematics, Stochastic Modelling and Applied Probability vol. 27. Berlin Heidelberg New York, Springer