Markov random fields with higher-order interactions

Scandinavian Journal of Statistics

Volumn 25, Issue 3, 1998, Pages 415-433

  Tjelmeland, Håkon ^a   Besag, Julian ^a  

^a NONE

Author keywords

Higher order interactions; Image restoration; Markov random fields; Maximum likelihood; Parameter estimation

Indexed keywords

EID: 0032361518     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9469.00113     Document Type: Article

References (48)

1. Abend, K., Harley, T. J. & Kanal, L. N. (1965). Classification of binary random patterns. IEEE Trans. Inform. Theory 4, 538-544.
2. Amit, Y., Grenander, U. & Piccioni, M. (1991). Structural image restoration through deformable templates. J. Amer. Statist. Assoc. 86, 376-387.
3. Aykroyd, R. G. & Green, P. (1991). Global and local priors, and the location of lesions using gamma camera imagery. Philos. Trans. Roy. Soc. London Ser. A 337, 323-342.
4. p version of the Hausdorff metric. Nieuw Arch. Wish. 10, 157-183.
5. Baddeley, A. & van Lieshout, M. N. M. (1993). Stochastic geometry models in high-level vision. J. Appl. Statist. 20, 235-256.
6. Bartlett, M. S. & Besag, J. (1969). Correlation properties of some nearest-neighbour models. Bull. Int. Statist. Inst. 43, 191-193.
7. Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems (with discussion). J. Roy. Statist. Soc. Ser. B 36, 192-236.
8. Besag, J. (1975). Statistical analysis of non-lattice data. The Statistician 24, 179-195.
9. Besag, J., Green, P., Higdon, D. & Mengersen, K. (1995). Bayesian computation and stochastic systems (with discussion). Statist. Sci. 10, 3-66.
10. Cai, H. (1998). A note on an exact sampling algorithm and Metropolis-Hastings Markov chains. To appear.
11. Clifford, P. (1990). Markov random fields in statistics. In Disorder in physical systems (eds G. Grimmett & D. J. Welsh). Clarendon Press, Oxford.
12. Clifford, P. & Middleton, R. D. (1989). Reconstruction of polygonal images. J. Appl. Statist. 16, 409-422.
13. Cressie, N. A. C. (1993). Statistics for spatial data. Wiley, New York.
14. Descombes, X., Mangin, J. F., Pechersky, E. & Sigelle, M. (1995). Fine structures preserving model for image processing. Proc. 9th SCIA 95 Uppsala, Sweden, 349-356.
15. Devijver, P. A. (1988). Image segmentation using causal Markov random field models. Lecture Notes in Comput. Sci. 301, 131-143.
16. Geman, D. (1990). Random fields and inverse problems in imaging, Lecture Notes in Mathematics 1427, Springer Verlag.
17. Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. PAMI 6, 721-741.
18. Geman, D., Geman, S., Graffigne, C. & Dong, P. (1990). Boundary detection by constrained optimization. IEEE Trans. PAMI 12, 609-628.
19. Geyer, C. J. (1994). On the convergence of Monte Carlo maximum likelihood calculations. J. Roy. Statist. Soc. Ser. B 56, 261-274.
20. Geyer, C. J. & Thompson, E. A. (1992). Constrained Monte Carlo maximum likelihood for dependent data (with discussion). J. Roy. Statist. Soc. Ser. B 54, 657-699.
21. Gray, A. J., Kay, J. W. & Titterington, D. M. (1994). An empirical study of the simulation of various models used for images. IEEE Trans. PAMI 16, 507-513.
22. Grenander, U. (1983). Tutorial in pattern theory. Report, Division of Applied Mathematics, Brown University.
23. Grenander, U. (1993). General pattern theory. Oxford University Press, Oxford.
24. Grenander, U. & Keenan, D. M. (1989). Towards automated image understanding. J. Appl. Statist. 16, 207-221.
25. Grenander, U. & Miller, M. I. (1994). Representations of knowledge in complex systems (with discussion). J. Roy. Statist. Soc. Ser. B 56, 549-603.
26. Grenander, U., Chow, Y. & Keenan, D. M. (1991). Hands: a pattern theoretic study of biological shapes. Springer, New York.
27. Häggström, O., Lieshout, M. N. M. & Møller, J. (1998). Characterisation results and Markov chain Monte Carlo algorithms including exact simulation for some spatial point processes. To appear.
28. Johnson, V E. (1994). A model for segmentation and analysis of noisy images. J. Amer. Statist. Assoc. 89, 230-241.
29. Kanal, L. N. (1980). Markov mesh models. Comput. Graphics Image Process. 12, 371-375.
30. Kendall, W. S. (1996). Perfect simulation for the area-interaction point process. In Probability perspective (eds C. C. Heyde & L. Accardi). World Scientific Press.
31. Kindermann, R. & Snell, J. L. (1980). Markov random fields and their applications. American Mathematical Society, Providence, R.I.
32. Kittler, J. (1986). Contribution to discussion of paper by J. Besag. J. Roy. Statist. Soc. Ser. B 48, 281-282.
33. Lacroix, V. (1987). Pixel labelling in a second-order Markov mesh. Sig. Process. 12, 59-82.
34. Mardia, K. V. & Hainsworth, T. J. (1993). Image warping and Bayesian reconstruction with grey-level templates. J. Appl. Statist. 20, 257-280.
35. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. & Teller, E. (1953). Equations of state calculations by fast computing machines. J. Chem. Phys. 21, 1087-1092.
36. Murdoch, D. J. & Green, P. J. (1998). Exact sampling from a continuous state space. Scand. J. Statist. 25, 483-502.
37. Møller, J., Syversveen, A. R. & Waagepetersen, R. (1998). Markov connected component fields. Scand. J. Statist. 25, 451-482.
38. Penttinen, A. (1984). Modelling interaction in spatial point patterns: parameter estimation by the maximum likelihood method. Jyväskylä Stud. Comput. Sci. Econom. Statist. 7.
39. Phillips, D. B. & Smith, A. F. M. (1993). Dynamic image analysis using Bayesian shape and texture models. J. Appl. Statist. 39, 299-322.
40. Propp, J. G. & Wilson, D. B. (1996). Exact sampling with coupled Markov chains and applications to statistical mechanics. Random Struct. Algorith. 9, 223-252.
41. Qian, W. & Titterington, D. M. (1991). Multidimensional Markov chain models for image textures. J. Roy. Statist. Soc. Ser. B 53, 661-674.
42. Ripley, B. D. (1987). Stochastic simulation. Wiley, New York.
43. Ripley, B. D. & Sutherland, A. I. (1990). Finding spiral structures in images of galaxies. Phil. Trans. Roy. Soc. Lond. Ser. A 332, 477-485.
44. Rue, H. (1995). New loss functions in Bayesian imaging. J. Amer. Statist. Assoc. 90, 900-908.
45. Swendsen, R. H. & Wang, J. S. (1987). Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett. 58, 86-88.
46. Tjelmeland, H. (1996). Stochastic models in reservoir characterization and Markov random fields for compact objects. Dr.ing. thesis, 1996:44, Norwegian University of Science and Technology, Trondheim, Norway.
47. Wilson, A. G. & Johnson, V. E. (1994). Models for shape deformation. In Bayesian statistics 5 (eds J. Berger, J. Bernardo, P. Dawid & A. Smith).
48. Wilson, A. G., Johnson, V. E., Yu, L. & Pizer, S. (1995). Scale-space image models for shape deformation. In Computing science and statistics: proc. 27th symposium on the interface. Springer-Verlag, New York.