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

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 60, Issue 3, 1998, Pages 643-659

  Nicholls, Geoff K ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Bayesian image analysis; Coloured triangulation; Discrete time metropolis process; Markov chain Monte Carlo method; Triangulation models

Indexed keywords

EID: 0012906846     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00145     Document Type: Article

References (19)

1. Arak, T., Clifford, P. and Surgailis, D. (1993) Point based polygonal models for random graphs. Adv. Appl. Probab., 25, 348-372.
2. Baddeley, A. J. and van Lieshout, M. N. M. (1993) Stochastic geometry models in high-level vision. J. Appl. Statist., 20, 233-258.
3. Bern, M. and Eppstein, D. (1995) Mesh generation and optimal triangulation. In Computing in Euclidean Geometry (eds D.-Z. Du and F. K. Hwang), pp. 47-123. Singapore: World Scientific.
4. Braun, J. and Sambridge, M. (1995) A numerical method for solving partial differential equations on highly irregular evolving grids. Nature, 376, 655-660.
5. Brown, W. G. (1964) Enumeration of triangulations of the disk. Proc. Loud. Math. Soc., 14, 746-768.
6. Clifford, P. and Nicholls, G. K. (1994) Simulating polygonal shape models with data. Technical Report. Department of Statistics, Oxford University, Oxford.
7. Geyer, C. J. (1992) Practical Markov chain Monte Carlo. Statist. Sci., 7, 473-511.
8. Geyer, C. J. and Moller, J. (1994) Simulation procedures and likelihood inference for spatial point processes. Scand. J. Statist., 21, 359-373.
9. Green, P. J. (1995) Reversible jump MCMC and Bayesian model determination. Biometrika, 82, 711-732.
10. Grenander, U. and Miller, M. I. (1994) Representations of knowledge in complex systems (with discussion). J. R. Statist. Soc. B, 56, 549-603.
11. Harris, T. E. (1956) The existence of stationary measure for certain Markov processes. In Proc. 3rd Berkeley Symp. Mathematical Statistics and Probability, vol. 2, pp. 113-124. Berkeley: University of California Press.
12. McInerney, T. and Terzopoulos, D. (1995) A dynamic finite element surface model for segmentation and tracking in multidimensional medical images with application to cardiac and 4D image analysis. Comput. Med. Imgng Graph., 19, 69-83.
13. Norman, G. E. and Filinov, V. S. (1969) Investigations of phase transitions by a Monte Carlo method. High Temp. Res. USSR, 7, 216-222.
14. O'Rourke, J. (1994) Computational Geometry in C. Cambridge: Cambridge University Press.
15. Pievatolo, A. and Green, P. J. (1998) Boundary detection through dynamic polygons. J. R. Statist. Soc. B, 60, 609-626.
16. Raftery, A. E. (1994) Change point and change curve modeling in stochastic processes and spatial statistics. J. Appl. Statist. Sci., 1, 403-423.
17. Sibson, R. (1978) Locally equiangular triangulations. Comput. J., 21, 243-245.
18. Stoyan, D. and Stoyan, H. (1994) Fractals, Random Shapes and Point Fields. New York: Wiley.
19. Tierney, L. (1995) Introduction to general state space Markov chain theory. In Markov Chain Monte Carlo in Practice (eds W. R. Gilks, S. Richardson and D. J. Spiegelhalter), pp. 59-74. London: Chapman and Hall.