Hostname: page-component-89b8bd64d-7zcd7 Total loading time: 0 Render date: 2026-05-09T02:38:43.919Z Has data issue: false hasContentIssue false
  • English
  • Français

Conditional cyclic Markov random fields

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  01 July 2016

John T. Kent ,
Kanti V. Mardia  and
Alistair N. Walder
John T. Kent*
Affiliation:
University of Leeds
Kanti V. Mardia*
Affiliation:
University of Leeds
Alistair N. Walder*
Affiliation:
University of Leeds
*
* Postal address for all authors: Department of Statistics, University of Leeds, Leeds LS2 9JT, UK.
* Postal address for all authors: Department of Statistics, University of Leeds, Leeds LS2 9JT, UK.
* Postal address for all authors: Department of Statistics, University of Leeds, Leeds LS2 9JT, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

Grenander et al. (1991) proposed a conditional cyclic Gaussian Markov random field model for the edges of a closed outline in the plane. In this paper the model is recast as an improper cyclic Gaussian Markov random field for the vertices. The limiting behaviour of this model when the vertices become closely spaced is also described and in particular its relationship with the theory of ‘snakes' (Kass et al. 1987) is established. Applications are given in Grenander et al. (1991), Mardia et al. (1991) and Kent et al. (1992).

Keywords

DEFORMABLE TEMPLATESCYCLIC STATIONARITYLIMITING BEHAVIOURSNAKES

MSC classification

Primary: 60G60: Random fields
Secondary: 60F05: Central limit and other weak theorems

Information

Type
Stochastic Geometry amd Statistical Applications
Information
Advances in Applied Probability , Volume 28 , Issue 1 , March 1996 , pp. 1 - 12
Copyright
Copyright © Applied Probability Trust 1996 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Besag, J. E. (1974) Spatial interaction and the statistical analysis of lattice systems (with discussion). J. R. Statist. Soc. B 36, 192–236.Google Scholar
Besag, J. E. (1986) On the statistical analysis of dirty pictures. J. R. Statist. Soc. B 48, 259–302.Google Scholar
Cootes, T. F., Taylor, C. J., Cooper, D. H. and Graham, J. (1992) Training models of shapes from sets of examples. British Machine Vision Conference, Leeds 1992, pp. 9–18. Springer, Berlin.Google Scholar
Grenander, U. (1989) Advances in pattern theory. Ann. Statist. 17, 1–30.Google Scholar
Grenander, U., Chow, Y. and Keenan, D. M. (1991) Hands: A Pattern Theoretic Study of Biological Shapes. Springer, Berlin.Google Scholar
Kass, M., Witkin, A. and Terzopoulos, D. (1987) Snakes: active contour models. Internat. J. Comp. Vis. 1, 321–331.CrossRefGoogle Scholar
Kent, J. T. (1994) The complex Bingham distribution and shape analysis. J. R. Statist. Soc. B 56, 285–299.Google Scholar
Kent, J. T., Mardia, K. V., Walder, A. N. and Haddon, J. (1992) Comparison of several deformable template algorithms. Report, Department of Statistics, University of Leeds.Google Scholar
Knoerr, A. P. (1988) Global models of natural boundaries: theory and applications. Reports in Pattern Analysis, 148. Division of Applied Maths. Brown University.Google Scholar
Mardia, K. V., Kent, J. T. and Walder, A. N. (1991) Statistical shape models in image analysis. In Computing Science and Statistics: Proc. 23rd Symp. on the Interface, ed. Keramidas, E. M., pp. 550–557. Interface Foundation of North America, Fairfax Station, VA.Google Scholar