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Bivariate random closed sets and nerve fibre degeneration

Part of: Stochastic processes Geometric probability and stochastic geometry Multivariate analysis Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

Guillermo Ayala  and
Amelia Simó
Guillermo Ayala*
Affiliation:
Universidad de Valencia
Amelia Simó*
Affiliation:
Universidad Jaume I
*
* Postal address: Departamento de Estadística e I.O. de la Universitat de València, Dr. Moliner, 50, 46100 Burjassot-Valencia, Spain.
** Postal address: Departamento de Matemáticas de la Universidad Jaume I, Castellón, Spain.
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Abstract

A biphase image, representing the normal and degenerated fibres in a vertical cross-section of a nerve, is considered. A random set model based on a Gibbs point process is proposed for the union of the two phases. A kind of independence between the degeneration process and the original fibres is defined and tested.

Keywords

GIBBS PROCESSRANDOM LABELLING

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 62M30: Spatial processes
Secondary: 62H11: Directional data; spatial statistics 60G55: Point processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 27 , Issue 2 , June 1995 , pp. 293 - 305
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

The original version of this paper was presented at the International Workshop on Stochastic Geometry, Stereology and Image Analysis held at the Universidad Internacional Menendez Pelayo, Valencia, Spain, on 21–24 September 1993.

References

Ayala, G. and Simó, A. (1994) Labelling random closed sets. Technical report, Universitat de Valencia and Universitat Jaume I.Google Scholar
Baddeley, A. J. and Møller, J. (1989) Nearest-neighbour Markov point processes and random sets. Internat. Statist. Rev. 57, 89–121.CrossRefGoogle Scholar
Baddeley, A. J. and Van Lieshout, M. (1991) Recognition of overlapping objects using Markov spatial processes. Technical report, CWI.Google Scholar
Bronshtein, I. and Semendyayev, K. (1978) Handbook of Mathematics. VNR, New York.Google Scholar
Bursell, S., Clermont, A., Shiba, T., and King, G. (1992) Evaluating retinal circulation using videofluorescein angiography in control and diabetic rats. Curr. Eye Res. 11, 287–295.CrossRefGoogle Scholar
Cressie, N. A. (1993) Statistics for Spatial Data, revised edn. Wiley, New York.CrossRefGoogle Scholar
Daley, D. and Vere-Jones, D. (1988) An Introduction to the Theory of Point Processes. Springer-Verlag, New York.Google Scholar
Diggle, P. (1993) Statistical Analysis of Spatial Point Patterns. Academic Press, London.Google Scholar
Geyer, C. J. and Møller, J. (1993) Simulation procedures and likelihood inference for spatial point processes. University of Minnesota and University of Aarhus.Google Scholar
Goldbaum, M., Katz, N., et al. (1990) Digital image processing for ocular fundus images. Ophthalmology Clinics of North America, 3.CrossRefGoogle Scholar
Good, P. (1994) Permutation Tests. Springer-Verlag, New York.CrossRefGoogle Scholar
Hanisch, K.-H. (1981) On classes of random sets and point processes. Serdica 7, 160–166.Google Scholar
Jensen, E., Kieu, K., and Gundersen, H. (1990) On the stereological estimation of reduced moment measures. Ann. Inst. Statist. Math. 42, 445–461.CrossRefGoogle Scholar
Lotwick, H. (1984), Some models for multitype spatial point processes with remarks on analysing multitype patterns. J. Appl. Prob. 21, 575–582.CrossRefGoogle Scholar
Lotwick, H. and Silverman, B. W. (1982) Methods for analysing spatial processes of several types of points. J.R. Statist. Soc. B44, 406–413.Google Scholar
Manly, B. (1991) Randomization and Monte Carlo Methods in Biology. Chapman and Hall, London.CrossRefGoogle Scholar
Mase, S. (1986) On the possible form of size distributions for Gibbsian processes of mutually non-intersecting balls. J. Appl. Prob. 23, 646–659.CrossRefGoogle Scholar
Matheron, G. (1975) Random Sets and Integral Geometry. Wiley, London.Google Scholar
Ripley, B. (1979) Simulating spatial patterns: dependent samples from a multivariate density. Appl. Statist. 28, 109–112.CrossRefGoogle Scholar
Ripley, B. and Kelly, F. (1977) Markov point processes. J. London Math. Soc. 15, 188–192.CrossRefGoogle Scholar
Ruiz, A. (1986) Estudio de la conducción y morfometría del nervio ciático de la rata albina en un modelo de neuropatía alcohólica experimental. PhD thesis, Universidad de Valencia.Google Scholar
Stoyan, D., Kendall, W., and Mecke, J. (1987) Stochastic Geometry and its Applications. Wiley, Berlin.Google Scholar
Strauss, D. J. (1975) A model for clustering. Biometrika 62, 467–475.CrossRefGoogle Scholar
Zähle, M. (1982) Random processes of Hausdorff rectifiable closed sets. Math. Nachr. 108, 49–72.CrossRefGoogle Scholar