Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-02T23:38:17.297Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimation of the density in a stationary Boolean model

Published online by Cambridge University Press:  14 July 2016

Michel Schmitt
Michel Schmitt*
Affiliation:
Thomson-CSF, Orsay
*
∗ Postal address: Thomson-CSF, Laboratoire Central de Recherches, Domaine de Corbeville, 91404 Orsay-Cedex, France.
Get access Rights & Permissions [Opens in a new window]

Abstract

A new and practically tractable formula for estimating the intensity of the underlying Poisson process of a Boolean model is given, assuming only almost sure boundedness of the primary grain.

Keywords

POISSON PROCESSMATHEMATICAL MORPHOLOGYRANDOM SETS
Type
Short Communications
Information
Journal of Applied Probability , Volume 28 , Issue 3 , September 1991 , pp. 702 - 708
Copyright
Copyright © Applied Probability Trust 1991 

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.)

References

[1] Matheron, G. (1975) Random Sets and Integral Geometry. Wiley, New York.Google Scholar
[2] Miles, R. E. (1975) On estimating aggregate and overall characteristics from thick sections by transmission microscopy. In Proc. 4th Internat. Congr. for Stereology, Gaithersburg. Google Scholar
[3] Preteux, F. and Schmitt, M. (1988) Boolean texture analysis and synthesis. Image Analysis and Mathematical Morphology, Volume 2: Theoretical Advances. Academic Press, New York.Google Scholar
[4] Serra, J. (1982) Image Analysis and Mathematical Morphology, ed. Serra, J. Academic Press, New York.Google Scholar
[5] Weil, W. (1988) Expectation formulas and isoperimetric properties for non-isotropic Boolean models. J. Microscopy 151, 235–245.Google Scholar
[6] Weil, W. and Wieacker, J. A. (1984) Densities for stationary random sets and point processes. Adv. Appl. Prob. 16, 324–346.CrossRefGoogle Scholar