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The Estimation of mean shape and mean particle number in overlapping particle systems in the plane

Part of: General convexity Geometric probability and stochastic geometry Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Wolfgang Weil
Wolfgang Weil*
Affiliation:
Universität Karlsruhe
*
* Postal address: Mathematisches Institut II, Universität Karlsruhe, 76128 Karlsruhe, Germany.
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Abstract

A stationary (but not necessarily isotropic) Boolean model Y in the plane is considered as a model for overlapping particle systems. The primary grain (i.e. the typical particle) is assumed to be simply connected, but no convexity assumptions are made. A new method is presented to estimate the intensity y of the underlying Poisson process (i.e. the mean number of particles per unit area) from measurements on the union set Y. The method is based mainly on the concept of convexification of a non-convex set, it also produces an unbiased estimator for a (suitably defined) mean body of Y, which in turn makes it possible to estimate the mean grain of the particle process.

Keywords

BOOLEAN MODELANISOTROPYINTENSITYMEAN GRAINCONVEXIFICATION

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes 52A10: Convex sets in $2$ dimensions (including convex curves)
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 27 , Issue 1 , March 1995 , pp. 102 - 119
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.

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