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The Estimation of mean shape and mean particle number in overlapping particle systems in the plane
Published online by Cambridge University Press: 01 July 2016
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.
MSC classification
- Type
- Stochastic Geometry and Statistical Applications
- Information
- Copyright
- Copyright © Applied Probability Trust 1995
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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