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Counting figures in planar random configurations

Published online by Cambridge University Press:  14 July 2016

A. M. Kellerer
A. M. Kellerer*
Affiliation:
University of Würzburg
*
∗Postal address: Versbacher Str. 5, D-8700 Würzburg, Federal Republic of Germany.
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Abstract

Random configurations are considered that are generated by a Poisson process of figures in the plane, and a recent result is used to derive formulae for the estimation of the number of figures, and their mean area and perimeter. The formulae require merely the determination of the area, the perimeter, and the Euler–Poincaré characteristic of the random configurations in a fixed field of view. There are no similar formulae for the standard deviations of the estimates; their magnitudes in typical cases are therefore assessed by Monte Carlo simulations.

Keywords

GEOMETRIC PROBABILITYRANDOM CLUMPINGPOISSON PROCESSIMAGE ANALYSISPARTICLE COUNTING
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 1 , March 1985 , pp. 68 - 81
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Research supported by EURATOM Contract B10–286–81 D and by GSI Contract 96731.

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