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On the number of clumps resulting from the overlap of randomly placed figures in a plane

Published online by Cambridge University Press:  14 July 2016

A. M. Kellerer
A. M. Kellerer*
Affiliation:
University of Würzburg
*
∗ Postal address: University of Würzburg, Versbacher Str. 5, D-8700 Würzburg, W. Germany. Research supported by EURATOM Contract BIO–286–81 D.
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Abstract

When two-dimensional figures, called laminae, are randomly placed on a plane domains result that can either be aggregates or individual laminae. The intersection of the union, U, of these domains with a specified field of view, F, in the plane is considered. The separate elements of the intersection are called clumps; they may be laminae, aggregates or partial laminae and aggregates. A formula is derived for the expected number of clumps minus enclosed voids. For bounded laminae homeomorphic to a closed disc with isotropic random direction the formula contains only their mean area and mean perimeter, the area and perimeter of F, and the intensity of the Poisson process.

Keywords

GEOMETRIC PROBABILITYPARTICLE COUNTINGOVERLAP CORRECTIONEDGE CORRECTIONRANDOM COVERAGE
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 1 , March 1983 , pp. 126 - 135
Copyright
Copyright © Applied Probability Trust 1983 

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