ON THE DILATED FACETS OF A POISSON-VORONOI TESSELLATION

Claudia Redenbach

Abstract

In this paper, the parallel set ΞR of the facets ((d−1)-faces) of a stationary Poisson-Voronoi tessellation in ℝ2 and ℝ3 is investigated. An analytical formula for the spherical contact distribution function of the tessellation allows for the derivation of formulae for the volume density and the specific surface area of ΞR. The densities of the remaining intrinsic volumes are studied by simulation. The results are used for fitting a dilated Poisson-Voronoi tessellation to the microstructure of a closed-cell foam.

Keywords
contact distribution function; intrinsic volumes; parallel set; surface density; stochastic geometry

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DOI: 10.5566/ias.v30.p31-38

Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)