Acta Stereologica



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Denis Allard

Some connectivity characteristics of a Boolean model

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On the 2D simple square grid (3D simple cubic grid), the Boolean model with deterministic square (cubic) primary grains is considered. Four connectivity characteristics are studied as a function of the grain proportion: the Euler-Poincaré characteristic (EPC), the number of connected components, the relative area (volume) occupied by the biggest connected component and the connectivity function (defined as the probability that two points of the grains belong to the same connected component). Using simulations, this paper shows the influence of grain and grid size on these characteristics, for both the square and the cubic grid.

Keywords : Boolean model, connectivity, discretization, Euler-Poincaré characteristic

To cite this article

Denis Allard, «Some connectivity characteristics of a Boolean model», Acta Stereologica [En ligne], Volume 12 (1993), Number 2 - Proceedings of the sixth European congress for stereology - Part one - Dec. 1993, 191-196 URL :

About: Denis Allard

Centre de Géostatistique, Ecole des Mines de Paris, 35 rue Saint-Honoré, 77305 Fontainebleau, France