Acta Stereologica



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Ivan Kohútek & Ivan Saxl

Properties of the Voronoi tessellation corresponding to the generalized planar Gauss-Poisson process

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The Voronoi mosaics corresponding to the planar Neyman—Scott process of point pairs and regular quadruples (vertices of a square) are investigated. The mean values of cell parameters are those of a Poisson—Voronoi tessellation (PVT) of the same intensity of generating points. If the inter—daughter distances are comparable with or smaller than the mean nearest neighbour distance of the parent process, then higher moments of cell area and perimeter distributions differ considerably from the PVT values. If, moreover, the orientation of clusters is fixed, then also a pronounced anisotropy of cell boundaries is observed. The results are compared with those of standard statistical quadrat testing methods and a good agreement is found.

Keywords : Gauss-Poisson process, planar Neyman-Scott process, point clusters, statistical testing, Voronoi tessellation

To cite this article

Ivan Kohútek & Ivan Saxl, «Properties of the Voronoi tessellation corresponding to the generalized planar Gauss-Poisson process», Acta Stereologica [En ligne], Volume 12 (1993), Number 2 - Proceedings of the sixth European congress for stereology - Part one - Dec. 1993, 155-160 URL :

About: Ivan Kohútek

Institute of Materials Research, Slovak Academy of Sciences, Watsonova 47, 043 53 Košice, Slovakia

About: Ivan Saxl

Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic