THE PIVOTAL TESSELLATION

Luis M Cruz-Orive

Abstract

The tessellation studied here is motivated by some stereological applications of a new expression for the motion invariant density of straight lines in R3. The term 'pivotal' stems from the fact that the tessellation is constructed within a plane which is isotropic through a fixed, 'pivotal' origin. Consider either a stationary point process, or a stationary random lattice of points in that plane. Through each point event draw a straight line which is perpendicular to the axis determined by the origin and the point event. The union of all such lines (called p-lines) constitutes the mentioned tessellation. We concentrate on the pivotal tessellation based on a stationary and isotropic planar Poisson point process; we show that this tessellation is not stationary.

Keywords
geometric probability; p-line; pivotal tessellation; Poisson point process; stereology; stochastic geometry

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DOI: 10.5566/ias.v28.p63-67

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