Titolo: Lectures on Random Voronoi Tessellations (Lecture Notes in Statistics, 87)
Editore: Springer
Data di pubblicazione: 1994
Lingua: Inglese
ISBN 10: 0387942645
ISBN 13: 9780387942643
Rilegatura: Brossura
Condizione: New

Descrizione articolo

Riassunto

Voronoi tessellations are produced by first considering a set of points (known as nuclei) in d-space, and then defining cells as the set of points which are closest to each nuclei. A random Voronoi tessellation is produced by supposing that the location of each nuclei is determined by some random process.

Contenuti

1. Introduction and background.- 1.1. Definitions, assumptions, and characteristics.- 1.2. History and applications.- 1.3. Related tessellations.- 2. Geometrical properties and other background material.- 2.1. On the geometric structure of Voronoi and Delaunay tessellations.- 2.2. Short diversion into integral geometry.- 3. Stationary Voronoi tessellations.- 3.1. Spatial point processes and stationarity.- 3.2. Palm measures and intensities of cells and facets.- 3.3. Mean value relations.- 3.4. Flat sections.- 4. Poisson-Voronoi tessellations.- 4.1. The homogeneous Poisson process.- 4.2. Mean value characteristics of Poisson-Voronoi facets.- 4.3. On the distribution of the typical Poisson-Delaunay cell and related statistics.- 4.4. On the distribution of the typical Poisson-Voronoi cell and related statistics.- 4.5. Simulation procedures for Poisson-Voronoi tessellations and other related models.- References.- Subject and author index.- Notation index.

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