MOMENTS OF THE LENGTH OF LINE SEGMENTS IN HOMOGENEOUS PLANAR STIT TESSELLATIONS

MOMENTS OF THE LENGTH OF LINE SEGMENTS IN HOMOGENEOUS PLANAR STIT TESSELLATIONS

Homogeneous planar tessellations stable under iteration (STIT tessellations) are considered. Using recent results about the joint distribution of direction and length of the typical I-, K- and J-segment we prove closed formulas for the first, second and higher moments of the length of these segments...

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Bibliographic Details
Main Author: Christoph Thäle
Format: Article
Language:English
Published: Slovenian Society for Stereology and Quantitative Image Analysis 2011-05-01
Series:Image Analysis and Stereology
Subjects:
conditional distribution
iteration (nesting)
linear segments
mean value relation
moments
random tessellation
stability
stochastic geometry
Online Access:http://www.ias-iss.org/ojs/IAS/article/view/850
Description
Summary:Homogeneous planar tessellations stable under iteration (STIT tessellations) are considered. Using recent results about the joint distribution of direction and length of the typical I-, K- and J-segment we prove closed formulas for the first, second and higher moments of the length of these segments given their direction. This especially leads to themean values and variances of these quantities andmean value relations as well as general moment relationships. Moreover, the relation between these mean values and certain conditional mean values (and also higher moments) is discussed. The results are also illustrated for several examples.
ISSN:1580-3139
1854-5165

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