SECOND MOMENT MEASURE AND K-FUNCTION FOR PLANAR STIT TESSELLATIONS

Viola Weiss, Joachim Ohser, Werner Nagel

Abstract

For STIT tessellations – stationary tessellations that are stable under the operation iteration of tessellations – the second-ordermeasure of the edge system is studied. A result is that this measure coincides with that one of a Boolean segment process. In the isotropic case an explicit formula for the pair-correlation function is given. An estimator for the covariance function of the edge length measure is derived and adapted to digitized images of tessellations. For m pixels of an image the algorithm is of complexity O(mlogm).

Keywords
covariance function; estimation; K-function; pair-correlation function; random tessellations; second moment measure; STIT tessellations; stochastic geometry

Full Text:

PDF


DOI: 10.5566/ias.v29.p121-131

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