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SECOND MOMENT MEASURE AND K-FUNCTION FOR PLANAR STIT TESSELLATIONS
June 2010
VIOLA WEISS, JOACHIM OHSER AND WERNER NAGEL
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).
Covariance Function, Estimation, K-function, Pair-correlation Function, Random Tessellations,
Second Moment Measure, STIT Tessellations, Stochastic Geometry
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