SECOND MOMENT MEASURE AND K-FUNCTION FOR PLANAR STIT TESSELLATIONS

Authors

  • Viola Weiss
  • Joachim Ohser
  • Werner Nagel

DOI:

https://doi.org/10.5566/ias.v29.p121-131

Keywords:

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

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).

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Published

2011-05-03

Issue

Vol. 29 No. 2 (2010)

Section

Original Research Paper

How to Cite

Weiss, V., Ohser, J., & Nagel, W. (2011). SECOND MOMENT MEASURE AND K-FUNCTION FOR PLANAR STIT TESSELLATIONS. Image Analysis and Stereology, 29(2), 121-131. https://doi.org/10.5566/ias.v29.p121-131