SECOND MOMENT MEASURE AND K-FUNCTION FOR PLANAR STIT TESSELLATIONS

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).