Second order analysis of geometric functionals of Boolean models
Abstract
This paper presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translation invariant Minkowski tensors as prominent examples, of stationary Boolean models. Special focus is put on the anisotropic case. In the (anisotropic) example of aligned rectangles, we provide explicit analytic formulae and compare them with simulation results. We discuss which information about the grain distribution second moments add to the mean values.
Cite
@article{arxiv.1601.06718,
title = {Second order analysis of geometric functionals of Boolean models},
author = {Daniel Hug and Michael A. Klatt and Günter Last and Matthias Schulte},
journal= {arXiv preprint arXiv:1601.06718},
year = {2016}
}
Comments
Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jensen. (The second version mainly resolves minor LaTeX problems.)