Estimation of the mean normal measure from flat sections
by Markus Kiderlen
Research Reports
Number 497 (August 2007)
We discuss the determination of the mean normal measure of a stationary random set $Z\subset \mathbb{R}^d$ by measurements taken in intersections of $Z$ with $k$-dimensional planes. We show that mean normal measures of sections with vertical planes determine the mean normal measure of $Z$, if $k\ge 3$ or $k=2$ and an additional mild assumption holds. The mean normal measures of finitely many flat sections are not sufficient for this purpose. On the other hand, a discrete mean normal measure can be verified by mean normal measures of intersections with almost all $m$-tuples of planes, when $m\ge \lfloor d/k\rfloor+1$. A consistent estimator for the mean normal measure of $Z$, based on stereological measurements in vertical sections, is also presented.
Published in Adv. Appl. Prob. 40, 31-48 (2008).
This primarily serves as Thiele Research Reports number 10-2007, but was also published in Research Reports