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Estimation of the mean normal measure from flat sections

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  • Department of Mathematical Sciences
We discuss the determination of the mean normal measure of a stationary random set Z in the extended convex ring in d-dimensional space 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>2 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> [d/k]. A consistent estimator for the mean normal measure of Z, based on stereological measurements in vertical sections, is also presented.

Original languageEnglish
JournalAdvances in Applied Probability
Pages (from-to)31-48
Number of pages18
Publication statusPublished - 2008

    Research areas

  • mean normal measure, stereology, Crofton formula

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