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- W4244395467 abstract "We discuss the determination of the mean normal measure of a stationary random set Z ⊂ ℝ d by taking measurements at the 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 ≥ 3 or if 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 (i.e. an a priori guess can be confirmed or discarded) using mean normal measures of intersections with m suitably chosen planes when m ≥ ⌊ d / k ⌋ + 1. This even holds for almost all m -tuples of k -dimensional planes are viable for verification. A consistent estimator for the mean normal measure of Z, based on stereological measurements in vertical sections, is also presented." @default.
- W4244395467 created "2022-05-12" @default.
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- W4244395467 date "2008-03-01" @default.
- W4244395467 modified "2023-10-14" @default.
- W4244395467 title "Estimation of the mean normal measure from flat sections" @default.
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- W4244395467 doi "https://doi.org/10.1017/s0001867800002366" @default.
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