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Stereological versions of integral geometric formulae for n-dimensional ellipsoids

Published online by Cambridge University Press:  24 August 2016

E. B. Jensen  and
J. Møller
E. B. Jensen*
Affiliation:
University of Aarhus
J. Møller*
Affiliation:
University of Aarhus
*
∗Postal address: Department of Theoretical Statistics, Institute of Mathematics, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark.
∗Postal address: Department of Theoretical Statistics, Institute of Mathematics, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark.
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Abstract

Recently, unbiased stereological estimators of moments of particle volume, based on measurements on lower-dimensional sections through the particles, have been developed by Jensen and Gundersen (1985). In this note, we derive an explicit form of these unbiased estimators valid for particles in Rn of ellipsoidal shape, and we establish a close relationship between the estimators and a known integral geometric formula for ellipsoids, due to Furstenberg and Tzkoni (1971). Furthermore, a stereological version of another integral geometric formula for n-dimensional ellipsoids, due to Guggenheimer (1973), is derived.

Keywords

GEOMETRIC PROBABILITYISOTROPIC SUBSPACESPARTICLE VOLUMEPOINT-SAMPLINGSTEREOLOGYUNIFORM RANDOM POINTS
Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 1031 - 1037
Copyright
Copyright © Applied Probability Trust 1986 

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References

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