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Stereological analysis of particles of varying ellipsoidal shape

Published online by Cambridge University Press:  14 July 2016

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

Stereological analysis of d-dimensional particles of ellipsoidal shape based on lower-dimensional sections through the particles is discussed. It is proved that the non-void intersections between three parallel hyperplanes and an ellipsoid uniquely determine the ellipsoid, and based on this fact we may reconstruct ellipsoids from sectional information. Combining this reconstruction with a new sampling procedure we obtain a useful tool for non-parametric stereological analysis of particle aggregates of ellipsoids. Finally, parametric models for ellipsoids which are mathematically convenient for the present set up are introduced and discussed.

Keywords

DISECTORELLIPSOIDSFLAT SECTIONSPALM DISTRIBUTIONSTEREOLOGYWISHART DISTRIBUTIONMARKED POINT PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 322 - 335
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

The author is also affiliated to the Stereologic and Electronmicroscopic Diabetes Research Laboratory, Aarhus University.

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