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Unbiased Stereological Estimation of d-Dimensional Volume in ℝn from an Isotropic Random Slice Through a Fixed Point

Part of: Global differential geometry Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

E. B. Vedel Jensen  and
K. Kiêu
E. B. Vedel Jensen*
Affiliation:
University of Aarhus
K. Kiêu*
Affiliation:
Institut National de la Recherche Agronomique
*
* Postal address: Department of Theoretical Statistics, Institute of Mathematics, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark.
** Postal address: Laboratoire de Biométrie, Institut National de la Recherche Agronomique, Route de Saint-Cyr, F-78000 Versailles, France.
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Abstract

Unbiased stereological estimators of d-dimensional volume in ℝn are derived, based on information from an isotropic random r-slice through a specified point. The content of the slice can be subsampled by means of a spatial grid. The estimators depend only on spatial distances. As a fundamental lemma, an explicit formula for the probability that an isotropic random r-slice in ℝn through O hits a fixed point in ℝn is given.

Keywords

CROFTON'S FORMULAINTEGRAL GEOMETRYISOTROPIC SUBSPACESSLICESSTEREOLOGY

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 53C65: Integral geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 26 , Issue 1 , March 1994 , pp. 1 - 12
Copyright
Copyright © Applied Probability Trust 1994 

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