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On second-order formulas in anisotropic stereology

Part of: General convexity Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Viktor Beneš
Viktor Beneš*
Affiliation:
Czech Technical University
*
* Postal address: Department of Mathemaics, FSI, Czech Technical University, Karlovo Nám. 13, 12135 Prague 2, Czech Republic.
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Abstract

Formulas for anisotropic stereology of fibre and surface processes are presented. They concern the relation between second-order quantities of the original process and its projections and sections. Various mathematical tools for handling these formulas are presented, including stochastic optimization. Finally applications in stereology are discussed, relating to intensity estimators using anisotropic sampling designs. Variances of these estimators are expressed and evaluated for processes with the Poisson property.

Keywords

ANISOTROPIC SAMPLINGBUFFON TRANSFORMESTIMATION VARIANCELENGTH INTENSITYPAIR CORRELATION FUNCTIONPROJECTION MEASURE

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 52A22: Random convex sets and integral geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 27 , Issue 2 , June 1995 , pp. 326 - 343
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

The original version of this paper was presented at the International Workshop on Stochastic Geometry, Stereology and Image Analysis held at the Universidad Internacional Menendez Pelayo, Valencia, Spain, on 21–24 September 1993.

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