Stereology with cylinder probes

Luis Manuel Cruz-Orive, Ximo Gual-Arnau

Abstract

Intersection formulae of Croton type for general geometric probes are well known in integral geometry.  For the special case of  cylinders with non necessarily convex direktrix, however, no equivalent formula seems to exist in the literature. We derive such formula resorting to motion invariant probability elements associated with test systems, instead of using a traditional approach. Because cylinders are seldom used as probes in stereological practice, however, this note is mainly of a theoretical nature.


Keywords
cylinders; integral geometry; motion invariant measures; ratio design; stereology; test system

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DOI: 10.5566/ias.2433

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Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)