Stereological Estimation of the Rose of Directions from the Rose of Intersections

Viktor Beneš and Ivan Sax
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Viktor Beneš: Dept. of Probability and Statistics, Charles University
Ivan Sax: Academy of Sciences of the Czech Republic, Mathematical Institute

A chapter in Recent Advances in Applied Probability, 2005, pp 65-96 from Springer

Abstract: Abstract The paper is a review on the problem from stochastic geometry stated in the title. This problem concerns anisotropy quantification of fibre and surface processes. The stereological equation connecting the rose of directions and the rose of intersections (for a specific test system) was first attacked by means of analytical methods. Later on, an analogue from convex geometry lead to a deeper investigation using the notion of a Steiner compact. Various estimators of the rose of directions and their properties are reviewed in the planar and spatial case. The methods are important for practice when quantifying real structures in material science, biomedicine, etc.

Keywords: Test Line; Apply Probability; Planar Anisotropy; Convex Geometry; Probe Orientation (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-23394-9_3

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DOI: 10.1007/0-387-23394-6_3

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