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

In: Recent Advances in Applied Probability

Author

Listed:
  • Viktor Beneš

    (Dept. of Probability and Statistics, Charles University)

  • Ivan Sax

    (Academy of Sciences of the Czech Republic, Mathematical Institute)

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.

Suggested Citation

  • Viktor Beneš & Ivan Sax, 2005. "Stereological Estimation of the Rose of Directions from the Rose of Intersections," Springer Books, in: Ricardo Baeza-Yates & Joseph Glaz & Henryk Gzyl & Jürgen Hüsler & José Luis Palacios (ed.), Recent Advances in Applied Probability, pages 65-96, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-23394-9_3
    DOI: 10.1007/0-387-23394-6_3
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