Stereology with Cylinder Probes

Authors

  • Luis Manuel Cruz-Orive University of Cantabria (E-Santander)
  • Ximo Gual-Arnau University Jaume I. E-12071 Castelló

DOI:

https://doi.org/10.5566/ias.2433

Keywords:

cylinders, integral geometry, motion invariant measures, ratio design, stereology, test system

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.

Author Biographies

  • Luis Manuel Cruz-Orive, University of Cantabria (E-Santander)
    Dept. of Mathematics, Statistics               
    and Computation,  (MATESCO),               
    Faculty of Sciences,
    University of Cantabria,         
    Avda. Los Castros, 48,
    E-39005 Santander, Spain
  • Ximo Gual-Arnau, University Jaume I. E-12071 Castelló

    Professor

    Department of Mathematics
    Institute of New Imaging Technologies

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Published

2020-11-25

Issue

Vol. 39 No. 3 (2020)

Section

Original Research Paper

License

Copyright (c) 2020 Image Analysis & Stereology

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Cruz-Orive, L. M., & Gual-Arnau, X. (2020). Stereology with Cylinder Probes. Image Analysis and Stereology, 39(3), 213-218. https://doi.org/10.5566/ias.2433