Stereology with cylinder probes


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



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


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


Department of Mathematics
Institute of New Imaging Technologies


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How to Cite

Cruz-Orive, L. M., & Gual-Arnau, X. (2020). Stereology with cylinder probes. Image Analysis and Stereology, 39(3), 213–218.



Original Research Paper

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