Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-05T15:54:11.259Z Has data issue: false hasContentIssue false
  • English
  • Français

Stereological analysis of particles of varying ellipsoidal shape

Published online by Cambridge University Press:  14 July 2016

J. Møller
J. Møller*
Affiliation:
Aarhus University
*
∗Postal address: Department of Theoretical Statistics, Institute of Mathematics, Ny Munkegade, DK-8000 Aarhus C, Denmark.
Get access Rights & Permissions [Opens in a new window]

Abstract

Stereological analysis of d-dimensional particles of ellipsoidal shape based on lower-dimensional sections through the particles is discussed. It is proved that the non-void intersections between three parallel hyperplanes and an ellipsoid uniquely determine the ellipsoid, and based on this fact we may reconstruct ellipsoids from sectional information. Combining this reconstruction with a new sampling procedure we obtain a useful tool for non-parametric stereological analysis of particle aggregates of ellipsoids. Finally, parametric models for ellipsoids which are mathematically convenient for the present set up are introduced and discussed.

Keywords

DISECTORELLIPSOIDSFLAT SECTIONSPALM DISTRIBUTIONSTEREOLOGYWISHART DISTRIBUTIONMARKED POINT PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 322 - 335
Copyright
Copyright © Applied Probability Trust 1988 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The author is also affiliated to the Stereologic and Electronmicroscopic Diabetes Research Laboratory, Aarhus University.

References

Cruz-Orive, L.-M. (1976) Particle size-shape distributions: the general spheroid problem. J. Microsc. 107, 235–253.Google Scholar
Cruz-Orive, L.-M. (1985) Estimating volumes from systematic hyperplane sections. J. Appl. Prob. 22, 518–530.Google Scholar
Gundersen, H. J. G. (1986) Stereology of arbitrary particles. J. Microsc. 143, 3–45.CrossRefGoogle ScholarPubMed
Howard, V., Reid, S., Baddeley, A. and Boyde, A. (1985) Unbiased estimation of particle density in the tandem scanning reflected light microscope. J. Microsc. 138, 203–212.Google Scholar
James, A. T. (1966) Inference on latent roots by calculation of hypergeometric functions of matrix argument. In Multivariate Analysis. Proceedings, Dayton, 1965 (Ed. Krishnaiah, P. R.), Academic Press, New York, 209–235.Google Scholar
Jensen, E. B. and Gundersen, H. J. G. (1987) The corpuscle problem: reevaluation using the disector. Acta Stereologica 6, Suppl. II, 105–122.Google Scholar
Mardia, K. V., Kent, J. T., and Bibby, J. M. (1979) Multivariate Analysis. Academic Press, London.Google Scholar
Matheron, G. (1975) Random Sets and Integral Geometry. Wiley, New York.Google Scholar
Mauchly, J. W. (1940) A significance test for ellipticity in the harmonic dial. Terrestrial Magnetism and Atmospheric Electricity 45, 145–148.CrossRefGoogle Scholar
Møller, J. (1986) Stereological analysis of particles of varying ellipsoidal shape. Research Report 150, Department of Theoretical Statistics, University of Aarhus.Google Scholar
Sterio, D. C. (1984) The unbiased estimation of number and sizes of arbitrary particles using the disector. J. Microsc. 134, 127–136.Google Scholar
Stoyan, D. (1982) Stereological formulae for size distributions via marked point processes. Prob. Math. Statist. 2, 161–166.Google Scholar
Stoyan, D. and Mecke, J. (1983) Stochastiche Geometrie. Eine Einführung. Akademie-Verlag, Berlin.Google Scholar