Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-23T18:21:17.020Z Has data issue: false hasContentIssue false
  • English
  • Français

Projected thick sections through multi-dimensional particle aggregates

Published online by Cambridge University Press:  14 July 2016

Pamela Davy
Pamela Davy*
Affiliation:
Australian National University
Get access Rights & Permissions [Opens in a new window]

Abstract

Formulae relating properties of a two-phase structure to properties of a section through that structure are well known in stereology. An exact description of the error introduced into these formulae when the projection of a thick slice is observed rather than a true section (i.e. a slice of zero thickness) is presented for a model of opaque particles distributed according to a homogeneous Poisson point process in En.

Keywords

PROJECTION OF THICK SECTION ONTO OBSERVATION FLATRANDOM CONVEX SETSSTEREOLOGYGEOMETRICAL PROBABILITYPOISSON POINT PROCESSHOMOGENEOUS POINT PROCESSISOTROPYERGODICITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 4 , December 1976 , pp. 714 - 722
Copyright
Copyright © Applied Probability Trust 1976 

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.)

References

Davy, P. J. and Miles, R. E. (1976) Sampling theory for opaque spatial specimens. To appear.Google Scholar
Giger, H. and Hadwiger, H. (1968) Über Treffzahlwahrscheinlichkeiten im Eikörperfeld. Z. Wahrscheinlichkeitsth, 10, 329–334.CrossRefGoogle Scholar
Giger, H. (1972) Grundgleichungen der Stereologie II. Metrika 18, 84–93.Google Scholar
Hadwiger, H. (1957) Vorlesungen über Inhalt, Oberfläche und Isoperimetrie. Springer, Berlin.CrossRefGoogle Scholar
Hadwiger, H. (1959) Normale Körper im euklidischen Raum und ihre topologischen und metrischen Eigenschaften. Math. Z. 71, 124–140.Google Scholar
Matheron, G. (1975) Random Sets and Integral Geometry. Wiley, New York.Google Scholar
Miles, R. E. (1974) The estimation of aggregate and overall characteristics from thick sections by transmission microscopy. In Electron Microscopy 1974, ed. Sanders, J. V. and Goodchild, D. J., Australian Academy of Science, Canberra, Vol. II, pp. 6–7.Google Scholar
Miles, R. E. (1976) On estimating aggregate and overall characteristics from thick sections by transmission microscopy. In Proceedings of the Fourth International Congress for Stereology held at NBS, Gaithersburg, Md. U.S.A., September 4–9, 1975. Special Publication 431, National Bureau of Standards, Washington, D.C., 3–12.Google Scholar
Streit, F. (1970) On multiple integral geometric integrals and their applications to probability theory. Canad. J. Math. 22, 151–163.Google Scholar