Acta Stereologica Acta Stereologica -  Volume 12 (1993)  Number 2 - Proceedings of the sixth European congress for stereology - Part one - Dec. 1993 

Second order stereology for anisotropic Boolean segment processes with application

Joël Chadœuf
Laboratoire de Biométrie, Domaine St Paul, BP 91, 84140 Montfavet, France
Viktor Beneš
Dept of Mathematics, FSI, Czech Technical University, Karlovo Nám. 13, 12135 Prague 2, Czech Republic
Pascal Monestiez
Laboratoire de Biométrie, Domaine St Paul, BP 91, 84140 Montfavet, France
André Kretzschmar
Laboratoire de Zoologie, Domaine St Paul, BP 91, 84140 Montfavet, France

Abstract

This paper describes statistical properties of various estimators of intensity of anisotropic boolean segment processes. In order to quantify the estimation variances, the pair correlation function of appropriate random measures has to be evaluated. The projections of the process on R1 and intersections with a system of (d−1)-dimensional parallel hyperplanes were studied. Some results of Beneš et al 1993 are used, where the second order stereological formula for the pair correlation function of the projection measure of anisotropic fibre processes was derived and estimation variances compared.

These results were applied to a study of soil porosity, where the earthworm burrow system were modelled by a segment process.

The variances of these estimators were compared and the convergence of the serial section estimator to the projection estimator illustrated. The variance of the serial section estimator decreases rapidly when the number of sections increases and flattens out to the variance of the projection estimator. This approximation was used to discuss the effect of the sample shape onto the variance of length intensity estimation by using serial sections.

Keywords : anisotropy, boolean segment process, estimation variance, length density

To cite this article

Joël Chadœuf, Viktor Beneš, Pascal Monestiez & André Kretzschmar, «Second order stereology for anisotropic Boolean segment processes with application», Acta Stereologica [En ligne], Volume 12 (1993), Number 2 - Proceedings of the sixth European congress for stereology - Part one - Dec. 1993, 175-180 URL : https://popups.ulg.ac.be/0351-580x/index.php?id=4721.