Acta Stereologica Acta Stereologica -  Volume 17 (1998)  Number 2 - Sep. 1998 

Multivariate unfolding problems

Viktor Beneš
Dept. of Mathematics FSI, Czech Technical University, Karlovo nám. 13, 12135 Prague 2, Czech Republic
Margarita Slámová
Research Institute for Metals, Panenské Břežany, 25070 Odolena Voda, Czech Republic


The classical stereological unfolding problem for particle systems is studied. While previously at most bivariate problems were solved, here a multivariate version is formulated. Then the unfolding of the joint trivariate distribution of size, shape factor and orientation of spheroidal particles is demonstrated using vertical uniform random sections. The formulation and solution is design-based, first the integral equations are derived, then a numerical solution is discussed. It is emphasized that under the conditional independence property of particle sections, the unfolding problem studied can be decomposed into a series of two simpler problems. The intensity NVestimator is obtained in the first step which is equivalent to the Wicksell problem of spheres. Finally an application of the results to the study of damage initiation in materials is presented.

Keywords : conditional independence, size-shape-orientation distribution, stereological unfolding, vertical sections

To cite this article

Viktor Beneš & Margarita Slámová, «Multivariate unfolding problems», Acta Stereologica [En ligne], Volume 17 (1998), Number 2 - Sep. 1998, 189-199 URL :