Acta Stereologica



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Viktor Beneš, Arun M. Gokhale & Margarita Slámová

Unfolding the bivariate size-orientation distribution

(Volume 15 (1996) — Number 1 - Mathematical foundations of stereology - Feb. 1996)
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A new stereological problem, unfolding the bivariate size-orientation distribution of platelike particles from vertical uniform random sections, is solved. While the theoretical double integral equation has been derived by Gokhale(1995), here we proceed by discretization. The input histogram of planar size-orientation parameters is transformed to the desired histogram of spatial quantities. The discretized equation is solved by means of an EM-algorithm. Practical application when investigating the damage initiation process in metal matrix composites follows. The data measured by an image analyser are transformed and some important parameters are derived from the bivariate distribution.

Keywords : platelike particles, size-orientation distribution, unfolding

To cite this article

Viktor Beneš, Arun M. Gokhale & Margarita Slámová, «Unfolding the bivariate size-orientation distribution», Acta Stereologica [En ligne], Volume 15 (1996), Number 1 - Mathematical foundations of stereology - Feb. 1996, 9-14 URL :

About: Viktor Beneš

Dept. of Mathematics FSI, Czech Technical University, Karlovo nám.13, 12135 Prague 2, Czech Republic

About: Arun M. Gokhale

School of  Material Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0245, USA

About: Margarita Slámová

Innovation and Technological Centre VÚK, Panenské Břežany, 25070 Odolena Voda, Czech Republic