Multivariate unfolding problems
Abstract
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.