ON THE STEREOLOGY OF ELLIPSOIDS AND CYLINDERS

The problem of deducing the shapes and spatial distribution of ellipsoids and cylinders from the distributions of ellipses in plane sections is considered. We show that most of the problems are either under- or over-determined by comparing the dimensionalities of the spaces over which the distribution of ellipses, and the distribution of ellipsoids or cylinders are defined. The information which can be determined if we make some assumption about the physical distribution is shown for two under-determined problems: we show how the distribution of shapes of triaxial ellipsoids can be found using the maximum entropy ansatz; and that a simple physical ansatz can be applied to recover the distribution of orientations of cylinders. For the over-determined problems, we show how a subset of the data can be used to solve the problems of finding the two-body distribution of isotropically arranged, monodisperse ellipsoids and the distribution of near contacts between long cylinders.