a1 Mathematics Department, University of Oklahoma, Norman, Oklahoma 73019, U.S.A.
a2 Mathematisches Institut II, Universität Karlsruhe, Englerstrasse 2, 7500 Karlsruhe 1, Germany
Random sectioning of particles (compact sets in 3 with interior points) is a familiar procedure in stereology where it is used to estimate particle quantities like volume or surface area from planar or linear sections (see, for example, the survey  or the book ). In the following, we study the problem whether the whole shape of a convex particle K can be estimated from random sections. If E is an IUR (isotropic, uniform, random) line or plane intersecting K then the intersection Xk = K E is a (k-dimensional, k = 1 or 2) random set. It is clear that the distribution of Xk determines K uniquely and that if E1,…, En are such flats, the most natural estimator for K would be the convex hull
(Received February 13 1991)
(Revised January 07 1992)