Stereological estimation of the rose of directions from the rose of intersections

Abstract

The paper is a review on the problem from stochastic geometry stated in the title. This problem concerns anisotropy quantification of fibre and surface processes. The stereological equation connecting the rose of directions and the rose of intersections (for a specific test system) was first attacked by means of analytical methods. Later on, an analogue from convex geometry lead to a deeper investigation using the notion of a Steiner compact. Various estimators of the rose of directions and their properties are reviewed in the planar and spatial case. The methods are important for practice when quantifying real structures in material science, biomedicine, etc. © 2005 Springer Science + Business Media, Inc.