SYMPOSIA PAPER Published: 01 January 1972

The Mathematical Foundations of Quantitative Stereology


Quantitative stereology is the generalized body of methods, applicable to any material, for the quantitative characterization of three-dimensional microstructures by means of two-dimensional sections through the solid or projections to a plane. We deal here with the mathematical aspects of the relationships linking the two-dimensional section (or projection) to the microstructural features in the three-dimensional material. Thus, one must consider the metric relationships as well as the geometrical and topological properties of microstructures in order to completely characterize a material. Topics selected for discussion include geometrical probabilities, particle characteristics and size distributions, curvature, topological relationships, and projected images.

Author Information

Underwood, EE
Georgia Institute of Technology, Atlanta, Ga.
Price: $25.00
Contact Sales
Reprints and Permissions
Reprints and copyright permissions can be requested through the
Copyright Clearance Center
Developed by Committee: E04
Pages: 3–38
DOI: 10.1520/STP36841S
ISBN-EB: 978-0-8031-4610-5
ISBN-13: 978-0-8031-0095-4