The Mathematical Foundations of Quantitative Stereology

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Abstract
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.