Survey of procedures for estimating the distribution of spherical particles from plane sections

Estimating the size distribution of particles in a sample volume from area analysis of a planar slice is one of the difficult fundamental problems of applied stereology. The original formulation of an integral equation by Wicksell (1925) as an approach to this problem led to the development of several procedures for solution, including a simple model of successive differences by Saltikov (1967), a generalized method of successive differences by Lewis et al (1973), a method of moments by Watson (1971), polynominal fits by Minerbo and Levy (1969), spectral differentiation and product integration by Anderssen and Jakemann (1975), and ridge regression and cross validation by Wahba (1979). This discussion presents yet another method (Histogram Method) for solution of the problem, and introduces a constrained minimum variance estimator procedure which eliminates the negative probability anomaly. Several examples of the use of the above methods in analysis of real data are given. The utility of the constrained minimum variance procedure used with the Saltikov and Histogram methods is demonstrated