Geometric probability based stereological corrections

Abstract

In mineral processing, a classic problem is that of estimating the particle composition distribution from particle sections. This problem occurs because mineralogical analysis is performed on particle sections rather than the particles. Thus one wishes to infer three-dimensional information (particle composition distribution) from two-dimensional information (particle sections). There are a number of different techniques available for estimating the particle composition distribution and these are called stereological corrections. This paper provides examples of very simple stereological corrections based on geometric probability equations as well as the principle of maximum entropy. The paper focuses on three methods. The first method is a simple entropy based model based on particle section information only. The second method also uses entropy, but the entropy is based on relating particles to particle sections, and is therefore more complex than the first. The third model uses both the particle section distribution and the linear intercept distribution. The most accurate model is that which uses both particle sections and linear intercepts.