Stereological correction of linear grade distributions for mineral liberation

Accurate measurement of the distribution of particle composition by image analysis requires a reliable method for the calculation of the stereological correction that must be applied to the composition distribution that is measured using linear and areal section measurements. Linear or areal measurements are usually obtained from SEM images of polished sections through a representative sample of the particle population. A stereological correction based on the solution f(v) of the inverse problem Kf(v) = F-l is developed in this paper. The kernel matrix was accurately measured using a sample of dolomite-sphalerite ore which was carefully fractionated using a batch magnetic-fluid separation technique. The solution of the inverse problem is obtained based on the minimization of \\kf(v) - F-l\\ + lambda Sigma(f)f(v)(f) Inf(v)(j) subject to the constraints f(v)(j) greater than or equal to 0 and Sigma(j)f(v)(j) = 1. A method is presented for selecting the most appropriate kernel to suit the mineralogical texture of the ore. The stereological correction is shown to be accurate by comparison against real laboratory data measured using magnetic-fluid fractionation techniques. The method is convenient and is suitable for routine use in image analysis systems. (C) 1998 Elsevier Science S.A. All rights reserved.