On the accuracy of fragment size measurement by image analysis in combination with some distribution functions

Abstract

Size distributions of fragments of crushed rock in conveyor belts and of blasted rock in a muckpile obtained by sieving are compared with the size distributions obtained by digital image analysis of photographs of the same materials taken on-site. Several calculation methods are tested, based on the raw distribution of fragment areas and on the volume-transformed ones. The influence of the calibration of the system on the results and the performance of the system in a non-calibrated mode are evaluated. The capacity of some distributions (Rosin-Rammler, Swebrec and lognormal) to fit the data in the coarse region (where particles can be delineated, i.e. discriminated individually) and to extrapolate to the non-delineated fines (where particles cannot be outlined and their contour delineated) is assessed. The error between the sizes measured and the sizes of the reference distributions (determined by sieving) increases from the coarse to the fines region. The maximum error at a given size depends primarily on its value relative to the fines cut-off (FCO) of the image analysis. In general, at sizes greater than the FCO, where the system is able to delineate fragments reliably, both volume and surface-based, calibrated, calculations can determine the sizes with maximum error expectancy of about 30%. Below the FCO, only the calibrated, volume calculation maintains a maximum error of 30%, down to sizes of about one fourth the FCO, rapidly increasing for smaller sizes. Where the calibration is done based on data above the FCO, errors can be large below this point, in excess of 80% at sizes half the FCO. In the fines range (sizes smaller than 0.2 times the FCO) the maximum errors can be close to or greater than 100% for most of the calculations and function fittings. Of the distributions tested, all of them are acceptable at sizes above the FCO; below that, the Swebrec function seems to adapt better towards the fines than the Rosin-Rammler and lognormal.