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

Abstract

SummarySize 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.

The Fragmentation Energy-Fan Model in Quarry Blasts

“…At this size the passing is calculated from the surface of non-delineated particles corrected by a factor. This factor defines the percentage of non-delineated material that is actually made of fines (Sanchidrián et al 2009), and was set during the system commissioning to a low value as no significant amount of fines is apparent in the images (since they bypass the crusher feed). Below 32 mm, the system extrapolates fragmentation through an analytical size distribution function which parameters are calculated from two points in the range of sizes in which delineation is reliable (Split Engineering 2010).…”

“…Although enhanced 2D technologies (often called 3D though they are not really determining fragmentation of a rock volume) to monitor fragmentation are available, such as LiDAR imaging-laser imaging detection and ranging (McKinnon and Marshall 2014;Oñederra et al 2015;Thurley 2013;Thurley et al 2015) or photogrammetry (Noy 2013(Noy , 2015Bamford et al 2016), 2D image analysis is still the most common tool used. Image analysis systems may show a poor performance at small sizes especially when they have not been calibrated (Sanchidrián et al 2009) and it is advisable to use additional tools to correct raw data on a blast per blast basis in order to get a good estimation of the actual size distribution (Sanchidrián et al 2006).…”

Segmentation algorithm of complex ore images based on templates transformation and reconstruction

“…However, the marking and segmenting of ore objects in a complex image are very challenging [1][2]. Some heterogeneous ore objects with various sizes are coexisting, and a number of small ores embedded into big ores bring about noise.…”

A real-time analysis of post-blast rock fragmentation using UAV technology

“…Image analysis techniques enable practical, fast, and relatively accurate measurement of rock fragmentation. However, the following limitations of image analysis have been identified [4]:…”