Representativity of 2D Shape Parameters for Mineral Particles in Quantitative Petrography

TLDR

The study aims to develop a numerical method for estimating sphericity, roundness, and roughness on artificially designed particles and to assess the interdependence of these shape parameters. The authors designed theoretical particles, optimized automated measurement conditions, quantified shape parameters (FD, So, Rw, ¥, S) using computer‑vision image processing, and analyzed their interrelationships. They determined that particle shape analysis requires minimum sizes of 150 or 50 pixels, that FD and So are independent of sphericity while Rw and ¥ depend on it and must be corrected, and introduced a new regularity parameter RBC that was validated in a case study.

Abstract

This paper introduces an assessment of the representation of shape parameter measurements on theoretical particles. The aim of the study was to establish a numerical method for estimating sphericity, roundness, and roughness on artificially designed particles and to evaluate their interdependence. The parameters studied included a fractal dimension (FD), solidity (So), Wadell’s roundness (Rw), a perimeter-area normalized ratio (¥), and sphericity (S). The methods of the work included: (a) the design of theoretical particles with different shapes, (b) the definition of optimal analysis conditions for automated measurements, (c) the quantification of particle parameters by computer vision-based image processing, and (d) the evaluation of interdependence between the parameters. The study established the minimum sizes required for analysis of the particle shape. These varied depending on the method used (150 pixels or 50 pixels). Evaluating the relationships between the parameters showed that FD and So are independent of S. Nevertheless, Rw and ¥ are clearly dependent on S and, thus, must be numerically corrected to Rwc and ¥c. FD, So, Rwc, and ¥c were used to establish, mathematically, a new regularity parameter (RBC) that reflects the degree of roundness of a particle. The process was applied to a case study and the evaluation of all parameters corroborated previous petrographic characterizations.