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. Minerals 2019, 9, 768 2 of 21 corners of the particle. Six categories of roundness for sediment grains have been established and, for each category, one grain of low and one of high sphericity was introduced [3,6-9]. The six categories are: Very angular, angular, subangular, sub-rounded, rounded, and well-rounded. Two-dimensional particle shape measurements are particularly applicable when individual particles cannot be extracted from the rock matrix (e.g., thin sections under an optical microscope). Microscopic images are two-dimensional. Therefore, they only show part of the shape of the three-dimensional particle. The assessed image is usually of particles lying on their most stable plane on a flat support, i.e., showing the largest projection area.Traditionally, roundness indices compare the outline of a 2D projection of the particle to a circle. The first comparison defines the roundness as the ratio ri/R, which was shown in [10] (where ri is the radius of the sharpest corner, and R is the radius of the smallest circumscribing sphere). On the other hand, [11] defined the roundness parameter based on the radius of the curvature of particle corners and the radius of the largest inscribed sphere.[6] and [7] used comparison charts with a class limit table for roundness. Some authors considered angularity to be the opposite of roundness, while others considered the degree of angularity [12] to be a combination of the angular relationship between the planes bounding a corner and the distance of the corner from the center of the particle. The overall particle form heavily influences the method. In addition, [12] presente...
