New parameter of roundness R: circularity corrected by aspect ratio

In this paper, we propose a new roundness parameter R, to denote circularity corrected by aspect ratio. The basic concept of this new roundness parameter is given by the following equation: $$ R=\mathrm{Circularity} + \left({\mathrm{Circularity}}_{\mathrm{perfect}\ \mathrm{circle}}-{\mathrm{Circularity}}_{\mathrm{aspect}\ \mathrm{ratio}}\right) $$ where Circularityperfect circle is the maximum value of circularity and Circularityaspect ratio is the circularity when only the aspect ratio varies from that of a perfect circle. Based on tests of digital circle and ellipse images using ImageJ software, the effective sizes and aspect ratios of such images for the calculation of R were found to range between 100 and 1024 pixels, and 10:1 to 10:10, respectively. R is thus given by $$ R = {\mathrm{C}}_{\mathrm{I}} + \left(0.913-{\mathrm{C}}_{\mathrm{AR}}\right) $$ where CI is the circularity measured using ImageJ software and CAR is the sixth-degree function of the aspect ratio measured using the same software. The correlation coefficient between the new parameter R and Krumbein’s roundness is 0.937 (adjusted coefficient of determination = 0.874). Results from the application of R to modern beach and slope deposits showed that R is able to quantitatively separate both types of material in terms of roundness. Therefore, we believe that the new roundness parameter R will be useful for performing precise statistical analyses of the roundness of particles in the future.