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Solid earth sciences
New parameter of roundness R: Circularity corrected by aspect ratio
Takashimizu Y, Iiyoshi M
Aspect ratio, Circularity, ImageJ software, Krumbein’s visual roundness, Roundness
Basic concept of transformation from a perfect circle. Narrow solid lines denote perfect circles before transformation. a) Only the perimeter increases; the area does not change. b) Only the area decreases; the perimeter does not change.
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 = Circularity + (Circularityperfect circle - Circularityaspect ratio)
where Circularity perfect circle is the maximum value of circularity and Circularity aspect 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 = CI + (0.913 - CAR)
where C I is the circularity measured using ImageJ software and C AR 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.