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Methodology

Solid earth sciences

201601201601

### 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 + (Circularity_{perfect circle} - Circularity_{aspect 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 = C_{I} + (0.913 - C_{AR})

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.