Abstract
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.
Highlights
Many studies have investigated particle shape in the natural world, mostly based on the definitions of sphericity and roundness of rock particles proposed by Wadell (1932)
We define a new roundness parameter, R, to denote the circularity corrected by aspect ratio, and present a case study of R calculation using ImageJ software released from the US National
Aspect ratio we examine the relationship between the aspect ratio measured using ImageJ software (ARI) and the widths of test ellipse images (Fig. 4), which were obtained by subjecting the test circle images in Fig. 2 to 10 % aspect ratio deformation intervals in Adobe Photoshop CS4
Summary
Many studies have investigated particle shape in the natural world, mostly based on the definitions of sphericity and roundness of rock particles proposed by Wadell (1932). We define a new roundness parameter, R, to denote the circularity corrected by aspect ratio, and present a case study of R calculation using ImageJ software Basic concept of this study The proposed concept for the new roundness parameter is quite simple: It is a correction of circularity using the aspect ratio of particles. The definition of circularity, corresponding to that of parameter K defined by Cox (1927), is given as follows: Circularity This indicates that circularity can be altered in two ways: by changes in area and by changes in the perimeter of a particle. If only the perimeter increases and the area does not change (Fig. 1a, towards the right), circularity decreases. A decrease in area in this way represents an increase in the aspect ratio of the particle image. Case study of parameter R calculation using ImageJ software In this chapter, we present a specific case study, demonstrating the calculation of the parameter R defined in the previous chapter, using ImageJ software
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