** Progress in Earth and Planetary Science is the official journal of the Japan Geoscience Union, published in collaboration with its 50 society members.

    ** Progress in Earth and Planetary Science is partly financially supported by a Grant-in-Aid for Publication of Scientific Research Results to enhance dissemination of information of scientific research.

    >>Japan Geoscience Union

    >>Links to 50 society members

    • Progress in Earth and Planetary Science
    • Progress in Earth and Planetary Science
    • Progress in Earth and Planetary Science
    • Progress in Earth and Planetary Science
    • Progress in Earth and Planetary Science
    Progress in Earth and Planetary Science

    Gallery View of PEPS Articles

    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 + (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.