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How round is round? A new approach to the topic 'roundness' by Fourier grain shape analysis

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Diepenbroek, M. , Bartholomä, A. and Ibbeken, H. (1992): How round is round? A new approach to the topic 'roundness' by Fourier grain shape analysis , Sedimentology, 39 (3), pp. 411-422 . doi: 10.1111/j.1365-3091.1992.tb02125.x
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Abstract:

Numerous methods for roundness measurement have been developed. None, however, has been generally accepted, because of conceptual and practical deficiencies. Modern image processing and Fourier grain shape analysis have eliminated the practical shortcomings, but the conceptual ones remained. Single, higher harmonics of the Fourier series, for example, fail to serve as reliable equivalents for roundness evaluation. The concept outlined in this paper recognizes three criteria for the evaluation of roundness. (1) All curvatures, convex as well as concave or plane elements, must be considered. (2) The positions of morphological elements are significant because salient parts of a particle are more easily abraded than protected ones. Consequently, the curvatures have to be weighted by their relative position on the particle. (3) Positions and curvatures of morphological elements have to be compared with the particle's ultimate abraded shape, which is assumed to be an ellipsoid. The ellipsoid reflects the aspect of form or sphericity. The distinction between sphericity and roundness is retained because there is no evidence that sphericity changes significantly during transport. The measurement is based on the outline of a particle's maximum projection plane, which is transformed to a Fourier series. Roundness data are derived from the complete amplitude spectrum. The aspect of sphericity is eliminated by subtracting the amplitude spectrum of the best approximating ellipse from the spectrum of the empirical shape. The residual amplitudes are normalized and summed. In a final step the resulting values are rescaled. This guarantees reasonable boundaries and a normal distribution of roundness values. The procedure is automated and its efficiency permits the calculation of large samples. Tests on fluvial and coastal gravel populations demonstrate that the method is sensitive to abrasional wear during all stages of roundness.

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