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

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.

Sampling surface and subsurface particle-size distributions in wadable gravel-and cobble-bed streams for analyses in sediment transport, hydraulics, and streambed monitoring

“…Further discussion of conceptual and practical issues regarding particle roundness are provided by Diepenbroek et al (1992).…”

Terrestrial Laser Scanning of grain roughness in a gravel-bed river

“…Surface grain-size has also been measured using emulsion-based photography (Kellerhals and Bray, 1971;Adams, 1979;Ibbeken and Schleyer, 1986;Church et al, 1987;Rice and Church, 1998), through direct measurement at grid-selected positions on the image, or by counting visible grains and conversion to a mean grain-size via a calibration relation (Church et al, 1987;Rice, 1995). This approach can be extremely time-consuming due to the post processing required, with even the more advanced photo-sieving procedures requiring manual identification and digitisation of grain boundaries (Ibbeken and Schleyer, 1986;Diepenbrook et al, 1992;Diepenbrook and De Jong, 1994;Ibbeken et al, 1998). More recently, digital imagery and automated image processing techniques have been introduced, that provide accurate representations of grain roughness but are limited to small areas (Butler et al, 1998(Butler et al, , 2001aLane, 2002, Sime andFerguson, 2003;Graham et al, 2005), with the exception of Carbonneau et al (2004Carbonneau et al ( , 2005) who have demonstrated some success in the use of aerial imagery for grain-size determination over larger areas of river channel.…”

New parameter of roundness R: circularity corrected by aspect ratio

“…However, such a method merely compares visual images, and therefore, the derived roundness values are not strictly quantitative. The second approach involves the quantitative determination of various shape parameters, and many evaluation methods have been designed to obtain relevant shape parameters (e.g., Schwarcz and Shane 1969;Orford and Whalley 1983;Diepenbroek et al 1992;Yoshimura and Ogawa 1993;Vallejo and Zhou 1995;Bowman et al 2001;Itabashi et al 2004;Drevin 2007;Blott and Pye 2008;Lira and Pina 2009;Roussillon et al 2009;Arasan et al 2011;Suzuki et al 2013Suzuki et al , 2015. Both approaches, however, involve the analysis of each individual particle, and therefore, production of several thousand to several tens of thousands of shape parameters for reliable analysis is time consuming.…”

“…Previous studies into particle shape have been discussed in a series of review articles (e.g., Barrett 1980;Clark 1981;Winkelmolen 1982;Diepenbroek et al 1992;Blott and Pye 2008), and in general, such studies have mainly taken one of two approaches to understanding particle shape. The first is a simple method that involves the examination of visual images of particle grains (e.g., Krumbein 1941;Rittenhouse 1943;Powers 1953;Pettijohn 1957;Lees 1963).…”