Mathematical Geology

, 38:871 | Cite as

Computational Methods for the Determination of Roundness of Sedimentary Particles

  • Günther R. DrevinEmail author


A number of subjective and objective methods have been proposed to determine the roundness of rock particles, roundness being one of three properties describing the shape of a particle.

Methods that make use of the Fourier transform of the polar coordinates of particles’ edge elements are proposed in this paper. Lowpass filters are used to smooth the profiles of rock particle, roundness is then determined from the differences between the original and smooth profiles. Further methods that are proposed make use of different measures of inequality to quantify the distribution of the energy among the transform coefficients of the profiles of rock particles. These values are then used to determine the roundness of the particles. Entropy and Emlen’s modified entropy are the measures of inequality that are used. Different methods of determining the centre point of a particle and different methods to interpolate the edge elements are compared. The sensitivity of the methods to different resolutions is also investigated.

The results obtained with the proposed methods are comparable to those obtained with an existing Fourier transform based method, however it is shown that the proposed methods are computationally less demanding. It is also shown that the proposed methods are better than the existing method when the comparison is based on the correlation between the mean roundness of samples of particles and the actual roundness of the particles.


Fourier transform entropy Emlen’s modified entropy Kullback–Leibler distance. 


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Copyright information

© Springer Science + Business Media, Inc. 2007

Authors and Affiliations

  1. 1.School of Computing ScienceMiddlesex UniversityLondonUnited Kingdom
  2. 2.Department of Computer Science and Information Systems, School for Computer, Statistical and Mathematical SciencesNorth-West UniversityPotchefstroomSouth Africa

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