Multiscale Roughness Analysis of Particles: Application to the Classification of Detrital Sediments

Abstract

The shape of detrital quartz grains, mainly acquired under the effect of mechanical transport agents, has been observed and described for a long time by sedimentologists. The roughness of these grains is recognized as an important parameter for analyzing sediments, but to quantify this parameter with a discriminant measure can be difficult. By using the concept of multiresolution analysis and the wavelet formalism, we develop a roughness descriptor for particles, possessing multiscale analysis capabilities. It allows analyses of wear and erosion phenomena acting on particles by decomposing the information on the shape into different resolution levels, each level corresponding to a different scale. Thus it becomes possible to differentiate coarse roughness from finer roughness of a grain's outline. This descriptor is invariant under affine geometric transformation and can therefore be used to compare sands stemming from a wide range of natural environments. An application to the analysis and the classification of detrital sediments, along with a comparison with Fourier and fractal grain shape analysis, illustrates the performance of the method.