Automatic computation of pebble roundness using digital imagery and discrete geometry

The shape of sedimentary particles is an important property, from which geographical hypotheses related to abrasion, distance of transport, river behavior, etc. can be formulated. In this paper, we use digital image analysis, especially discrete geometry, to automatically compute some shape parameters such as roundness, i.e. a measure of how much the corners and edges of a particle have been worn away. In contrast to previous work in which traditional digital images analysis techniques, such as Fourier transform, are used, we opted for a discrete geometry approach that allowed us to implement Wadell's original index, which is known to be more accurate, but more time consuming to implement in the field. Our implementation of Wadell's original index is highly correlated (92%) with the roundness classes of Krumbein's chart, used as a ground-truth. In addition, we show that other geometrical parameters, which are easier to compute, can be used to provide good approximations of roundness. We also used our shape parameters to study a set of pebbles digital images taken from the Progo basin river network (Indonesia). The results we obtained are in agreement with previous work and open new possibilities for geomorphologists thanks to automatic computation.