Identification of primary shape descriptors on 3D scanned particles

Abstract

The number of global mechanical equilibria as a shape descriptor (among others, for sedimentary particles) is at the forefront of current geophysical research. Although the technology is already available to provide scanned, 3D images of the particles (appearing as fine spatial discretization of smooth surfaces), nevertheless, the automated identification and measurement of global equilibria on such 3D images has not been solved so far. The main difficulty lies in the algorithmic distinction between local equilibria (associated with the small un-evenness of the pebble's surface) and global equilibria, associated with the overall shape. The former are easily measured, however, only the latter provide meaningful physical information. Here we provide and illustrate an algorithm to detect global equilibrium points on a finely discretized, polyhedral surface provided by 3D scan of sedimentary particles.