Defining and computing stable representations of volume shapes from discrete trace using volume primitives: Application to 3D image analysis in soil science

This paper presents an innovative approach for defining and computing stable (intrinsic) representations describing volume shapes from discrete traces without any a priori information. We assume that the discrete trace of the volume shape is defined by a binary 3D image where all marked points define the shape. Our basic idea is to describe the corresponding volume using a set of patches of volume primitives (bowls, cylinders, cones…). The volume primitives representation is assumed to optimize a criterion ensuring its stability and including a characterization of its scale (trade-off: fitting errors/number of patches). Our criterion takes also into account the preservation of topological properties of the initial shape representation (number of connected components, adjacency relationships…). We propose an efficient computing way to optimize this criterion using optimal region growing in an adjacency valuated graph representing the primitives and their adjacency relationships. Our method is applied to the modelling of porous media from 3D soil images. This new geometrical and topological representation of the pore network can be used to characterize soil properties.