Computers & Geosciences 33 (2007) 1140–1161 Representing geometric structures in 3D tomography soil images: Application to pore-space modeling Olivier Monga à , Fatou Ndeye Ngom, Jean Franc - ois Delerue Laboratoire MAT (UCAD2/IRD), UR Geodes, Centre IRD de Dakar, BP 1386, CP 18524, Dakar, Senegal Received 28 November 2005; received in revised form 12 October 2006; accepted 16 November 2006 Abstract Only in the last decade have geoscientists started to use 3D computed tomography (CT) images of soil for better understanding and modeling of soil properties. In this paper, we propose one of the first approaches to allow the definition and computation of stable (intrinsic) geometric representations of structures in 3D CT soil images. This addresses the open problem set by the description of volume shapes from discrete traces without any a priori information. The basic concept involves representing the volume shape by a piecewise approximation using simple volume primitives (bowls, cylinders, cones, etc.). This typical representation is assumed to optimize a criterion ensuring its stability. This criterion includes the representation scale, which characterizes the trade-off between the fitting error and the number of patches. We also take into account the preservation of topological properties of the initial shape: the number of connected components, adjacency relationships, etc. We propose an efficient computation method for this piecewise approximation using cylinders or bowls. For cylinders, we use optimal region growing in a valuated adjacency graph that represents the primitives and their adjacency relationships. For bowls, we compute a minimal set of Delaunay spheres recovering the skeleton. Our method is applied to modeling of a coarse pore space extracted from 3D CT soil images. The piecewise bowls approximation gives a geometric formalism corresponding to the intuitive notion of pores and also an efficient way to compute it. This geometric and topological representation of coarse pore space can be used, for instance, to simulate biological activity in soil. r 2007 Elsevier Ltd. All rights reserved. Keywords: 3D computed tomography soil images; Functional minimization; Soil properties; Geometric modeling; Computational geometry; Region growing; Delaunay triangulation 1. Introduction This article deals with the modeling of geometric structures from 3D computed tomography (CT) soil images. The aim is to propose a generic approach for computing geometrical representations of soil structures relevant for soil properties. To achieve this goal, the generic problem set by the definition and computation of stable (intrinsic) representa- tions of volume shapes from discrete traces is dealt with. This problem is also a key point in various application fields (medicine, industrial inspection, robotics, etc.) in which CT yields 3D volume images describing structural and topological information. Many methods devoted to surface modeling from 3D images have been developed within the last two decades, mainly for medical applications (Ayache, ARTICLE IN PRESS www.elsevier.com/locate/cageo 0098-3004/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.cageo.2006.11.015 à Corresponding author. E-mail address: Olivier.Monga@ird.sn (O. Monga).