Modelling Complex Volume Shape Using Ellipsoid: Application to Pore Space Representation

Natural shapes have complex volume forms that are usually difficult to model using simple analytical equations. The complexity of the representation is due to the heterogeneity of the physical environment and the variety of phenomena involved. In this study we consider the representation of the porous media. Thanks to the technological advances in Computed Topography scanners, the acquisition of images of complex shapes becomes possible. However, and unfortunately, the image data is not directly usable for simulation purposes. In this paper, we investigate the modeling of such shapes using a piece wise approximation of image data by ellipsoids. We propose to use a split-merge strategy and a region growing algorithm to optimize a functional including an error term and a scale term. The input of our algorithm is voxel-based shape description and the result is a set of tangent or disjoint ellipsoids representing the shape in an intrinsic way. We apply our method to represent 3D soil pore space from CT volume images. Within this specific context, we validate our geometrical modelling by using it for water draining simulation in porous media.