Dynamic 3D Models with Local and Global Deformations: Deformable Superquadrics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
From volume medical images to quadratic surface patches
Computer Vision and Image Understanding
Algorithmic geometry
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
DXSoil, a library for 3D image analysis in soil science
Computers & Geosciences
Coupling pore-scale networks to continuum-scale models of porous media
Computers & Geosciences
Visualization of grids conforming to geological structures: a topological approach
Computers & Geosciences
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This paper focuses on the modeling of soil microstructures using generalized cylinders, with a specific application to pore space. The geometric modeling of these microstructures is a recent area of study, made possible by the improved performance of computed tomography techniques. X-scanners provide very-high-resolution 3D volume images (3-5@mm) of soil samples in which pore spaces can be extracted by thresholding. However, in most cases, the pore space defines a complex volume shape that cannot be approximated using simple analytical functions. We propose representing this shape using a compact, stable, and robust piecewise approximation by means of generalized cylinders. This intrinsic shape representation conserves its topological and geometric properties. Our algorithm includes three main processing stages. The first stage consists in describing the volume shape using a minimum number of balls included within the shape, such that their union recovers the shape skeleton. The second stage involves the optimum extraction of simply connected chains of balls. The final stage copes with the approximation of each simply optimal chain using generalized cylinders: circular generalized cylinders, tori, cylinders, and truncated cones. This technique was applied to several data sets formed by real volume computed tomography soil samples. It was possible to demonstrate that our geometric representation supplied a good approximation of the pore space. We also stress the compactness and robustness of this method with respect to any changes affecting the initial data, as well as its coherence with the intuitive notion of pores. During future studies, this geometric pore space representation will be used to simulate biological dynamics.