Segmentation of 3D pore space from CT images using curvilinear skeleton: application to numerical simulation of microbial decomposition

Recent advances in 3D X-ray Computed Tomographic (CT) sensors have stimulated research efforts to unveil the extremely complex micro-scale processes that control the activity of soil microorganisms. Voxel-based description (up to hundreds millions voxels) of the pore space can be extracted, from grey level 3D CT scanner images, by means of simple image processing tools. Classical methods for numerical simulation of biological dynamics using mesh of voxels, such as Lattice Boltzmann Model (LBM), are too much time consuming. Thus, the use of more compact and reliable geometrical representations of pore space can drastically decrease the computational cost of the simulations. Several recent works propose basic analytic volume primitives (e.g. spheres, generalized cylinders, ellipsoids) to define a piece-wise approximation of pore space for numerical simulation of draining, diffusion and microbial decomposition. Such approaches work well but the drawback is that it generates approximation errors. In the present work, we study another alternative where pore space is described by means of geometrically relevant connected subsets of voxels (regions) computed from the curvilinear skeleton. Indeed, many works use the curvilinear skeleton (3D medial axis) for analyzing and partitioning 3D shapes within various domains (medicine, material sciences, petroleum engineering, etc.) but only a few ones in soil sciences. Within the context of soil sciences, most studies dealing with 3D medial axis focus on the determination of pore throats. Here, we segment pore space using curvilinear skeleton in order to achieve numerical simulation of microbial decomposition (including diffusion processes). We validate simulation outputs by comparison with other methods using different pore space geometrical representations (balls, voxels).Comment: preprint, submitted to Computers & Geosciences 202

3D shape extraction segmentation and representation of soil microstructures using generalized cylinders

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 mu m) 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

Simulación dinámica y deformaciones de superfícies paramétricas

Se desarrolla un modelo basado en NURBS, BSplines4D, de representación de superficies parametrizadas en 4D. El objetivo es la representación y simulación dinámica de superficies deformables basadas en el modelo; se realiza un estudio de las ecuaciones del movimiento, asociando un funcional de energía para medir la deformación de objetos, realizando un estudio riguroso sobre los métodos de integración y de discretización, tanto temporal como espacial, determinando su adecuación para resolver el sistema de ecuaciones diferenciales generado. El movimiento y la simulación de la deformación se realizan exclusivamente usando los puntos de control 4D, obteniendo una eficiencia numérica y computacional excelentes. La determinación del modelo BSplines4D se realiza tras un estudio pormenorizado de los modelos existentes. También se ha utilizado para desarrollar un modelo, N-Scodef, de deformaciones de formas libres (FFD), utilizando deformaciones geométricas basadas en restricciones. Se han establecido las condiciones para aplicar restricciones con trayectorias no rectilíneas, representadas por curvas B-Spline 4D. La deformación se adapta de forma precisa a la forma descrita por las curvasEs desenvolupa un model basat en NURBS, Bsplines4D, de representació de superfícies parametritzades en 4D. L'objectiu és la representació i simulació dinàmica de superfícies deformables basades en el model; es realitza un estudi de les equacions del moviment, associant un funcional d'energia per mesurar la deformació d'objectes, realitzant un estudi rigorós sobre els mètodes d'integració i discretització, tant temporal com espacial, determinant la seva adequació per resoldre el sistema d'equacions diferencials generat. El moviment i la simulació de la deformació es realitzen exclusivament utilitzant els punts de control 4D, obtenint una eficiència numèrica i computacional excel·lents. La determinació del model Bsplines4D es realitza després d'un estudi detallat dels models existents. També s'ha utilitzat per desenvolupar un model, N-Scodef, de deformacions de formes lliures (FFD), utilitzant deformacions geomètriques basades en restriccions. S'han establert les condicions per aplicar restriccions amb trajectòries no rectilínies, representades per corbes B-Spline 4D. La deformació s'adapta de forma precisa a la forma descrita per les corbesBsplines4D, a NURBS based model, is presented. The model allows the representation of 4D parameterized surfaces. The objective is the representation and dynamic simulation of deformable surfaces based on this model; a study of the movement equations has been made, associating to them an energy functional to measure the objects' deformation. A rigorous study on the integration and discretization, both temporal and spatial, is made to evaluate its suitability to solve the system of differential equations generated. The movement and simulation of the deformation is performed only using the 4D control points. An excellent numeric and computational efficiency is achieved. The Bsplines4D model is obtained after a detailed study on the existent models. The model has been also used to develop a free-form deformable (FFD) model, N-Scodef, using geometric constraint-based deformations. The conditions to apply constraints with non rectilinear trajectories, based on 4D B-Spline curves, have been established. The deformations fit precisely to the curves form