ℓ_1-Based Construction of Polycube Maps from Complex Shapes

Polycube maps of triangle meshes have proved useful in a wide range of applications, including texture mapping and hexahedral mesh generation. However, constructing either fully automatically or with limited user control a low-distortion polycube from a detailed surface remains challenging in practice. We propose a variational method for deforming an input triangle mesh into a polycube shape through minimization of the ℓ_1-norm of the mesh normals, regularized via an as-rigid-as-possible volumetric distortion energy. Unlike previous work, our approach makes no assumption on the orientation, or on the presence of features in the input model. User-guided control over the resulting polycube map is also offered to increase design flexibility. We demonstrate the robustness, efficiency, and controllability of our method on a variety of examples, and explore applications in hexahedral remeshing and quadrangulation

Quantitative characterisation of the geometry and topology of pore space in 3D rock images

In this thesis, a suite of techniques and algorithms is presented to tackle three main tasks. Firstly, many existing image-related approaches (processing or analysis) need to be extended from low-dimensional space (e.g. 2D) to a higher-dimensional space(3D). In addition, they often also need to be improved to achieve better accuracy and more efficiency to enable processing ofmassive volumetric images. Frequently new / techniques or algorithms also need to be developed to cover the gap in these previous requirements. Based on these approaches, the second task is to extract the geometric and topological properties of the pore space directly from 3D images of rock samples. The third task is then to study and to establish the relationship between the microstructure and the macroscopic properties by constructing realistic network structures for network models or by conducting some numerical experiments such as mercury injection etc. In the framework of the methodology presented in this thesis, many commonly used image processing and analysis approaches form the basis of the pore space quantification procedure. These primarily include 3D Euclidean distance transformations, 3D geodesic distance transformations, component labelling (clustering), and morphological operations. Among these techniques, some are either unavailable in 3D discrete space or are of too low-efficiency for handling the huge size of rock samples, and others simply did not exist prior to my work. The next level of the methodology is. to quantify the pore space. In order to process 3D images efficiently thus, firstly, the medial axis (skeleton) of the object (e.g. the pore space) is generated so that simple and compact basic information of the object remains while irrelevant redundant information is neglected in the resultant skeleton image. Having obtained the skeleton of an object, most of the geometric and topological quantities of this object can then be easily derived. After reviewing many existing algorithms, a more accurate and efficient thinning algorithm is presented to meet the specific requirements for the study of pore microstructure. Furthermore, general geometric and topological properties of the pore space are calculated and analysed, including pore size distribution, bond (or node) radii/length/volume, shape factor and coordination number etc. As an important contribution, a novel algorithm to compute the Euler-Poincare characteristic (Euler number) is presented and a new topological descriptor is introduced to overcome the limitations of the Euler number and the coordination number. To validate the methodology and to carry out some basic analysis of the microstructure of porous media, I investigate the geometric and topologic features directly from 3D binary images of rock samples. The volum~tric pore size distribution is obtained, and the frequency of pore inscribed radii (or diameter) is calculated, the shape of cross sections along pore channels is quantified as the shape factor and the corresponding algorithm is created. In this study, many quantities for describing the morphological properties of porous media have been successfully introduced. To carry this novel methodology into the use of network models for the prediction of flow processes, three rock samples are selected and analysed. A new approach is developed for partitioning the pore space into the network of nodes and bonds. This partitioning differs from existing methods and it aims to solve some specific problems which often occur in unconsolidated (high porosity) porous media. Following this some single/multi-phase properties are calculated for these three rock samples, such as absolute permeabilities and relative p.ermeabilities. A number of relations between pore size and the absolute permeability, or between pore connectivity and absolute permeability, are explored. The comprehensive relation between pore size, connectivity and absolute permeabilities is also studied and preliminary results are given. This research has created new tools that will play important roles in the analysis of porous media.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Quantitative characterisation of the geometry and topology of pore space in 3D rock images

Abstract unavailable please refer to PD