Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure

Developing a model and a language to identify and specify the integrity constraints in spatial datacubes

La qualité des données dans les cubes de données spatiales est importante étant donné que ces données sont utilisées comme base pour la prise de décision dans les grandes organisations. En effet, une mauvaise qualité de données dans ces cubes pourrait nous conduire à une mauvaise prise de décision. Les contraintes d'intégrité jouent un rôle clé pour améliorer la cohérence logique de toute base de données, l'un des principaux éléments de la qualité des données. Différents modèles de cubes de données spatiales ont été proposés ces dernières années mais aucun n'inclut explicitement les contraintes d'intégrité. En conséquence, les contraintes d'intégrité de cubes de données spatiales sont traitées de façon non-systématique, pragmatique, ce qui rend inefficace le processus de vérification de la cohérence des données dans les cubes de données spatiales. Cette thèse fournit un cadre théorique pour identifier les contraintes d'intégrité dans les cubes de données spatiales ainsi qu'un langage formel pour les spécifier. Pour ce faire, nous avons d'abord proposé un modèle formel pour les cubes de données spatiales qui en décrit les différentes composantes. En nous basant sur ce modèle, nous avons ensuite identifié et catégorisé les différents types de contraintes d'intégrité dans les cubes de données spatiales. En outre, puisque les cubes de données spatiales contiennent typiquement à la fois des données spatiales et temporelles, nous avons proposé une classification des contraintes d'intégrité des bases de données traitant de l'espace et du temps. Ensuite, nous avons présenté un langage formel pour spécifier les contraintes d'intégrité des cubes de données spatiales. Ce langage est basé sur un langage naturel contrôlé et hybride avec des pictogrammes. Plusieurs exemples de contraintes d'intégrité des cubes de données spatiales sont définis en utilisant ce langage. Les designers de cubes de données spatiales (analystes) peuvent utiliser le cadre proposé pour identifier les contraintes d'intégrité et les spécifier au stade de la conception des cubes de données spatiales. D'autre part, le langage formel proposé pour spécifier des contraintes d'intégrité est proche de la façon dont les utilisateurs finaux expriment leurs contraintes d'intégrité. Par conséquent, en utilisant ce langage, les utilisateurs finaux peuvent vérifier et valider les contraintes d'intégrité définies par l'analyste au stade de la conception

Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

Topologically Consistent Models for Efficient Big Geo-Spatio-Temporal Data Distribution

Geo-spatio-temporal topology models are likely to become a key concept to check the consistency of 3D (spatial space) and 4D (spatial + temporal space) models for emerging GIS applications such as subsurface reservoir modelling or the simulation of energy and water supply of mega or smart cities. Furthermore, the data management for complex models consisting of big geo-spatial data is a challenge for GIS and geo-database research. General challenges, concepts, and techniques of big geo-spatial data management are presented. In this paper we introduce a sound mathematical approach for a topologically consistent geo-spatio-temporal model based on the concept of the incidence graph. We redesign DB4GeO, our service-based geo-spatio-temporal database architecture, on the way to the parallel management of massive geo-spatial data. Approaches for a new geo-spatio-temporal and object model of DB4GeO meeting the requirements of big geo-spatial data are discussed in detail. Finally, a conclusion and outlook on our future research are given on the way to support the processing of geo-analytics and -simulations in a parallel and distributed system environment

Finite Element Modeling Driven by Health Care and Aerospace Applications

This thesis concerns the development, analysis, and computer implementation of mesh generation algorithms encountered in finite element modeling in health care and aerospace. The finite element method can reduce a continuous system to a discrete idealization that can be solved in the same manner as a discrete system, provided the continuum is discretized into a finite number of simple geometric shapes (e.g., triangles in two dimensions or tetrahedrons in three dimensions). In health care, namely anatomic modeling, a discretization of the biological object is essential to compute tissue deformation for physics-based simulations. This thesis proposes an efficient procedure to convert 3-dimensional imaging data into adaptive lattice-based discretizations of well-shaped tetrahedra or mixed elements (i.e., tetrahedra, pentahedra and hexahedra). This method operates directly on segmented images, thus skipping a surface reconstruction that is required by traditional Computer-Aided Design (CAD)-based meshing techniques and is convoluted, especially in complex anatomic geometries. Our approach utilizes proper mesh gradation and tissue-specific multi-resolution, without sacrificing the fidelity and while maintaining a smooth surface to reflect a certain degree of visual reality. Image-to-mesh conversion can facilitate accurate computational modeling for biomechanical registration of Magnetic Resonance Imaging (MRI) in image-guided neurosurgery. Neuronavigation with deformable registration of preoperative MRI to intraoperative MRI allows the surgeon to view the location of surgical tools relative to the preoperative anatomical (MRI) or functional data (DT-MRI, fMRI), thereby avoiding damage to eloquent areas during tumor resection. This thesis presents a deformable registration framework that utilizes multi-tissue mesh adaptation to map preoperative MRI to intraoperative MRI of patients who have undergone a brain tumor resection. Our enhancements with mesh adaptation improve the accuracy of the registration by more than 5 times compared to rigid and traditional physics-based non-rigid registration, and by more than 4 times compared to publicly available B-Spline interpolation methods. The adaptive framework is parallelized for shared memory multiprocessor architectures. Performance analysis shows that this method could be applied, on average, in less than two minutes, achieving desirable speed for use in a clinical setting. The last part of this thesis focuses on finite element modeling of CAD data. This is an integral part of the design and optimization of components and assemblies in industry. We propose a new parallel mesh generator for efficient tetrahedralization of piecewise linear complex domains in aerospace. CAD-based meshing algorithms typically improve the shape of the elements in a post-processing step due to high complexity and cost of the operations involved. On the contrary, our method optimizes the shape of the elements throughout the generation process to obtain a maximum quality and utilizes high performance computing to reduce the overheads and improve end-user productivity. The proposed mesh generation technique is a combination of Advancing Front type point placement, direct point insertion, and parallel multi-threaded connectivity optimization schemes. The mesh optimization is based on a speculative (optimistic) approach that has been proven to perform well on hardware-shared memory. The experimental evaluation indicates that the high quality and performance attributes of this method see substantial improvement over existing state-of-the-art unstructured grid technology currently incorporated in several commercial systems. The proposed mesh generator will be part of an Extreme-Scale Anisotropic Mesh Generation Environment to meet industries expectations and NASA\u27s CFD visio