On Volumetric Shape Reconstruction from Implicit Forms

International audienceIn this paper we report on the evaluation of volumetric shape reconstruction methods that consider as input implicit forms in 3D. Many visual applications build implicit representations of shapes that are converted into explicit shape representations using geometric tools such as the Marching Cubes algorithm. This is the case with image based reconstructions that produce point clouds from which implicit functions are computed, with for instance a Poisson reconstruction approach. While the Marching Cubes method is a versatile solution with proven efficiency, alternative solutions exist with different and complementary properties that are of interest for shape modeling. In this paper, we propose a novel strategy that builds on Centroidal Voronoi Tessellations (CVTs). These tessellations provide volumetric and surface representations with strong regularities in addition to provably more accurate approximations of the implicit forms considered. In order to compare the existing strategies, we present an extensive evaluation that analyzes various properties of the main strategies for implicit to explicit volumetric conversions: Marching cubes, Delaunay refinement and CVTs, including accuracy and shape quality of the resulting shape mesh

Unstructured surface and volume decimation of tessellated domains

A general algorithm for decimating unstructured discretized data sets is presented. The discretized space may be a planar triangulation, a general 3D surface triangulation, or a 3D tetrahedrization. The decimation algorithm enforces Dirichlet boundary conditions, uses only existing vertices, and assumes manifold geometry. Local dynamic vertex removal is performed without history information while preserving the initial topology and boundary geometry. The tessellation at each step of the algorithm is preserved and, in the pathological case, every interior vertex is a candidate for removal. The research focuses on how to remove a vertex from an existing unstructured n-dimensional tessellation, not on the formulation of decimation criteria. Criteria for removing a candidate vertex may be based on geometric properties or any scalar governing function specific to the application. Use of scalar functions to adaptively control or optimize tessellation resolution is particularly applicable to the computer graphics, computational fluids, and structural analysis disciplines. Potential applications in the geologic exploration and medical or industrial imaging fields are promising

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

This paper presents HDGlab, an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation available in HDGlab. Ultimately, this is expected to make this relatively new advanced discretisation method more accessible to the computational engineering community. HDGlab presents some features not available in other implementations of the HDG method that can be found in the free domain. First, it implements high-order polynomial shape functions up to degree nine, with both equally-spaced and Fekete nodal distributions. Second, it supports curved isoparametric simplicial elements in two and three dimensions. Third, it supports non-uniform degree polynomial approximations and it provides a flexible structure to devise degree adaptivity strategies. Finally, an interface with the open-source high-order mesh generator Gmsh is provided to facilitate its application to practical engineering problems

Reconstruction of surfaces from unorganized three-dimensional point clouds

In dieser Arbeit wird ein neuer Algorithmus zur Rekonstruktion von Flächen aus dreidimensionalen Punktwolken präsentiert. Seine besonderen Eigenschaften sind die Rekonstruktion von offenen Flächen mit Rändern, Datensätzen mit variabler Punktdichte und die Behandlung von scharfen Kanten, d.h. Stellen mit unendlicher Krümmung. Es werden formale Argumente angegeben, die erklären, warum der Algorithmus korrekt arbeitet. Sie bestehen aus einer Definition von 'Rekonstruktion' und dem Beweis der Existenz von Punktmengen für die der Algorithmus erfolgreich ist. Diese mathematische Analyse konzentriert sich dabei auf kompakte Flächen mit beschränkter Krümmung und ohne Ränder. Weitere Beiträge sind die Anwendung des Flächenrekonstruktionsverfahrens für die interaktive Modellierung von Flächen und eine Prozedur für die Glättung von verrauschten Punktwolken. Zusätzlich kann der Algorithmus leicht für die lokal beschränkte Rekonstruktion eingesetzt werden, wenn nur ein Teil des Datensatzes zur Rekonstruktion herangezogen werden soll.In this thesis a new algorithm for the reconstruction of surfaces from three-dimensional point clouds is presented. Its particular features are the reconstruction of open surfaces with boundaries, data sets with variable density, and the treatment of sharp edges, that is, locations of infinite curvature. We give formal arguments which explain why the algorithm works well. They consist of a definition of 'reconstruction', and the demonstration of existence of sampling sets for which the algorithm is successful. This mathematical analysis focuses on compact surfaces of limited curvature without boundary. Further contributions are the application of the surface reconstruction algorithm for interactive shape design and a smoothing procedure for noise elimination in point clouds. Additionally, the algorithm can be easily applied for locally-restricted reconstruction if only a subset of the data set has to be considered for reconstruction

Granite: A scientific database model and implementation

The principal goal of this research was to develop a formal comprehensive model for representing highly complex scientific data. An effective model should provide a conceptually uniform way to represent data and it should serve as a framework for the implementation of an efficient and easy-to-use software environment that implements the model. The dissertation work presented here describes such a model and its contributions to the field of scientific databases. In particular, the Granite model encompasses a wide variety of datatypes used across many disciplines of science and engineering today. It is unique in that it defines dataset geometry and topology as separate conceptual components of a scientific dataset. We provide a novel classification of geometries and topologies that has important practical implications for a scientific database implementation. The Granite model also offers integrated support for multiresolution and adaptive resolution data. Many of these ideas have been addressed by others, but no one has tried to bring them all together in a single comprehensive model. The datasource portion of the Granite model offers several further contributions. In addition to providing a convenient conceptual view of rectilinear data, it also supports multisource data. Data can be taken from various sources and combined into a unified view. The rod storage model is an abstraction for file storage that has proven an effective platform upon which to develop efficient access to storage. Our spatial prefetching technique is built upon the rod storage model, and demonstrates very significant improvement in access to scientific datasets, and also allows machines to access data that is far too large to fit in main memory. These improvements bring the extremely large datasets now being generated in many scientific fields into the realm of tractability for the ordinary researcher. We validated the feasibility and viability of the model by implementing a significant portion of it in the Granite system. Extensive performance evaluations of the implementation indicate that the features of the model can be provided in a user-friendly manner with an efficiency that is competitive with more ad hoc systems and more specialized application specific solutions

Aeronautical engineering: A continuing bibliography with indexes (supplement 193)

This bibliography lists 682 reports, articles and other documents introduced into the NASA scientific and technical information system in October 1985

Mesh Compression

Die Kompression von Netzen ist eine weitgefächerte Forschungsrichtung mit Anwendungen in den verschiedensten Bereichen, wie zum Beispiel im Bereich der Handhabung extrem großer Modelle, beim Austausch von dreidimensionalem Inhalt über das Internet, im elektronischen Handel, als anpassungsfähige Repräsentation für Volumendatensätze usw. In dieser Arbeit wird das Verfahren der Cut-Border Machine beschrieben. Die Cut-Border Machine kodiert Netze, indem ein Teilbereich durch das Netz wächst (region growing). Kodiert wird die Art und Weise, wie neue Netzelemente dem wachsenden Teilbereich einverleibt werden. Das Verfahren der Cut-Border Machine kann sowohl auf Dreiecksnetze als auch auf Tetraedernetze angewendet werden. Trotz der einfachen Struktur des Verfahrens kann eine sehr hohe Kompressionsrate erzielt werden. Im Falle von Tetraedernetzen erreicht die Cut-Border Machine die beste Kompressionsrate von allen bekannten Verfahren. Die einfache Struktur der Cut-Border Machine ermöglicht einerseits die Realisierung direkt in Hardware und ist auch als Implementierung in Software extrem schnell. Auf der anderen Seite erlaubt die Einfachheit eine theoretische Analyse des Algorithmus. Gezeigt werden konnte, dass für ebene Triangulierungen eine leicht modifizierte Version der Cut-Border Machine lineare Laufzeiten in der Zahl der Knoten erzielt und dass die komprimierte Darstellung nur linearen Speicherbedarf benötigt, d.h. nicht mehr als fünf Bits pro Knoten. Neben der detaillierten Beschreibung der Cut-Border Machine mit mehreren Verbesserungen und Optimierungen, enthält die Arbeit eine Einführung zu Netzen und geeigneten Datenstrukturen und entwickelt mehrere Kodierungsverfahren, die im Bereich der Netzkompression Anwendung finden. Eine breite Übersicht verwandter Arbeiten gibt Einblick in des Forschungsgebiet. Weiterhin wird die Effizienz mehrerer in der Literatur beschriebener Verfahren verbessert. Insbesondere konnte die algorithmisch erzielte obere Schranke für die KodiMesh Compression is a broad research area with applications in a lot of different areas, such as the handling of very large models, the exchange of three dimensional content over the internet, electronic commerce, the flexible representation of volumetric data and so on. In this thesis the mesh compression method of the Cut-Border Machine is described. The Cut-Border Machine encodes meshes by growing a region through the mesh and encoding the way, in which the mesh elements are incorporated into the growing region. The Cut-Border Machine can be applied to triangular and tetrahedral meshes. Although the method is not too complicated, it achieves very good compression rates. In the tetrahedral case the Cut-Border Machine performs best among all known methods. The simple nature of the Cut-Border Machine allows on the one hand for a hardware implementation and performs also as software implementation extremely well. On the other hand the simplicity allows for a theoretical analysis of the Cut-Border Machine. It could be shown, that for planar triangulations a slightly modified version of the Cut-Border Machine runs in linear time in the number of vertices and that the compressed representation only consumes linear storage space, i.e. no more than five bits per vertex. Besides the detailed description of the Cut-Border Machine with several improvements and optimizations, the thesis gives an introduction to meshes and appropriate data structures, develops several coding techniques useful for mesh compression and gives a broad overview of related work. Furthermore the author improves the encoding efficiency of several other compression techniques. In particular could the algorithmically achieved upper bound for the encoding of planar triangulations be improved to ten percent above the theoretical limit, what is the best known result up to now

Extraction of topological structures in 2D and 3D vector fields

feature extraction, feature tracking, vector field visualizationMagdeburg, Univ., Fak. für Informatik, Diss., 2008von Tino WeinkaufZsfassung in dt. Sprach

Analysis and Generation of Quality Polytopal Meshes with Applications to the Virtual Element Method

This thesis explores the concept of the quality of a mesh, the latter being intended as the discretization of a two- or three- dimensional domain. The topic is interdisciplinary in nature, as meshes are massively used in several fields from both the geometry processing and the numerical analysis communities. The goal is to produce a mesh with good geometrical properties and the lowest possible number of elements, able to produce results in a target range of accuracy. In other words, a good quality mesh that is also cheap to handle, overcoming the typical trade-off between quality and computational cost. To reach this goal, we first need to answer the question: ''How, and how much, does the accuracy of a numerical simulation or a scientific computation (e.g., rendering, printing, modeling operations) depend on the particular mesh adopted to model the problem? And which geometrical features of the mesh most influence the result?'' We present a comparative study of the different mesh types, mesh generation techniques, and mesh quality measures currently available in the literature related to both engineering and computer graphics applications. This analysis leads to the precise definition of the notion of quality for a mesh, in the particular context of numerical simulations of partial differential equations with the virtual element method, and the consequent construction of criteria to determine and optimize the quality of a given mesh. Our main contribution consists in a new mesh quality indicator for polytopal meshes, able to predict the performance of the virtual element method over a particular mesh before running the simulation. Strictly related to this, we also define a quality agglomeration algorithm that optimizes the quality of a mesh by wisely agglomerating groups of neighboring elements. The accuracy and the reliability of both tools are thoroughly verified in a series of tests in different scenarios