356 research outputs found

    Doctor of Philosophy

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    dissertationThe medial axis of an object is a shape descriptor that intuitively presents the morphology or structure of the object as well as intrinsic geometric properties of the object’s shape. These properties have made the medial axis a vital ingredient for shape analysis applications, and therefore the computation of which is a fundamental problem in computational geometry. This dissertation presents new methods for accurately computing the 2D medial axis of planar objects bounded by B-spline curves, and the 3D medial axis of objects bounded by B-spline surfaces. The proposed methods for the 3D case are the first techniques that automatically compute the complete medial axis along with its topological structure directly from smooth boundary representations. Our approach is based on the eikonal (grassfire) flow where the boundary is offset along the inward normal direction. As the boundary deforms, different regions start intersecting with each other to create the medial axis. In the generic situation, the (self-) intersection set is born at certain creation-type transition points, then grows and undergoes intermediate transitions at special isolated points, and finally ends at annihilation-type transition points. The intersection set evolves smoothly in between transition points. Our approach first computes and classifies all types of transition points. The medial axis is then computed as a time trace of the evolving intersection set of the boundary using theoretically derived evolution vector fields. This dynamic approach enables accurate tracking of elements of the medial axis as they evolve and thus also enables computation of topological structure of the solution. Accurate computation of geometry and topology of 3D medial axes enables a new graph-theoretic method for shape analysis of objects represented with B-spline surfaces. Structural components are computed via the cycle basis of the graph representing the 1-complex of a 3D medial axis. This enables medial axis based surface segmentation, and structure based surface region selection and modification. We also present a new approach for structural analysis of 3D objects based on scalar functions defined on their surfaces. This approach is enabled by accurate computation of geometry and structure of 2D medial axes of level sets of the scalar functions. Edge curves of the 3D medial axis correspond to a subset of ridges on the bounding surfaces. Ridges are extremal curves of principal curvatures on a surface indicating salient intrinsic features of its shape, and hence are of particular interest as tools for shape analysis. This dissertation presents a new algorithm for accurately extracting all ridges directly from B-spline surfaces. The proposed technique is also extended to accurately extract ridges from isosurfaces of volumetric data using smooth implicit B-spline representations. Accurate ridge curves enable new higher-order methods for surface analysis. We present a new definition of salient regions in order to capture geometrically significant surface regions in the neighborhood of ridges as well as to identify salient segments of ridges

    Semi-automatic transfer function generation for volumetric data visualization using contour tree analyses

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    Multiple dataset visualization (MDV) framework for scalar volume data

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    Many applications require comparative analysis of multiple datasets representing different samples, conditions, time instants, or views in order to develop a better understanding of the scientific problem/system under consideration. One effective approach for such analysis is visualization of the data. In this PhD thesis, we propose an innovative multiple dataset visualization (MDV) approach in which two or more datasets of a given type are rendered concurrently in the same visualization. MDV is an important concept for the cases where it is not possible to make an inference based on one dataset, and comparisons between many datasets are required to reveal cross-correlations among them. The proposed MDV framework, which deals with some fundamental issues that arise when several datasets are visualized together, follows a multithreaded architecture consisting of three core components, data preparation/loading, visualization and rendering. The visualization module - the major focus of this study, currently deals with isosurface extraction and texture-based rendering techniques. For isosurface extraction, our all-in-memory approach keeps datasets under consideration and the corresponding geometric data in the memory. Alternatively, the only-polygons- or points-in-memory only keeps the geometric data in memory. To address the issues related to storage and computation, we develop adaptive data coherency and multiresolution schemes. The inter-dataset coherency scheme exploits the similarities among datasets to approximate the portions of isosurfaces of datasets using the isosurface of one or more reference datasets whereas the intra/inter-dataset multiresolution scheme processes the selected portions of each data volume at varying levels of resolution. The graphics hardware-accelerated approaches adopted for MDV include volume clipping, isosurface extraction and volume rendering, which use 3D textures and advanced per fragment operations. With appropriate user-defined threshold criteria, we find that various MDV techniques maintain a linear time-N relationship, improve the geometry generation and rendering time, and increase the maximum N that can be handled (N: number of datasets). Finally, we justify the effectiveness and usefulness of the proposed MDV by visualizing 3D scalar data (representing electron density distributions in magnesium oxide and magnesium silicate) from parallel quantum mechanical simulation

    Isosurface modelling of soft objects in computer graphics.

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    There are many different modelling techniques used in computer graphics to describe a wide range of objects and phenomena. In this thesis, details of research into the isosurface modelling technique are presented. The isosurface technique is used in conjunction with more traditional modelling techniques to describe the objects needed in the different scenes of an animation. The isosurface modelling technique allows the description and animation of objects that would be extremely difficult, or impossible to describe using other methods. The objects suitable for description using isosurface modelling are soft objects. Soft objects merge elegantly with each other, pull apart, bubble, ripple and exhibit a variety of other effects. The representation was studied in three phases of a computer animation project: modelling of the objects; animation of the objects; and the production of the images. The research clarifies and presents many algorithms needed to implement the isosurface representation in an animation system. The creation of a hierarchical computer graphics animation system implementing the isosurface representation is described. The scalar fields defining the isosurfaces are represented using a scalar field description language, created as part of this research, which is automatically generated from the hierarchical description of the scene. This language has many techniques for combining and building the scalar field from a variety of components. Surface attributes of the objects are specified within the graphics system. Techniques are described which allow the handling of these attributes along with the scalar field calculation. Many animation techniques specific to the isosurface representation are presented. By the conclusion of the research, a graphics system was created which elegantly handles the isosurface representation in a wide variety of animation situations. This thesis establishes that isosurface modelling of soft objects is a powerful and useful technique which has wide application in the computer graphics community

    Electronic structure of bulk and low dimensional systems analyzed by Angle-Resolved Photoemission Spectroscopy

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    Tesis doctoral inédita. Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física de la Materia Condensada . Fecha de lectura: 15-09-200

    Diamond-based models for scientific visualization

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    Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains including scientific visualization, finite element analysis and shape modeling and analysis. A popular class of such approaches is based on the regular simplex bisection operator, which bisects simplices (e.g. line segments, triangles, tetrahedra) along the midpoint of a predetermined edge. Regular simplex bisection produces adaptive simplicial meshes of high geometric quality, while simplifying the extraction of crack-free, or conforming, approximations to the original dataset. Efficient multiresolution representations for such models have been achieved in 2D and 3D by clustering sets of simplices sharing the same bisection edge into structures called diamonds. In this thesis, we introduce several diamond-based approaches for scientific visualization. We first formalize the notion of diamonds in arbitrary dimensions in terms of two related simplicial decompositions of hypercubes. This enables us to enumerate the vertices, simplices, parents and children of a diamond. In particular, we identify the number of simplices involved in conforming updates to be factorial in the dimension and group these into a linear number of subclusters of simplices that are generated simultaneously. The latter form the basis for a compact pointerless representation for conforming meshes generated by regular simplex bisection and for efficiently navigating the topological connectivity of these meshes. Secondly, we introduce the supercube as a high-level primitive on such nested meshes based on the atomic units within the underlying triangulation grid. We propose the use of supercubes to associate information with coherent subsets of the full hierarchy and demonstrate the effectiveness of such a representation for modeling multiresolution terrain and volumetric datasets. Next, we introduce Isodiamond Hierarchies, a general framework for spatial access structures on a hierarchy of diamonds that exploits the implicit hierarchical and geometric relationships of the diamond model. We use an isodiamond hierarchy to encode irregular updates to a multiresolution isosurface or interval volume in terms of regular updates to diamonds. Finally, we consider nested hypercubic meshes, such as quadtrees, octrees and their higher dimensional analogues, through the lens of diamond hierarchies. This allows us to determine the relationships involved in generating balanced hypercubic meshes and to propose a compact pointerless representation of such meshes. We also provide a local diamond-based triangulation algorithm to generate high-quality conforming simplicial meshes

    The Multiscale Morphology Filter: Identifying and Extracting Spatial Patterns in the Galaxy Distribution

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    We present here a new method, MMF, for automatically segmenting cosmic structure into its basic components: clusters, filaments, and walls. Importantly, the segmentation is scale independent, so all structures are identified without prejudice as to their size or shape. The method is ideally suited for extracting catalogues of clusters, walls, and filaments from samples of galaxies in redshift surveys or from particles in cosmological N-body simulations: it makes no prior assumptions about the scale or shape of the structures.}Comment: Replacement with higher resolution figures. 28 pages, 17 figures. For Full Resolution Version see: http://www.astro.rug.nl/~weygaert/tim1publication/miguelmmf.pd

    Three-Dimensional Structural Analysis of Temple 16 and Rosalila at Copan Ruinas

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    Temple 16 is an ancient Maya structure located at the heart of the Copán Ruinas Acropolis in Western Honduras. Temple 16 contains several earlier structures within it that were built on top of each other throughout Copán’s history. One of these earlier structures, Rosalila, is one of the most culturally significant structures within the Acropolis due to its preservation. An intricate series of archeological tunnels have been excavated throughout Temple 16 to allow for its study. However, significant cracking has been observed within Rosalila and several tunnels have experienced partial collapse. This not only poses a life safety issue for those utilizing the tunnels, but also demonstrates the risk to invaluable cultural heritage. To this end, this thesis aims to provide a rigorous structural assessment of Temple 16 and the buried Rosalila structure, accounting for its complex 3D tunnel system, to understand the leading causes of tunnel collapse and structure deterioration. Geometric data was collected of the acropolis, Temple 16, Rosalila, and the complex network of tunnels using a combination of ground-based lidar and uncrewed aerial systems. The resulting point clouds were vectorized to yield a series of connected surfaces, which were then meshed as a solid to facilitate finite element analysis. Analyses were conducted to understand both the current stress distribution within Temple 16 as well as to study the impact of various hypothetical tunnel backfilling scenarios to provide recommendations for preservation and tunnel safety. The generated finite element models were analyzed under three water saturation levels to account for the impact of heavy rainy seasons and water infiltration on the stress levels of the tunnels. From the analyses, sixty-three highly stressed areas were identified among the current tunnel system, with most of them being close or directly underneath Rosalila. From the tested hypothetical backfilling scenarios, it was found that, backfilling excavated sections can improve or worsen these stress concentrations depending on the location of the tunnel within the system. Finally, by analyzing Rosalila’s current geometry, it was observed that the structure experiences high levels of stress on its southern side due to its location within Temple 16. From this, it was concluded that fixing exposed areas of Rosalila that were affected by excavation on its southern side can significantly alleviate the existing deterioration and improve the stress flow in these areas. Advisors: Christine E. Wittich & Richard L. Wood
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