Diamond-based models for scientific visualization

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

New data structures and algorithms for the efficient management of large spatial datasets

[Resumen] En esta tesis estudiamos la representación eficiente de matrices multidimensionales, presentando nuevas estructuras de datos compactas para almacenar y procesar grids en distintos ámbitos de aplicación. Proponemos varias estructuras de datos estáticas y dinámicas para la representación de matrices binarias o de enteros y estudiamos aplicaciones a la representación de datos raster en Sistemas de Información Geográfica, bases de datos RDF, etc. En primer lugar proponemos una colección de estructuras de datos estáticas para la representación de matrices binarias y de enteros: 1) una nueva representación de matrices binarias con grandes grupos de valores uniformes, con aplicaciones a la representación de datos raster binarios; 2) una nueva estructura de datos para representar matrices multidimensionales; 3) una nueva estructura de datos para representar matrices de enteros con soporte para consultas top-k de rango. También proponemos una nueva representación dinámica de matrices binarias, una nueva estructura de datos que proporciona las mismas funcionalidades que nuestras propuestas estáticas pero también soporta cambios en la matriz. Nuestras estructuras de datos pueden utilizarse en distintos dominios. Proponemos variantes específicas y combinaciones de nuestras propuestas para representar grafos temporales, bases de datos RDF, datos raster binarios o generales y datos raster temporales. También proponemos un nuevo algoritmo para consultar conjuntamente un conjuto de datos raster (almacenado usando nuestras propuestas) y un conjunto de datos vectorial almacenado en una estructura de datos clásica, mostrando que nuestra propuesta puede ser más rápida y usar menos espacio que otras alternativas. Nuestras representaciones proporcionan interesantes trade-offs y son competitivas en espacio y tiempos de consulta con representaciones habituales en los diferentes dominios.[Resumo] Nesta tese estudiamos a representación eficiente de matrices multidimensionais, presentando novas estruturas de datos compactas para almacenar e procesar grids en distintos ámbitos de aplicación. Propoñemos varias estruturas de datos estáticas e dinámicas para a representación de matrices binarias ou de enteiros e estudiamos aplicacións á representación de datos raster en Sistemas de Información Xeográfica, bases de datos RDF, etc. En primeiro lugar propoñemos unha colección de estruturas de datos estáticas para a representación de matrices binarias e de enteiros: 1) unha nova representación de matrices binarias con grandes grupos de valores uniformes, con aplicacións á representación de datos raster binarios; 2) unha nova estrutura de datos para representar matrices multidimensionais; 3) unha nova estrutura de datos para representar matrices de enteiros con soporte para consultas top-k. Tamén propoñemos unha nova representación dinámica de matrices binarias, unha nova estrutura de datos que proporciona as mesmas funcionalidades que as nosas propostas estáticas pero tamén soporta cambios na matriz. As nosas estruturas de datos poden utilizarse en distintos dominios. Propoñemos variantes específicas e combinacións das nosas propostas para representar grafos temporais, bases de datos RDF, datos raster binarios ou xerais e datos raster temporais. Tamén propoñemos un novo algoritmo para consultar conxuntamente datos raster (almacenados usando as nosas propostas) con datos vectoriais almacenados nunha estrutura de datos clásica, amosando que a nosa proposta pode ser máis rápida e usar menos espazo que outras alternativas. As nosas representacións proporcionan interesantes trade-offs e son competitivas en espazo e tempos de consulta con representacións habituais nos diferentes dominios.[Abstract] In this thesis we study the efficient representation of multidimensional grids, presenting new compact data structures to store and query grids in different application domains. We propose several static and dynamic data structures for the representation of binary grids and grids of integers, and study applications to the representation of raster data in Geographic Information Systems, RDF databases, etc. We first propose a collection of static data structures for the representation of binary grids and grids of integers: 1) a new representation of bi-dimensional binary grids with large clusters of uniform values, with applications to the representation of binary raster data; 2) a new data structure to represent multidimensional binary grids; 3) a new data structure to represent grids of integers with support for top-k range queries. We also propose a new dynamic representation of binary grids, a new data structure that provides the same functionalities that our static representations of binary grids but also supports changes in the grid. Our data structures can be used in several application domains. We propose specific variants and combinations of our generic proposals to represent temporal graphs, RDF databases, OLAP databases, binary or general raster data, and temporal raster data. We also propose a new algorithm to jointly query a raster dataset (stored using our representations) and a vectorial dataset stored in a classic data structure, showing that our proposal can be faster and require less space than the usual alternatives. Our representations provide interesting trade-offs and are competitive in terms of space and query times with usual representations in the different domains

Lazy Image Processing: An Investigation into Applications of Lazy Functional Languages to Image Processing

The suitability of lazy functional languages for image processing applications is investigated by writing several image processing algorithms. The evaluation is done from an application programmer's point of view and the criteria include ease of writing and reading, and efficiency. Lazy functional languages are claimed to have the advantages that they are easy to write and read, as well as efficient. This is partly because these languages have mechanisms to improve modularity, such as higher-order functions. Also, they have the feature that no subexpression is evaluated until its value is required. Hence, unnecessary operations are automatically eliminated, and therefore programs can be executed efficiently. In image processing the amount of data handled is generally so large that much programming effort is typically spent in tasks such as managing memory and routine sequencing operations in order to improve efficiency. Therefore, lazy functional languages should be a good tool to write image processing applications. However, little practical or experimental evidence on this subject has been reported, since image processing has mostly been written in imperative languages. The discussion starts from the implementation of simple algorithms such as pointwise and local operations. It is shown that a large number of algorithms can be composed from a small number of higher-order functions. Then geometric transformations are implemented, for which lazy functional languages are considered to be particularly suitable. As for representations of images, lists and hierarchical data structures including binary trees and quadtrees are implemented. Through the discussion, it is demonstrated that the laziness of the languages improves modularity and efficiency. In particular, no pixel calculation is involved unless the user explicitly requests pixels, and consecutive transformations are straightforward and involve no quantisation errors. The other items discussed include: a method to combine pixel images and images expressed as continuous functions. Some benchmarks are also presented

The development of GIS to aid conservation of architectural and archaeological sites using digital terrestrial photogrammetry

This thesis is concerned with the creation and implementation of an Architectural/Archaeological information System (A/AIS) by integrating digital terrestrial photogrammetry and CAD facilities as applicable to the requirements of architects, archaeologists and civil engineers. Architects and archaeologists are involved with the measurement, analysis and recording of the historical buildings and monuments. Hard-copy photogrammetric methods supporting such analyses and documentation are well established. But the requirement to interpret, classify and quantitatively process photographs can be time consuming. Also, they have limited application and cannot be re-examined if the information desired is not directly presented and a much more challenging extraction of 3-D coordinates than in a digital photogrammetric environment. The A/AIS has been developed to the point that it can provide a precise and reliable technique for non-contact 3-D measurements. The speed of on-line data acquisition, high degree of automation and adaptability has made this technique a powerful measurement tool with a great number of applications for architectural or archaeological sites. The designed tool (A/AIS) has been successful in producing the expected results in tasks examined for St. Avit Senieur Abbey in France, Strome Castle in Scotland, Gilbert Scott Building of Glasgow University, Hunter Memorial in Glasgow University and Anobanini Rock in Iran. The goals of this research were: to extract, using digital photogrammetric digitising, 3-D coordinates of architectural/archaeological features, to identify an appropriate 3-D model, to import 3-D points/lines into an appropriate 3-D modeller, to generate 3-D objects. to design and implement a prototype architectural Information System using the above 3-D model, to compare this approach to traditional approaches of measuring and archiving required information. An assessment of the contribution of digital photogrammetry, GIS and CAD to the surveying, conservation, recording and documentation of historical buildings and cultural monuments include digital rectification and restitution, feature extraction for the creation of 3-D digital models and the computer visualisation are the focus of this research

Contribution to structural parameters computation: volume models and methods

Bio-CAD and in-silico experimentation are getting a growing interest in biomedical applications where scientific data coming from real samples are used to compute structural parameters that allow to evaluate physical properties. Non-invasive imaging acquisition technologies such as CT, mCT or MRI, plus the constant growth of computer capabilities, allow the acquisition, processing and visualization of scientific data with increasing degree of complexity. Structural parameters computation is based on the existence of two phases (or spaces) in the sample: the solid, which may correspond to the bone or material, and the empty or porous phase and, therefore, they are represented as binary volumes. The most common representation model for these datasets is the voxel model, which is the natural extension to 3D of 2D bitmaps. In this thesis, the Extreme Vertices Model (EVM) and a new proposed model, the Compact Union of Disjoint Boxes (CUDB), are used to represent binary volumes in a much more compact way. EVM stores only a sorted subset of vertices of the object¿s boundary whereas CUDB keeps a compact list of boxes. In this thesis, methods to compute the next structural parameters are proposed: pore-size distribution, connectivity, orientation, sphericity and roundness. The pore-size distribution helps to interpret the characteristics of porous samples by allowing users to observe most common pore diameter ranges as peaks in a graph. Connectivity is a topological property related to the genus of the solid space, measures the level of interconnectivity among elements, and is an indicator of the biomechanical characteristics of bone or other materials. The orientation of a shape can be defined by rotation angles around a set of orthogonal axes. Sphericity is a measure of how spherical is a particle, whereas roundness is the measure of the sharpness of a particle's edges and corners. The study of these parameters requires dealing with real samples scanned at high resolution, which usually generate huge datasets that require a lot of memory and large processing time to analyze them. For this reason, a new method to simplify binary volumes in a progressive and lossless way is presented. This method generates a level-of-detail sequence of objects, where each object is a bounding volume of the previous objects. Besides being used as support in the structural parameter computation, this method can be practical for task such as progressive transmission, collision detection and volume of interest computation. As part of multidisciplinary research, two practical applications have been developed to compute structural parameters of real samples. A software for automatic detection of characteristic viscosity points of basalt rocks and glasses samples, and another to compute sphericity and roundness of complex forms in a silica dataset.El Bio-Diseño Asistido por Computadora (Bio-CAD), y la experimentacion in-silico est an teniendo un creciente interes en aplicaciones biomedicas, en donde se utilizan datos cientificos provenientes de muestras reales para calcular par ametros estructurales que permiten evaluar propiedades físicas. Las tecnologías de adquisicion de imagen no invasivas como la TC, TC o IRM, y el crecimiento constante de las prestaciones de las computadoras, permiten la adquisicion, procesamiento y visualizacion de datos científicos con creciente grado de complejidad. El calculo de parametros estructurales esta basado en la existencia de dos fases (o espacios) en la muestra: la solida, que puede corresponder al hueso o material, y la fase porosa o vacía, por tanto, tales muestras son representadas como volumenes binarios. El modelo de representacion mas comun para estos conjuntos de datos es el modelo de voxeles, el cual es una extension natural a 3D de los mapas de bits 2D. En esta tesis se utilizan el modelo Extreme Verrtices Model (EVM) y un nuevo modelo propuesto, the Compact Union of Disjoint Boxes (CUDB), para representar los volumenes binarios en una forma mucho mas compacta. El modelo EVM almacena solo un subconjunto ordenado de vertices de la frontera del objeto mientras que el modelo CUDB mantiene una lista compacta de cajas. En esta tesis se proponen metodos para calcular los siguientes parametros estructurales: distribucion del tamaño de los poros, conectividad, orientacion, esfericidad y redondez. La distribucion del tamaño de los poros ayuda a interpretar las características de las muestras porosas permitiendo a los usuarios observar los rangos de diametro mas comunes de los poros mediante picos en un grafica. La conectividad es una propiedad topologica relacionada con el genero del espacio solido, mide el nivel de interconectividad entre los elementos, y es un indicador de las características biomecanicas del hueso o de otros materiales. La orientacion de un objeto puede ser definida por medio de angulos de rotacion alrededor de un conjunto de ejes ortogonales. La esfericidad es una medida de que tan esferica es una partícula, mientras que la redondez es la medida de la nitidez de sus aristas y esquinas. En el estudio de estos parametros se trabaja con muestras reales escaneadas a alta resolucion que suelen generar conjuntos de datos enormes, los cuales requieren una gran cantidad de memoria y mucho tiempo de procesamiento para ser analizados. Por esta razon, se presenta un nuevo metodo para simpli car vol umenes binarios de una manera progresiva y sin perdidas. Este metodo genera una secuencia de niveles de detalle de los objetos, en donde cada objeto es un volumen englobante de los objetos previos. Ademas de ser utilizado como apoyo en el calculo de parametros estructurales, este metodo puede ser de utilizado en otras tareas como transmision progresiva, deteccion de colisiones y calculo de volumen de interes. Como parte de una investigacion multidisciplinaria, se han desarrollado dos aplicaciones practicas para calcular parametros estructurales de muestras reales. Un software para la deteccion automatica de puntos de viscosidad característicos en muestras de rocas de basalto y vidrios, y una aplicacion para calcular la esfericidad y redondez de formas complejas en un conjunto de datos de sílice

Design and Optimization of Graph Transform for Image and Video Compression

The main contribution of this thesis is the introduction of new methods for designing adaptive transforms for image and video compression. Exploiting graph signal processing techniques, we develop new graph construction methods targeted for image and video compression applications. In this way, we obtain a graph that is, at the same time, a good representation of the image and easy to transmit to the decoder. To do so, we investigate different research directions. First, we propose a new method for graph construction that employs innovative edge metrics, quantization and edge prediction techniques. Then, we propose to use a graph learning approach and we introduce a new graph learning algorithm targeted for image compression that defines the connectivities between pixels by taking into consideration the coding of the image signal and the graph topology in rate-distortion term. Moreover, we also present a new superpixel-driven graph transform that uses clusters of superpixel as coding blocks and then computes the graph transform inside each region. In the second part of this work, we exploit graphs to design directional transforms. In fact, an efficient representation of the image directional information is extremely important in order to obtain high performance image and video coding. In this thesis, we present a new directional transform, called Steerable Discrete Cosine Transform (SDCT). This new transform can be obtained by steering the 2D-DCT basis in any chosen direction. Moreover, we can also use more complex steering patterns than a single pure rotation. In order to show the advantages of the SDCT, we present a few image and video compression methods based on this new directional transform. The obtained results show that the SDCT can be efficiently applied to image and video compression and it outperforms the classical DCT and other directional transforms. Along the same lines, we present also a new generalization of the DFT, called Steerable DFT (SDFT). Differently from the SDCT, the SDFT can be defined in one or two dimensions. The 1D-SDFT represents a rotation in the complex plane, instead the 2D-SDFT performs a rotation in the 2D Euclidean space