Estructuras geométricas jerárquicas para la modelización de escenas 3d

This work surveys on the principal hierarchical geometric structures used to represent 3D scenes. We also present the basic algorithms to work with them, an overview on some recent works and a comparative discussion. This work has been the outcomes of the graduate course "Estructuras geometricas jerarquicas" given within the Software Phd. program at Software Department of this university

Estructuras geométricas jerárquicas para la modelización de escenas 3D

This work surveys on the principal hierarchical geometric structures used to represent 3D scenes. We also present the basic algorithms to work with them, an overview on some recent works and a comparative discussion. This work has been the outcomes of the graduate coursePostprint (published version

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

Texture-Based Segmentation and Finite Element Mesh Generation for Heterogeneous Biological Image Data

The design, analysis, and control of bio-systems remain an engineering challenge. This is mainly due to the material heterogeneity, boundary irregularity, and nonlinear dynamics associated with these systems. The recent developments in imaging techniques and stochastic upscaling methods provides a window of opportunity to more accurately assess these bio-systems than ever before. However, the use of image data directly in upscaled stochastic framework can only be realized by the development of certain intermediate steps. The goal of the research presented in this dissertation is to develop a texture-segmentation method and a unstructured mesh generation for heterogeneous image data. The following two new techniques are described and evaluated in this dissertation: 1. A new texture-based segmentation method, using the stochastic continuum concepts and wavelet multi-resolution analysis, is developed for characterization of heterogeneous materials in image data. The feature descriptors are developed to efficiently capture the micro-scale heterogeneity of macro-scale entities. The materials are then segmented at a representative elementary scale at which the statistics of the feature descriptor stabilize. 2. A new unstructured mesh generation technique for image data is developed using a hierarchical data structure. This representation allows for generating quality guaranteed finite element meshes. The framework for both the methods presented in this dissertation, as such, allows them for extending to higher dimensions. The experimental results using these methods conclude them to be promising tools for unifying data processing concepts within the upscaled stochastic framework across biological systems. These are targeted for inclusion in decision support systems where biological image data, simulation techniques and artificial intelligence will be used conjunctively and uniformly to assess bio-system quality and design effective and appropriate treatments that restore system health

Método Grid-Quadtree para seleção de parâmetros do algoritmo support vector classification (SVC)

Orientador : Prof. Dr. Arinei Carlos Lindbeck da SilvaTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 01/06/2016Inclui referências : f. 143-149Área de concentração : Programação matemáticaResumo: O algoritmo Support Vector Classification (SVC) é uma técnica de reconhecimento de padrões, cuja eficiência depende da seleção de seus parâmetros: constante de regularização C, função kernel e seus respectivos parâmetros. A escolha equivocada dessas variáveis impacta diretamente na performance do algoritmo, acarretando em fenômenos indesejáveis como o overfitting e o underfitting. O problema que estuda a procura de parâmetros ótimos para o SVC, em relação às suas medidas de desempenho, é denominado seleção de modelos do SVC. Em virtude do amplo domínio de convergência do kernel gaussiano, a maioria dos métodos destinados a solucionar esse problema concentra-se na seleção da constante C e do parâmetro ? do kernel gaussiano. Dentre esses métodos, a busca por grid é um dos de maior destaque devido à sua simplicidade e bons resultados. Contudo, por avaliar todas as combinações de parâmetros (C, ?) dentre o seu espaço de busca, a mesma necessita de muito tempo de processamento, tornando-se impraticável para avaliação de grandes conjuntos de dados. Desta forma, o objetivo deste trabalho é propor um método de seleção de parâmetros do SVC, usando o kernel gaussiano, que combine a técnica quadtree à busca por grid, para reduzir o número de operações efetuadas pelo grid e diminuir o seu custo computacional. A ideia fundamental é empregar a quadtree para desenhar a boa região de parâmetros, evitando avaliações desnecessárias de parâmetros situados nas áreas de underfitting e overfitting. Para isso, desenvolveu-se o método grid-quadtree (GQ), utilizando-se a linguagem de programação VB.net em conjunto com os softwares da biblioteca LIBSVM. Na execução do GQ, realizou-se o balanceamento da quadtree e criou-se um procedimento denominado refinamento, que permitiu delinear a curva de erro de generalização de parâmetros. Para validar o método proposto, empregaram-se vinte bases de dados referência na área de classificação, as quais foram separadas em dois grupos. Os resultados obtidos pelo GQ foram comparados com os da tradicional busca por grid (BG) levando-se em conta o número de operações executadas por ambos os métodos, a taxa de validação cruzada (VC) e o número de vetores suporte (VS) associados aos parâmetros encontrados e a acurácia do SVC na predição dos conjuntos de teste. A partir das análises realizadas, constatou-se que o GQ foi capaz de encontrar parâmetros de excelente qualidade, com altas taxas VC e baixas quantidades de VS, reduzindo em média, pelo menos, 78,8124% das operações da BG para o grupo 1 de dados e de 71,7172% a 88,7052% para o grupo 2. Essa diminuição na quantidade de cálculos efetuados pelo quadtree resultou em uma economia de horas de processamento. Além disso, em 11 das 20 bases estudadas a acurácia do SVC-GQ foi superior à do SVC-BG e para quatro delas igual. Isso mostra que o GQ é capaz de encontrar parâmetros melhores ou tão bons quanto os da BG executando muito menos operações. Palavras-chave: Seleção de modelos do SVC. Kernel gaussiano. Quadtree. Redução de operações.Abstract: The Support Vector Classification (SVC) algorithm is a pattern recognition technique, whose efficiency depends on its parameters selection: the penalty constant C, the kernel function and its own parameters. A wrong choice of these variables values directly impacts on the algorithm performance, leading to undesirable phenomena such as the overfitting and the underfitting. The task of searching for optimal parameters with respect to performance measures is called SVC model selection problem. Due to the Gaussian kernel wide convergence domain, many model selection approaches focus in determine the constant C and the Gaussian kernel ? parameter. Among these, the grid search is one of the highlights due to its easiest way and high performance. However, since it evaluates all parameters combinations (C, ?) on the search space, it requires high computational time and becomes impractical for large data sets evaluation. Thus, the aim of this thesis is to propose a SVC model selection method, using the Gaussian kernel, which integrates the quadtree technique with the grid search to reduce the number of operations performed by the grid and its computational cost. The main idea of this study is to use the quadtree to determine the good parameters region, neglecting the evaluation of unnecessary parameters located in the underfitting and the overfitting areas. In this regard, it was developed the grid-quadtree (GQ) method, which was implemented on VB.net development environment and that also uses the software of the LIBSVM library. In the GQ execution, it was considered the balanced quadtree and it was created a refinement procedure, that allowed to delineate the parameters generalization error curve. In order to validate the proposed method, twenty benchmark classification data set were used, which were separated into two groups. The results obtained via GQ were compared with the traditional grid search (GS) ones, considering the number of operations performed by both methods, the cross-validation rate (CV) and the number of support vectors (SV) associated to the selected parameters, and the SVC accuracy in the test set. Based on this analyzes, it was concluded that GQ was able to find excellent parameters, with high CV rates and few SV, achieving an average reduction of at least 78,8124% on GS operations for group 1 data and from 71,7172% to 88,7052% for group 2. The decrease in the amount of calculations performed by the quadtree lead to savings on the computational time. Furthermore, the SVC-GQ accuracy was superior than SVC-GS in 11 of the 20 studied bases and equal in four of them. These results demonstrate that GQ is able to find better or as good as parameters than BG, but executing much less operations. Key words: SVC Model Selection. Gaussian kernel. Quadtree. Reduction Operation

The Cost of Balancing Generalized Quadtrees

A balanced quadtree has no adjacent elements of vastly different size. Refining a quadtree to balance it is a preliminary step in many finite element, mesh generation and computer graphics rendering algorithms. A cost of balancing is the creation of a somewhat larger quadtree. The paper considers several different definitions of balance, and their application to quadtrees of various shapes, dimensions, and degrees. It presents new results that provide tight upper and lower bounds for this cost of quadtree balancing in many common cases. INTRODUCTION Motivation The quadtree is a common spatial data structure arising in many geometric applications. It describes a square, cubic, tetrahedral or other polytopal domain as a hierarchy of shapes, and appears in work on image data compression, solid modeling, and many other applications. A particular continuity condition on quadtrees is important in some of these applications, and has been rediscovered and renamed several times by researcher..