Projeções Multidimensionais são úteis para gerar visualizações adequadas para apoiar a análise exploratória de uma grande variedade de dados complexos e de alta dimensionalidade. Tarefas de análise visual de dados têm se beneficiado de projeções para explorar dados textuais, de imagens, de sensores, entre outros. Porém, diferentes técnicas de projeção e diferentes parametrizações de uma mesma técnica produzem resultados distintos para um mesmo conjunto de dados, pois as técnicas adotam estratégias distintas para representar os dados originais em um espaço cuja dimensionalidade permite sua visualização. Atualmente, ainda há poucos recursos para avaliar a qualidade dessas projeções e, em geral, as soluções existentes avaliam propriedades específicas, demandando grande esforço do analista para uma avaliação mais abrangente. Neste trabalho, introduzimos um arcabouço para computar medidas de avaliação de projeções com enfoque em análise de vizinhanças e de agrupamentos. Para elaborar este arcabouço, foi realizado um estudo de percepção para entender melhor como os usuários observam as projeções e foi conduzida uma investigação de representações dos dados capazes de favorecer a identificação de vizinhanças e de agrupamentos. Os padrões identificados no estudo de percepção auxiliaram a validar a representação dos dados, em que foi proposto um modelo de grafo, chamado de Extended Minimum Spanning Tree (EMST), capaz de capturar características condizentes com as observações dos participantes no estudo. O grafo EMST também foi validado por meio de dois estudos comparativos de identificação de vizinhanças e de agrupamentos. Com base neste arcabouço foram propostas cinco medidas de qualidade de projeções multidimensionais, duas delas para avaliar características relacionadas à separação visual das classes, e outras três para avaliar a preservação de propriedades do espaço original, especificamente a separação das classes, as vizinhanças e os agrupamentos. As medidas são ilustradas por meio de sua aplicação a conjuntos de dados artificiais, favorecendo a sua interpretação, bem como a conjuntos de dados reais, evidenciando a sua potencial utilidade em cenários reais. Também é apresentada uma comparação das novas medidas de preservação de vizinhanças com medidas similares descritas na literatura, permitindo identificar diferenças e semelhanças entre elas. / Multidimensional projections are valuable tools to generate visualizations that support exploratory analysis of a wide variety of complex high-dimensional data. Many examples are found in the literature of visual data analysis tasks that employ projections to explore, for instance, text, image, network and sensor data. Nonetheless, dierent projection techniques applied to a particular data set, or even alternative parameterizations of a single technique, can produce very distinct outcomes, as techniques adopt different strategies to reduce data dimensionality. Few resources are available to support assessing projection quality and, in general, existing solutions focus on specific properties. Thus, a broader assessment typically requires considerable human effort. In this work we introduce a framework to compute projection evaluation measures that focus on neighborhoods and clusters. To elaborate this framework we conducted (i) an experimental study to better understand how users perceive projections and (ii) an investigation of possible data representations capable of favoring the identification of neighborhoods and clusters. The observations resulting from the experimental study have been considered to propose and validate a novel graph data model, called Extended Minimum Spanning Tree (EMST), which captures data properties shown to be consistent with the observations by the participants in the study. The EMST graph has been validated by means of two comparative studies conducted to identify neighborhoods and clusters in multidimensional data. Under this framework, five novel measures of projection quality are introduced, two of them to assess properties related to the visual separation of classes, and three to assess the preservation of data properties in the original space, in particular the preservation of class separation, the preservation of neighborhoods and the preservation of groups. The quality measures have been applied to projections of synthetic data sets, favoring their understanding and interpretation, and also to projections of real data sets, illustrating their potential applicability in real scenarios. The newly introduced neighborhood preservation measures are also compared with existing methods in order to illustrate their differences and similarities.

In this dissertation, we first introduce an equal-area spherical map, HEALPix, which is borrowed from astrophysics. Its associated sample pattern is uniformly distributed over the sphere surface. Then we discuss its application in environment mapping. Although the HEALPix representation is more balanced than the traditional cubemap, it cannot utilize the built-in hardware operations like cubemap, and the mipmapping construction is more complicated. Therefore, its rendering speed is not comparable to that of the cubemap. This motivates us to invent a new six-face spherical map, called isocube. Unlike cubemap, isocube is an equal-area mapping, i.e., each texel spans the same area and is equally important. Due to the six-face representation, isocube can fit nicely into the cubemap hardware and hence can fully exploit the hardware operations tailored for cubemap. In addition, its mapping computation only involves a small overhead. Therefore the look-up speed for isocube is very fast. / Next we discuss another application of HEALPix map, the dynamic environment sequence sampling. Previous work only considers the static case where the environment map is approximated by finite directional light sources. In the dynamic case, the individual regeneration of samples for each frame may introduce abrupt, changes in the rendering animation. To handle this temporal inconsistency problem, we propose spherical q2-tree based on IIEALPix map. The adaptiveness of the quadtree can suppress the abrupt changes between consecutive frames, and hence a rather smooth rendering can be produced. This method, however, generates sample pattern independently for each environment frame, and therefore it may still cause unexpected, lumps in some situations. To fully utilize the temporal coherence in the sequence, we present a global sampling approach which treats the dynamic environment sequence as a all volume and performs sampling in the volume. The volumetric sampling adapts the sample number according to each frame and restricts the temporal/spatial changes within small subdivided volumes, and hence ensures a smooth sampling sequence. Within the framework, we present a volumetric importance metric and develop a binary-quad tree to perform stratification. Experimental results show that our volumetric sampling method can generate light samples with a better temporal consistency. / Spherical map is the foundation for many applications in computer graphics, such as environment mapping, precomputed radiance transfer, radiosity and image-based rendering. For these applications that involve intensive computation on spherical domain, it is generally desirable to employ equal-area and uniform spherical maps as the underlying parameterization. However, equal-area spherical maps are less exploited in graphics. / Wan, Liang. / "August 2007." / Adviser: Tien-Tsin Wong. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1121. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 118-123). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

Projeções Multidimensionais são úteis para gerar visualizações adequadas para apoiar a análise exploratória de uma grande variedade de dados complexos e de alta dimensionalidade. Tarefas de análise visual de dados têm se beneficiado de projeções para explorar dados textuais, de imagens, de sensores, entre outros. Porém, diferentes técnicas de projeção e diferentes parametrizações de uma mesma técnica produzem resultados distintos para um mesmo conjunto de dados, pois as técnicas adotam estratégias distintas para representar os dados originais em um espaço cuja dimensionalidade permite sua visualização. Atualmente, ainda há poucos recursos para avaliar a qualidade dessas projeções e, em geral, as soluções existentes avaliam propriedades específicas, demandando grande esforço do analista para uma avaliação mais abrangente. Neste trabalho, introduzimos um arcabouço para computar medidas de avaliação de projeções com enfoque em análise de vizinhanças e de agrupamentos. Para elaborar este arcabouço, foi realizado um estudo de percepção para entender melhor como os usuários observam as projeções e foi conduzida uma investigação de representações dos dados capazes de favorecer a identificação de vizinhanças e de agrupamentos. Os padrões identificados no estudo de percepção auxiliaram a validar a representação dos dados, em que foi proposto um modelo de grafo, chamado de Extended Minimum Spanning Tree (EMST), capaz de capturar características condizentes com as observações dos participantes no estudo. O grafo EMST também foi validado por meio de dois estudos comparativos de identificação de vizinhanças e de agrupamentos. Com base neste arcabouço foram propostas cinco medidas de qualidade de projeções multidimensionais, duas delas para avaliar características relacionadas à separação visual das classes, e outras três para avaliar a preservação de propriedades do espaço original, especificamente a separação das classes, as vizinhanças e os agrupamentos. As medidas são ilustradas por meio de sua aplicação a conjuntos de dados artificiais, favorecendo a sua interpretação, bem como a conjuntos de dados reais, evidenciando a sua potencial utilidade em cenários reais. Também é apresentada uma comparação das novas medidas de preservação de vizinhanças com medidas similares descritas na literatura, permitindo identificar diferenças e semelhanças entre elas. / Multidimensional projections are valuable tools to generate visualizations that support exploratory analysis of a wide variety of complex high-dimensional data. Many examples are found in the literature of visual data analysis tasks that employ projections to explore, for instance, text, image, network and sensor data. Nonetheless, dierent projection techniques applied to a particular data set, or even alternative parameterizations of a single technique, can produce very distinct outcomes, as techniques adopt different strategies to reduce data dimensionality. Few resources are available to support assessing projection quality and, in general, existing solutions focus on specific properties. Thus, a broader assessment typically requires considerable human effort. In this work we introduce a framework to compute projection evaluation measures that focus on neighborhoods and clusters. To elaborate this framework we conducted (i) an experimental study to better understand how users perceive projections and (ii) an investigation of possible data representations capable of favoring the identification of neighborhoods and clusters. The observations resulting from the experimental study have been considered to propose and validate a novel graph data model, called Extended Minimum Spanning Tree (EMST), which captures data properties shown to be consistent with the observations by the participants in the study. The EMST graph has been validated by means of two comparative studies conducted to identify neighborhoods and clusters in multidimensional data. Under this framework, five novel measures of projection quality are introduced, two of them to assess properties related to the visual separation of classes, and three to assess the preservation of data properties in the original space, in particular the preservation of class separation, the preservation of neighborhoods and the preservation of groups. The quality measures have been applied to projections of synthetic data sets, favoring their understanding and interpretation, and also to projections of real data sets, illustrating their potential applicability in real scenarios. The newly introduced neighborhood preservation measures are also compared with existing methods in order to illustrate their differences and similarities.

Published Article / This study was conducted to ascertain which of two techniques would result in more diagnostic films of patients with possible neck trauma. Twenty individuals were examined at the Radiology Department, Universitas hospital, Bloemfontein. Two exposures were done on each member of the sample: firstly the swimmers projection and secondly the orientation of the patient's arms was reversed. Using specific criteria to standardize evaluation, the films were evaluated by a radiologist. The adapted swimmers projection had better results in 50% of the categories. The swimmers projection was better in 33.3% of the categories. One category for both projections (16.7%) was equal.

Les revêtements composites métal/céramique s'imposent aujourd'hui comme une réponse au fort besoin industriel d'amélioration de la fiabilité des pièces sous sollicitations multiples. Le procédé de projection plasma est envisagé pour la réalisation de tels revêtements avec d'excellentes propriétés tribologiques. Du fait de leur mode d'élaboration, la microstructure des revêtements projetés plasma est complexe et les propriétés en dépendant hétérogènes. Afin d'optimiser le comportement tribologique de ces dépôts, l'objectif de cette étude est d'établir des relations entre microstructure et propriétés tribologiques.<br />Utilisant la souplesse du procédé de projection plasma, notamment celui de projection réactive particulièrement développé pour cette étude, des dépôts composites présentant une large gamme de microstructures ont été obtenus. Pour cela, divers paramètres ont été étudiés : la nature des poudres métalliques projetées (alliages de titane ou de cuivre), la nature du renfort céramique (exogène et/ou endogène), le mode de projection (projection plasma réactive, mode RPS et en surpression, mode HPPS ou co-projection) et les conditions de projection propres à chaque procédé. Une caractérisation des dépôts a été menée, jusqu'à une échelle fine. Le niveau de renforcement de ces microstructures composites fines a été, en particulier, étudié par nanoindentation. Pour chaque mode de projection, deux dépôts composites ont été sélectionnés pour étudier leur comportement tribologique à l'aide d'un essai de frottement de type « pion-disque ». Cet essai a montré une sensibilité élevée à la microstructure et a ainsi permis de déterminer le rôle de certaines caractéristiques microstructurales des dépôts composites sur leurs propriétés tribologiques.<br />A partir d'observations métallographiques et d'analyses des faciès d'usure, un mécanisme d'usure commun aux deux types de dépôts, élaborés par co-projection et par projection réactive, a été mis en évidence. L'influence de la microstructure caractéristique de ces dépôts sur leur comportement tribologique a également été examinée.

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Building on the work of Longuet-Higgins in 1972 and Calderbank and Macpherson in 2009, we study the combinatorics of symmetric configurations of hyperplanes and points in projective space, called generalized Cox configurations. To do so, we use the formalism of morphisms between incidence systems. We notice that the combinatorics of Cox configurations are closely related to incidence systems associated to certain Coxeter groups. Furthermore, the incidence geometry of projective space P (V ), where V is a vector space, can be viewed as an incidence system of maximal parabolic subalgebras in a semisimple Lie algebra g, in the special case g = pgl (V ) the projective general linear Lie algebra of V . Using Lie theory, the Coxeter incidence system for the Coxeter group, whose Coxeter diagram is the underlying diagram of the Dynkin diagram of the g, can be embedded into the parabolic incidence system for g. This embedding gives a symmetric geometric configuration which we call a standard parabolic configuration of g. In order to construct a generalized Cox configuration, we project a standard parabolic configuration of type Dn into the parabolic incidence system of projective space using a process called parabolic projection, which maps a parabolic subalgebra of the Lie algebra to a parabolic subalgebra of a lower dimensional Lie algebra. As a consequence of this construction, we obtain Cox configurations and their analogues in higher dimensional projective spaces. We conjecture that the generalized Cox configurations we construct using parabolic projection are nondegenerate and, furthermore, any non-degenerate Cox configuration is obtained in this way. This conjecture yields a formula for the dimension of the space of non-degenerate generalized Cox configurations of a fixed type, which enables us to develop a recursive construction for them. This construction is closely related to Longuet-Higgins’ recursive construction of (generalized) Clifford configurations but our examples are more general and involve the extra parameters.

The purpose of this thesis is to develop a set of tracking systems for Multiple Persons on DSP-Based. There are three sub-systems in our tracking system, including ¡§Moving Object Detection¡¨, ¡§Contour Matching¡¨ and ¡§Ellipse Algorism¡¨. First of all, the system utilizes CCD camera to capture the image which we want to control, and then detects the moving object from the continuous image array. If the system detects an invador, it will make the position of this invador with the coordinate projection, and then lock the invador's head to track. Finally, the tracking system marks the coordinate separately and exports it in LCD. From the results of the experiment, this system does meet the expectation and obtain good performance and strong robustness.