This dissertation delivers a new computational framework for the automatic generation of geometric feature patterns for industrial design and architectural facades on free-form surfaces. Such patterns include holes in a speaker grill, showerhead holes, protrusions on ceramics or bumpy textures on a panel. These patterns play a key role in making a designed object aesthetically pleasing as well as functional. Computer Aided Design (CAD) systems currently offer tools for generating simple patterns, such as uniformly spaced rectangular or radial patterns. However, they are not applicable to more general cases required in industrial design, including arbitrarily shaped target geometry and graded feature sizes. These tools are limited in several ways: (1) They cannot be applied to free-form geometries used in industrial design, (2) Patterning of these features happens within a single working plane and is not applicable to highly curved surfaces, and (3) Created features lack anisotropy and spatial variations, such as changes in the size and orientation of geometric features within a given region. This thesis proposes a new method of taking input for a target region along with sizing metrics. It will generate feature patterns automatically in three steps: (1) packing isotropic or anisotropic cells tightly in a target region, (2) scaling features according to the specified sizing metrics, and (3) adding features on the base geometry. This approach automatically generates complex patterns that conform to the boundary of any specified region. User input of a small number of geometric features (called “seed features”) of desired size and orientation in preferred locations also can be specified within the target domain. These geometric seed features are then transformed into tensors and used as boundary conditions to generate a Riemannian metric tensor field. A form of the Laplace heat equation is used to generate the field over the target domain, subject to specified boundary conditions. The field represents the anisotropic pattern of the geometric features. The system is implemented as a plugin module in a commercial CAD package to add geometric features to the target region of the model using two set operations, union and subtraction. This method facilitates the creation of a complex pattern of hundreds of geometric features in minutes. All the features are accessible from the CAD system and can be manipulated individually if required by the user. This allows the industrial designer or architect to explore more alternatives by avoiding the tedious and time-consuming manual generation of these geometric patterns.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-03-03T11:28:48Z No. of bitstreams: 1 gildodealmeidaleonel.pdf: 24098922 bytes, checksum: 16845fd58b93cf751e3ef6da19f65159 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-03-06T20:02:53Z (GMT) No. of bitstreams: 1 gildodealmeidaleonel.pdf: 24098922 bytes, checksum: 16845fd58b93cf751e3ef6da19f65159 (MD5) / Made available in DSpace on 2017-03-06T20:02:53Z (GMT). No. of bitstreams: 1 gildodealmeidaleonel.pdf: 24098922 bytes, checksum: 16845fd58b93cf751e3ef6da19f65159 (MD5) Previous issue date: 2011-01-17 / Campos tensoriais arbitrários são úteis em diversas áreas do conhecimento como a física, engenharias e áreas da saúde. Um dos principais interesses de profissionais destas áreas é a investigação de objetos colineares e coplanares representados pelos tensores. Esses objetos são formados por subconjuntos estruturados de tensores presentes no campo e que capturam alguma continuidade geométrica. Pela sua natureza multivariada, a visualização de elementos organizados é uma tarefa desafiadora. Geralmente, utilizam-se métodos de detecção direta destas estruturas para que o observador possa analisá-las. A proposta desta dissertação é explorar o fato de que o movimento estimula percepções complexas de forma inata no sistema visual humano. A abordagem desenvolvida utiliza um sistema de rastreamento de partículas e é parametrizado por campos tensoriais de forma que o comportamento das partículas represente as características do campo e tenha um aprimoramento que possibilite o melhor entendimento e a interpretação da informação proveniente dos tensores. / Arbitrary tensor fields are useful in several areas as physics, engineering and medicine. The investigation of collinear and coplanar objects represented by tensors is the main focus of research in these areas. These objects are formed by structured tensorial fields which captures some geometric continuity. The visualization of strutured elements is a challenging task because of their multivariate nature. To be analysed by the user, direct methods are usually used for detecting these structures. The proposal of this dissertation is to explore the fact that movement increases the perception of complex shapes, that are observed in a innate form by the human visual system. The approach developed uses a particle tracing system and is parameterized by tensor fields, so the particles flow represents the characteristics of the field and make an improvement that enables better understanding and interpretation of information derived from tensors.

While tensors occur in many areas of science and engineering, little has been done to visualize tensors with order higher than two. Tensors of higher orders can be used for example to describe complex diffusion patterns in magnetic resonance imaging (MRI). Recently, we presented a method for tracking lines in higher order tensor fields that is a generalization of methods known from first order tensor fields (vector fields) and symmetric second order tensor fields. Here, this method is applied to magnetic resonance imaging where tensor fields are used to describe diffusion patterns for example of hydrogen in the human brain. These patterns align to the internal structure and can be used to analyze interconnections between different areas of the brain, the so called tractography problem. The advantage of using higher order tensor lines is the ability to detect crossings locally, which is not possible in second order tensor fields. In this paper, the theoretical details will be extended and tangible results will be given on MRI data sets.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-05-30T18:07:09Z No. of bitstreams: 1 joseluizribeirodesouzafilho.pdf: 14599386 bytes, checksum: b6c429c2f45228c7e68a7f951c5456ba (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-06-01T11:49:25Z (GMT) No. of bitstreams: 1 joseluizribeirodesouzafilho.pdf: 14599386 bytes, checksum: b6c429c2f45228c7e68a7f951c5456ba (MD5) / Made available in DSpace on 2017-06-01T11:49:25Z (GMT). No. of bitstreams: 1 joseluizribeirodesouzafilho.pdf: 14599386 bytes, checksum: b6c429c2f45228c7e68a7f951c5456ba (MD5) Previous issue date: 2013-02-22 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Análise e visualização de campos tensoriais simétricos de segunda ordem é um pro blema desafiador, pois eles geralmente representam dados multivariados. Trabalhos nessa área utilizam de diferentes estratégias para tornar perceptíveis propriedades desejadas dos campos. Essas propriedades são, por exemplo, estruturas colineares e coplanares. Em casos como campos tensoriais que representam tecidos orgânicos obtidos por ressonância magnética, ressaltar essas estruturas pode ser útil para a área médica de diagnóstico e neurociência por exemplo. Um tipo específico de visualização consiste na observação da propagação de partículas sobre os campos. Mas, grande parte desses métodos não des creve interações entre partículas e são estáticos. Essa dissertação propõe um método que induz o sistema perceptual humano a perceber de forma mais intuitiva essas estruturas, utilizando dinâmica de fluidos. Foram propostas modificações de uma implementação específica das Equações de Navier-Stokes, chamada Hidrodinâmica de Partículas Suavi zadas (SPH). Diferente de outras abordagens, o modelo proposto explora interação entre partículas para ressaltar a percepção de estruturas subjacentes no campo tensorial. Foi proposta uma força externa para manter partículas em regiões de interesse e também a aplicação de uma distorção na função núcleo, ambas baseadas nas informações dos tenso res. A distorção faz com que as partículas se alinhem de acordo com estruturas colineares e coplanares consecutivas do campo, exibindo continuidades e também conectividades. / Analysis and visualization of symmetric second order tensor fields are challenging since they generally represent multivariate data. Works in this area use different approaches to enhance desired properties of the field. Those properties are, for example, colinear and coplanar structures. In some cases, such as tensor fields obtained by magnetic resonance imaging of organic tissues, highlighting those structures can be useful for studies in neu roscience and diagnostics, for example. A specific technique of visualization consists in observing particles’ trajectories along the field. But, most of those methods are static and does not present interaction between particles. This work proposes a method that induces the human perceptual system to visualize more intuitively those structures, using fluid dynamics. Modifications in a specific implementation of Navier-Stokes equations, called Smoothed Particle Hydrodynamics (SPH) were proposed. Different from other ap proaches, interactions between particles are used to enhance the perception of underlying structures in a tensor field. It was also proposed an external force to keep particles around areas of interest and a distortion in the kernel functions, both based on tensors’ informa tion.The distortion forces particles to align according to consecutive colinear and coplanar structures of a field, showing continuities and connectivities.

Cette thèse s’inscrit dans le contexte de la synthèse d’images texturées. Dans l’objectif d’assurer une reproduction fidèle des motifs et des variations d’orientations d’une texture initiale, un algorithme de synthèse de texture à deux étapes « structure/texture » est proposé. Il s’agit, dans une première étape, de réaliser la synthèse d’une couche de structure caractérisant la géométrie de l’exemplaire et représentée par un champ de tenseurs de structure et, dans une deuxième étape, d’utiliser le champ de structure résultant pour contraindre la synthèse d’une couche de texture portant des variations plus locales. Une réduction du temps d’exécution est ensuite développée, fondée notamment sur l’utilisation de pyramides Gaussiennes et la parallélisation des calculs mis en oeuvre.Afin de démontrer la capacité de l’algorithme proposé à reproduire fidèlement l’aspect visuel des images texturées considérées, la méthode est testée sur une variété d’échantillons de texture et évaluée objectivement à l’aide de statistiques du 1er et du 2nd ordre du champ d’intensité et d’orientation. Les résultats obtenus sont de qualité supérieure ou équivalente à ceux obtenus par des algorithmes de la littérature. Un atout majeur de l’approche proposée est son aptitude à synthétiser des textures avec succès dans de nombreuses situations où les algorithmes existants ne parviennent pas à reproduire les motifs à grande échelle.L’approche de synthèse structure/texture proposée est étendue à la synthèse de texture couleur. La synthèse de texture 3D est ensuite abordée et, finalement, une extension à la synthèse de texture de forme spécifiée par une texture imposée est mise en oeuvre, montrant la capacité de l’approche à générer des textures de formes arbitraires en préservant les caractéristiques de la texture initiale. / This work is a part of the texture synthesis context. Aiming to ensure a faithful reproduction of the patterns and variations of orientations of the input texture, a two-stage structure/texture synthesis algorithm is proposed. It consists of synthesizing the structure layer showing the geometry of the exemplar and represented by the structure tensor field in the first stage, and using the resulting tensor field to constrain the synthesis of the texture layer holding more local variations, in the second stage. An acceleration method based on the use of Gaussian pyramids and parallel computing is then developed.In order to demonstrate the ability of the proposed algorithm to faithfully reproduce the visual aspect of the considered textures, the method is tested on various texture samples and evaluated objectively using statistics of 1st and 2nd order of the intensity and orientation field. The obtained results are of better or equivalent quality than those obtained using the algorithms of the literature. A major advantage of the proposed approach is its capacity in successfully synthesizing textures in many situations where traditional algorithms fail to reproduce the large-scale patterns.The structure/texture synthesis approach is extended to color texture synthesis. 3D texture synthesis is then addressed and finally, an extension to the synthesis of specified form textures using an imposed texture is carried out, showing the capacity of the approach in generating textures of arbitrary forms while preserving the input texture characteristics.

L'objet de cette thèse est d'étendre le cadre théorique et les méthodes numériques du transport optimal à des objets plus généraux que des mesures de probabilité. En premier lieu, nous définissons des modèles de transport optimal entre mesures positives suivant deux approches, interpolation et couplage de mesures, dont nous montrons l'équivalence. De ces modèles découle une généralisation des métriques de Wasserstein. Dans une seconde partie, nous développons des méthodes numériques pour résoudre les deux formulations et étudions en particulier une nouvelle famille d'algorithmes de "scaling", s'appliquant à une grande variété de problèmes. La troisième partie contient des illustrations ainsi que l'étude théorique et numérique, d'un flot de gradient de type Hele-Shaw dans l'espace des mesures. Pour les mesures à valeurs matricielles, nous proposons aussi un modèle de transport optimal qui permet un bon arbitrage entre fidélité géométrique et efficacité algorithmique. / This thesis generalizes optimal transport beyond the classical "balanced" setting of probability distributions. We define unbalanced optimal transport models between nonnegative measures, based either on the notion of interpolation or the notion of coupling of measures. We show relationships between these approaches. One of the outcomes of this framework is a generalization of the p-Wasserstein metrics. Secondly, we build numerical methods to solve interpolation and coupling-based models. We study, in particular, a new family of scaling algorithms that generalize Sinkhorn's algorithm. The third part deals with applications. It contains a theoretical and numerical study of a Hele-Shaw type gradient flow in the space of nonnegative measures. It also adresses the case of measures taking values in the cone of positive semi-definite matrices, for which we introduce a model that achieves a balance between geometrical accuracy and algorithmic efficiency.

L'un des problèmes fondamentaux de l'imagerie cardiaque par résonance magnétique du tenseur de diffusion (IRM-TD) est sa faible résolution spatiale, à cause des limitations matérielles des scanners IRM actuels. L'objectif principal de ce travail de thèse est de développer de nouvelles approches pour améliorer la résolution des données d'IRM-TD afin de mieux représenter l'architecture myocardique du coeur humain et de la comparer avec des résultats issus d'autres techniques d'investigation telles que l'imagerie par lumière polarisée. Dans ce cadre, le travail porte sur trois parties principales. La première concerne le développement d'une nouvelle approche pour l'interpolation des champs de vecteurs propres principaux issus de l'IRM-TD cardiaque humaine. Cette approche consiste d'abord à supprimer les vecteurs corrompus par le bruit au lieu de débruiter de manière uniforme le champ entier de vecteurs, et ensuite à interpoler le champ de vecteurs en utilisant la modèle Thin-Plate-Spline (TPS) afin d'exploiter la corrélation entre les composantes du vecteur. La deuxième partie concerne une nouvelle famille de méthodes d'interpolation pour les champs de tenseurs, basée soit sur les angles d'Euler soit sur le quaternion. Ces méthodes exploitent les caractéristiques du tenseur et préservent les paramètres de tenseurs, tels que le déterminant du tenseur, l'anisotropie fractionnelle (FA) et la diffusivité moyenne (MD). En outre, cette partie compare les principales approches d'interpolation au niveau des images pondérées en diffusion et des champs de tenseurs, et les résultats montrent qu'il serait préférable d'effectuer l'interpolation des données d'IRM-TD au niveau des champs de tenseurs. La troisième partie étudie le changement des paramètres MD et FA après un infarctus du myocarde chez les cochons, et l'influence des méthodes d'interpolation sur ces paramètres dans la zone infarctus et la zone distante. Les résultats montrent que la zone infarctus présente une diminution significative de FA et une augmentation significative de MD, comparée avec la zone distante, et que les méthodes d'interpolations du tenseur ont plus d'influence sur FA que sur MD, ce qui suggère que l'interprétation de ces paramètres cliniques après l'interpolation doive être prise avec précaution. / One of fundamental problems in human cardiac diffusion tensor magnetic resonance imaging (DT-MRI) is its poor spatial resolution, due to the hardware limitations of MRI scanners. The main purpose of this PhD work is to develop new approaches to improving the resolution of cardiac DT-MRI data in order to better understand the myocardial architecture of the heart and compare it with results issues from other investigation techniques such as polarized light imaging. Within this framework, the present work is composed of three main parts. The first part concerns a new approach to interpolating primary eigenvector fields from human cardiac DT-MRI using Thin Plate Spline (TPS) model. This approach removes the noise-corrupted vectors rather than denoising the whole vector field in a uniform manner, and uses TPS model in order to exploit the correlation between vector components during interpolation. The second part is dealt with a new category of feature-based methods for diffusion tensor field interpolation using either Euler angles or quaternion. These feature-based methods well preserve tensor parameters, such as tensor determinant, fractional anisotropy (FA) and mean diffusivity (MD) values. In this part are also compared the main interpolation approaches at the level of diffusion weighted images and tensor fields. The results show that the interpolation of DT-MRI data should be performed at the level of tensor fields. The last part investigates changes in MD and FA after myocardial infarction in porcine hearts, and the influence of diffusion tensor interpolation methods on FA and MD in both infarction and remote region. It is found that the infarction region showed significantly decreased FA and increased MD than the remote region, and that diffusion tensor interpolations have more significant influence on FA than on MD, which suggests that precaution should be taken when performing the clinical analysis based on the parameters after diffusion tensor interpolations.