In this work the electronic and structural properties of anatase TiO2 (100) surface and gold adsorption have been investigated by using the first-principles calculations based on density functional theory (DFT). TiO2 is a wide band-gap material and to this effects it finds numerous applications in technology such as, cleaning of water, self-cleaning, coating, solar cells and so on. Primarily, the relation between the surface energy of the anatase (100)-1x1 phase and the TiO2-layers is examined. After an appropriate atomic layer has been chosen according to the stationary state of the TiO2 slab, the adsorption behavior of the Au atom and in the different combinations are searched for both the surface and the surface which is supported by a single Au atom/atoms. It has been observed that a single Au atom tends to adsorb to the surface which has an impurity of Au atom or atoms. Although, the high metal concentration on the surface have increased the strength of the adsorption, it is indicated that the system gains a metallic property which is believed to cause problems in the applications. In addition, the gold clusters of the dimer (Au2) and the trimer (Au3) have been adsorbed on the surface and their behavior on the surface is investigate. It is observed that the interaction between Au atoms in the atomic cluster each other is stronger than that of gold clusters and the surface.

This thesis describes theory and algorithms for use with Radial Basis Functions (RBFs), emphasising techniques motivated by three particular application areas. In Part I, we apply RBFs to the problem of interpolating to integral data. While the potential of using RBFs for this purpose has been established in an abstract theoretical context, their use has been lacking an easy to check sufficient condition for finding appropriate parent basic functions, and explicit methods for deriving integral basic functions from them. We present both these components here, as well as explicit formulations for line segments in two dimensions and balls in three and five dimensions. We also apply these results to real-world track data. In Part II, we apply Hermite and pointwise RBFs to the problem of surface reconstruction. RBFs are used for this purpose by representing the surface implicitly as the zero level set of a function in 3D space. We develop a multilevel piecewise technique based on scattered spherical subdomains, which requires the creation of algorithms for constructing sphere coverings with desirable properties and for blending smoothly between levels. The surface reconstruction method we develop scales very well to large datasets and is very amenable to parallelisation, while retaining global-approximation-like features such as hole filling. Our serial implementation can build an implicit surface representation which interpolates at over 42 million points in around 45 minutes. In Part III, we apply RBFs to the problem of animation control in the area of motion synthesis---controlling an animated character whose motion is entirely the result of simulated physics. While the simulation is quite well understood, controlling the character by means of forces produced by virtual actuators or muscles remains a very difficult challenge. Here, we investigate the possibility of speeding up the optimisation process underlying most animation control methods by approximating the physics simulator with RBFs.

Many computer vision applications such as image filtering, segmentation and stereovision can be formulated as optimization problems. Recently discrete, convex, globally optimal methods have received a lot of attention. Many graph-based methods suffer from metrication artefacts, segmented contours are blocky in areas where contour information is lacking. In the first part of this work, we develop a discrete yet isotropic energy minimization formulation for the continuous maximum flow problem that prevents metrication errors. This new convex formulation leads us to a provably globally optimal solution. The employed interior point method can optimize the problem faster than the existing continuous methods. The energy formulation is then adapted and extended to multi-label problems, and shows improvements over existing methods. Fast parallel proximal optimization tools have been tested and adapted for the optimization of this problem. In the second part of this work, we introduce a framework that generalizes several state-of-the-art graph-based segmentation algorithms, namely graph cuts, random walker, shortest paths, and watershed. This generalization allowed us to exhibit a new case, for which we developed a globally optimal optimization method, named "Power watershed''. Our proposed power watershed algorithm computes a unique global solution to multi labeling problems, and is very fast. We further generalize and extend the framework to applications beyond image segmentation, for example image filtering optimizing an L0 norm energy, stereovision and fast and smooth surface reconstruction from a noisy cloud of 3D points

Oxide ultra-thin film surfaces have properties and structures that are significantly different from the terminations of the corresponding bulk crystals. For example, surface structures of epitaxial ultra-thin oxide films are highly influenced by the crystallinity and electronegativity of the metal substrates they grown on. Some enhanced properties of the novel reconstructions are related to catalysis, sensing and microelectronics, which has resulted in an increasing interest in this field. Ultra-thin TiO_x films were grown on Au(111) substrates in this work. Two well-ordered structures within monolayer coverage - honeycomb (HC) and pinwheel - were generated and investigated. Special attention has been paid to the uniform (2 x 2) Ti₂O₃ HC phase including its regular structure and imperfections such as domain boundaries (DBs) and point defects. Linear DBs with long-range repeating units have been observed; density functional theory (DFT) modelling has been used to simulate their atomic structures and calculate their formation energies. Rotational DBs/defects show up less frequently, however a six-fold symmetrical 'snowflake' DB loop stands out. Two types of point defects have been discovered and assigned to Ti vacancies and oxygen vacancies/hydroxyl groups. Their diffusion manners and pairing habits have been discussed within an experimental context. The results of growing NbO_x ultra-thin films on Au(111) are also presented in this thesis. An identical looking (2 x 2) HC structure to the Ti₂O₃ ultra-thin film has been formed; a stoichiometry of Nb2O3 is suggested. Another interesting reconstruction is a hollow triangle structure. Various sizes have been found, and sides of these equilateral triangles all show a double-line feature aligned along the { 1 ₁⁻ } directions of the Au(111) lattice. Chemical composition characterisations of NbO_x thin films are still required as is DFT modelling. Experimental techniques used in this thesis include scanning tunnelling microscopy (STM), low energy electron diffraction (LEED), and X-ray photoelectron spectroscopy (XPS). Ultra-thin oxide films were created by physical vapour deposition (PVD) in ultra-high vacuum (UHV) systems.

Image-based 3D reconstruction refers to the capture and virtual reconstruction of real scenes, through the use of ordinary camera sensors. A common approach is the use of the algorithms Structure from Motion, Multi-view Stereo and Poisson Surface Reconstruction, that fares well for many types of scenes. However, a problem that this pipeline suffers from is that it often falters when it comes to texture-less surfaces and areas, such as those found in man-made environments. Building facades, roads and walls often lack detail and easily trackable feature points, making this approach less than ideal for such scenes. To remedy this weakness, this thesis investigates an expanded approach, incorporating line segment detection and line cloud generation into the already existing point cloud-based pipeline. Texture-less objects such as building facades, windows and roofs are well-suited for line segment detection, and line clouds are fitting for encoding 3D positional data in scenes consisting mostly of objects featuring many straight lines. A number of approaches have been explored in order to determine the usefulness of line clouds in this context, each of them addressing different aspects of the reconstruction procedure.

Métodos de representação de superfícies a partir de pontos não-organizados se mantêm como uma das principais vertentes científicas que aquecem o estado-da-arte em Computação Gráfica e, significativamente, estão sendo reconhecidos como uma ferramenta interessante para definição de interfaces móveis no contexto de simulações numéricas de escoamento de fluidos. Não é difícil encontrar motivos para tais fatos: pelo lado da computação gráfica, por exemplo, a manipulação de conjuntos de pontos massivos com geometrias complexas e sujeitos a informações ruidosas ainda abre margem para novas metodologias. Já no âmbito da mecânica dos fluidos, onde os dados não são originados de \\emph tridimensionais, mas sim de interfaces entre fluidos imiscíveis, mecanismos de representação de superfícies a partir de pontos não-organizados podem apresentar características computacionais e propriedades geométricas que os tornem atrativos para aplicações em simulação de fenômenos físicos. O objetivo principal dessa tese de doutorado foi, portanto, o desenvolvimento de técnicas de representação de superfícies a partir de pontos não-organizados, que sejam capazes de suprir restrições de importantes trabalhos prévios. Nesse sentido, primeiramente focalizamos a elaboração de técnicas baseadas em formulações de mínimos-quadrados-móveis e de uma técnica robusta de partição da unidade implícita adaptativa em duas vias. Além de mecanismos de representação de superfícies a partir de pontos não-organizados, também propusemos um método promissor para representação de interfaces em simulação numérica de escoamento de fluidos multifásicos. Para isso, embasamo-nos numa abordagem Lagrangeana (livre-de-malhas), fundamentada no método dos mínimos-quadrados-móveis algébricos e apresentamos diversos resultados numéricos, estudos de convergências e comparações que evidenciam o potencial dessa metodologia para simulações numéricas de fenômenos físicos. Apesar de a contribuição principal deste trabalho ser o desenvolvimento de métodos para representação de superfícies a partir de pontos não-organizados, a experiência que adquirimos no desenvolvimento dessas técnicas nos conduziu à elaboração de mecanismos para representação de dados volumétricos não-organizados. Por conta disso, apresentamos dois mecanismos de representação a partir de dados volumétricos não-organizados com o intuito de serem aplicáveis a informações oriundas de malhas contendo células arbitrárias, isto é, propusemos a definição de um método de rendering unificado / Surface reconstruction from unorganized points has been one of the most promising scientific research areas in Computer Graphics. In addition, it has been used successfully for the definition of fluid interface in numerical simulation of fluid flow. There are several reasons to that fact: for instance, considering Computer Graphics, we have the handling of out-of-core data from complicated geometries and subject to noisy information that brings out opportunities for the development of new techniques. Further, considering Numerical Fluid Mechanics, where the input data does not come from tridimensional scanners, but from fluid interfaces, schemes that define the surface from unorganized points can offer geometrical and computational properties useful to numerical fluid flow simulation. The main goal of this project was the development of novel techniques for reconstructing surfaces from unorganized points with the capability to overcome the main drawbacks of important previous work. To that end, first we focused on the development of techniques based on moving-least-squares and on a robust twofold partition of unity Implicits. Added to the development of surface reconstruction from unorganized points, we proposed a novel scheme for defining fluid flow interfaces. We approach a meshless Lagrangian based on algebraic moving-least-squares surfaces. In addition, we presented several numerical results, convergence tests and comparisons, which state the power of the method to numerical simulation of physical phenomena. Although our main contributions were focused on surface reconstruction from points, we proposed methods to function reconstruction from unorganized volumetric data. Thus, we present two schemes to represent volumetric data from arbitrary meshes, i.e., a unified rendering scheme

Les surfaces complexes ont des applications dans divers domaines tels que ceux de la photonique, de l'énergie, du biomédical, du transport... Par contre, elles posent de véritables défis quant à leur spécification, fabrication et mesure ainsi que lors de l'évaluation de leur défaut de forme. Les processus de fabrication et de mesure de surfaces complexes sont fortement tributaires des dimensions, des tolérances et des formes spécifiées. Afin de rendre exploitable les informations données par le système de mesure, une étape importante de traitement s'impose. Il s'agit ici de la reconstruction de surfaces afin de reconstituer la géométrie et la topologie de la surface sous-jacente et d'en extraire les informations nécessaires pour des besoins de métrologie dimensionnelle (caractéristiques dimensionnelles et évaluation des défauts de forme). Dans la catégorie des surfaces asphériques pour lesquelles un modèle mathématique est associé, le processus de traitement de données géométriques, non nécessairement organisées, se fait par l'association du modèle aux données. Les résidus d'association recherchés en optique sont typiquement de l'ordre du nanomètre. Dans ce cadre, nous proposons l'utilisation de l'algorithme L-BFGS qui n'a encore jamais été utilisé en métrologie. Ce dernier permet de résoudre des problèmes d'optimisation non-linéaires, sans contraintes et d'une manière robuste, automatique et rapide. La méthode L-BFGS reste efficace pour des données contenant plusieurs millions de points. Dans la catégorie des surfaces gauches et notamment des aubes de turbines, la fabrication, la mesure et le traitement sont à une toute autre échelle, sub-micrométrique. Les surfaces gauches ne sont généralement pas définies par un modèle mathématique mais sont représentées par des modèles paramétriques de type B-Spline et/ou NURBS. Dans ce cadre, nous exposons un état de l'art détaillé et proposons une nouvelle approche itérative d'association B-Spline. L'algorithme s'affranchit de tous les problèmes liés à l'initialisation et au paramétrage initial. Par conséquent, un tel algorithme constitue une nouveauté dans ce domaine. Nous établissons une étude approfondie en évoquant les avantages et les limites actuelles de cette approche sur des exemples de courbes fermées en 2D. Nous complétons ensuite cette étude par des perspectives d'amélioration et de généralisation aux surfaces en 3D. / Complex surfaces exhibit real challenges in regard to their design specification, their manufacturing, their measurement and the evaluation of their manufacturing defects. They are classified according to their geometric/shape complexity as well as to their required tolerance. Thus, the manufacturing and measurement processes used are selected accordingly. In order to transcribe significant information from the measured data, a data processing scheme is essential. Here, processing involves surface reconstruction in the aim of reconstituting the underlying geometry and topology to the points and extracting the necessary metrological information (form and/or dimensional errors). For the category of aspherical surfaces, where a mathematical model is available, the processing of the data, which are not necessarily organized, is done by fitting/associating the aspherical model to the data. The sought precision in optics is typically nanometric. In this context, we propose the L-BFGS optimization algorithm, first time used in metrological applications and which allows solving unconstrained, non-linear optimization problems precisely, automatically and fast. The L-BFGS method remains efficient and performs well even in the presence of very large amounts of data.In the category of general freeform surfaces and particularly turbine blades, the manufacturing, measurement and data processing are all at a different scale and require sub-micrometric precision. Freeform surfaces are generally not defined by a mathematical formula but are rather represented using parametric models such as B-Splines and NURBS. We expose a detailed state-of-the-art review of existing reconstruction algorithms in this field and then propose a new active contour deformation of B-Splines approach. The algorithm is independent of problems related to initialization and initial parameterization. Consequently, it is a new algorithm with promising results. We then establish a thorough study and a series of tests to show the advantages and limitations of our approach on examples of closed curves in the plane. We conclude the study with perspectives regarding improvements of the method and its extension to surfaces in 3D.

Un problème toujours d'actualité est la reconstruction automatique de la surface d'une scène à partir du flot d'images prises par une caméra en mouvement. Il se résout en général en deux étapes : le calcul de la géométrie où les poses de la caméra et un nuage épars de points 3D de la scène sont simultanément estimés, et un calcul de stéréo dense qui permet d'obtenir une surface en estimant la profondeur de tous les pixels. L' approche que nous proposons se distingue des précédentes en cumulant les caractéristiques suivantes. La surface est une 2-variété, ce qui est utile pour les traitements ou utilisations ultérieurs. Elle est calculée directement à partir du nuage épars donné par la première étape, afin d'éviter la seconde étape coûteuse et pour obtenir une modélisation compacte d'une scène complexe. Le calcul est incrémental afin d'avoir un résultat pendant la lecture de la vidéo. Le principe est le suivant. A chaque itération, de nouveaux points 3D sont estimés et insérés dans une triangulation de Delaunay 3D. Celle-ci partitionne l'espace en tétraèdres vides et pleins grâce à l'information de visibilité également fournie par la première étape. On met aussi à jour une seconde partition en tétraèdres intérieurs et extérieurs dont le bord est la 2-variété recherchée. Sous certaines hypothèses, et contrairement à la seule méthode précédente ayant les même propriétés et hypothèses, la complexité d'une itération est bornée. Notre méthode a été expérimentée sur des séquences synthétiques et réelles, dont une séquence longue de 2;5 km prise en milieu urbain avec une caméra omnidirectionnelle. La qualité du résultat est proche de celle obtenue par la méthode globale (non incrémentale) qui a servi d'inspiration, mais le temps de calcul ne permet pas actuellement une utilisation en-ligne sur un PC standard. On a aussi étudié l'intérêt d'ajouter des contours dans le processus de reconstruction. / The automatic reconstruction of a scene surface from images taken by a moving camera is still an active research topic. This problem is usually solved in two steps : first estimate the camera poses and a sparse cloud of 3D points using Structure-from-Motion, then apply dense stereo to obtain the surface by estimating the depth for all pixels. Compared to the previous approaches, ours accumulates the following properties. The output surface is a 2-manifold, which is useful for applications and postprocessing. It is computed directly from the sparse point cloud provided by the first step, so as to avoid the second and time consuming step and to obtain a compact model of a complex scene. The computation is incremental to allow access to intermediary results during the processing. The principle is the following. At each iteration, new 3D points are estimated and added to a 3D Delaunay triangulation; the tetrahedra are labeled as free-space or matter thanks to the visibility information provided by the first step. We also update a second partition of outside and inside tetrahedra whose boundary is the target 2-manifold. Under some assumptions, the time complexity of one iteration is bounded (there is only one previous method with the same properties, but its complexity is greater than that). Our method is experimented on synthetic and real sequences, including a 2:5 km. long urban sequence taken by an omnidirectional camera. The surface quality is similar to that of the batch method which inspired us. However, the computations are not yet real-time on a commodity PC. We also study the use of contours in thereconstruction process.

A reconstrução de superfícies a partir de nuvens de pontos faz parte de um novo paradigma de modelagem em que modelos computacionais para objetos reais são reconstruídos a partir de dados amostrados sobre a superfície dos mesmos. O principal problema que surge nesse contexto é o fato de que não são conhecidas relações de conectividade entre os pontos que compõe a amostra. Os objetivos do presente trabalho são estudar métodos implícitos para a reconstrução de superfícies e propor algumas melhorias pouco exploradas por métodos já existentes. O uso de funções implícitas no contexto da reconstrução conduz a métodos mais robustos em relação a ruídos, no entanto, uma das principais desvantagens de tais métodos está na dificuldade de capturar detalhes finos e sharp features. Nesse sentido, o presente trabalho propõe o uso de abordagens adaptativas, tanto na poligonalização de superfícies quanto na aproximação de superfícies. Além disso, questões relativas à robustez das soluções locais e à qualidade da malha também são abordadas. Por fim, o método desenvolvido é acoplado aumsoftware traçador de raios afimde se obterumamaneira de modelar cenas tridimensionais utilizando nuvens de pontos, além dos objetos gráficos tradicionais. Os resultados apresentados mostram que muitas das soluções propostas oferecem um incremento à qualidade dos métodos de reconstrução anteriormente propostos / Surface reconstruction from point clouds is part of a new modeling paradigm in which computational models for real objects are reconstructed from data sampled from their surface. The main problem that arises in this context is the fact that there are no known connectivity relationships amongst the points that compose the sample. The objectives of the present work are to study implicit methods for surface reconstruction and to propose some improvements scarcely explored by previous work. The use of implicit functions in the context of surface reconstruction leads to less noise sensitive methods; however, one major drawback of such methods is the difficulty in capturing fine details and sharp features. Towards this, the present work proposes the use of adaptive approaches, not only in the polygonization but also in the surface approximation. Besides, robustness issues in local solutions and mesh quality are also tackled. Finally, the developed method is embedded in a ray tracer software in order to set a basis for modeling tridimensional scenes using point sets, in addition to traditional graphic objects. The presented results show that a great deal of the proposed solutions offer a quality increase to the reconstruction method previously proposed

La modélisation géométrique d'objets fabriqués par l'homme à partir de données 3D est l'un des plus grands défis de la vision par ordinateur et de l'infographie. L'objectif à long terme est de générer des modèles de type CAO de la manière la plus automatique possible. Pour atteindre cet objectif, des problèmes difficiles doivent être résolus, notamment (i) le passage à l'échelle du processus de modélisation sur des données d'entrée massives, (ii) la robustesse de la méthodologie contre des mesures d'entrées erronés, et (iii) la qualité géométrique des modèles de sortie. Les méthodes existantes fonctionnent efficacement pour reconstruire la surface des objets de forme libre. Cependant, dans le cas d'objets fabriqués par l'homme, il est difficile d'obtenir des résultats dont la qualité approche celle des représentations hautement structurées, comme les modèles CAO. Dans cette thèse, nous présentons une série de contributions dans ce domaine. Tout d'abord, nous proposons une méthode de classification basée sur l'apprentissage en profondeur pour distinguer des objets dans des environnements complexes à partir de nuages de points 3D. Deuxièmement, nous proposons un algorithme pour détecter des primitives planaires dans des données 3D à différents niveaux d'abstraction. Enfin, nous proposons un mécanisme pour assembler des primitives planaires en maillages polygonaux compacts. Ces contributions sont complémentaires et peuvent être utilisées de manière séquentielle pour reconstruire des modèles de ville à différents niveaux de détail à partir de données 3D aéroportées. Nous illustrons la robustesse, le passage à l'échelle et l'efficacité de nos méthodes sur des données laser et multi-vues stéréo sur des scènes composées d'objets fabriqués par l'homme. / Geometric modeling of man-made objects from 3D data is one of the biggest challenges in Computer Vision and Computer Graphics. The long term goal is to generate a CAD-style model in an as-automatic-as-possible way. To achieve this goal, difficult issues have to be addressed including (i) the scalability of the modeling process with respect to massive input data, (ii) the robustness of the methodology to various defect-laden input measurements, and (iii) the geometric quality of output models. Existing methods work well to recover the surface of free-form objects. However, in case of manmade objects, it is difficult to produce results that approach the quality of high-structured representations as CAD models.In this thesis, we present a series of contributions to the field. First, we propose a classification method based on deep learning to distinguish objects from raw 3D point cloud. Second, we propose an algorithm to detect planar primitives in 3D data at different level of abstraction. Finally, we propose a mechanism to assemble planar primitives into compact polygonal meshes. These contributions are complementary and can be used sequentially to reconstruct city models at various level-of-details from airborne 3D data. We illustrate the robustness, scalability and efficiency of our methods on both laser and multi-view stereo data composed of man-made objects.