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One of the fundamental problems in computer vision is point set registration. Point set registration finds use in many important applications and in particular can be considered one of the crucial stages involved in the reconstruction of models of physical objects and environments from depth sensor data. The problem of globally aligning multiple point sets, representing spatial shape measurements from varying sensor viewpoints, into a common frame of reference is a complex task that is imperative due to the large number of critical functions that accurate and reliable model reconstructions contribute to. In this thesis we focus on improving the quality and feasibility of model and environment reconstruction through the enhancement of multi-view point set registration techniques. The thesis makes the following contributions: First, we demonstrate that employing kernel density estimation to reason about the unknown generating surfaces that range sensors measure allows us to express measurement variability, uncertainty and also to separate the problems of model design and viewpoint alignment optimisation. Our surface estimates define novel view alignment objective functions that inform the registration process. Our surfaces can be estimated from point clouds in a datadriven fashion. Through experiments on a variety of datasets we demonstrate that we have developed a novel and effective solution to the simultaneous multi-view registration problem. We then focus on constructing a distributed computation framework capable of solving generic high-throughput computational problems. We present a novel task-farming model that we call Semi-Synchronised Task Farming (SSTF), capable of modelling and subsequently solving computationally distributable problems that benefit from both independent and dependent distributed components and a level of communication between process elements. We demonstrate that this framework is a novel schema for parallel computer vision algorithms and evaluate the performance to establish computational gains over serial implementations. We couple this framework with an accurate computation-time prediction model to contribute a novel structure appropriate for addressing expensive real-world algorithms with substantial parallel performance and predictable time savings. Finally, we focus on a timely instance of the multi-view registration problem: modern range sensors provide large numbers of viewpoint samples that result in an abundance of depth data information. The ability to utilise this abundance of depth data in a feasible and principled fashion is of importance to many emerging application areas making use of spatial information. We develop novel methodology for the registration of depth measurements acquired from many viewpoints capturing physical object surfaces. By defining registration and alignment quality metrics based on our density estimation framework we construct an optimisation methodology that implicitly considers all viewpoints simultaneously. We use a non-parametric data-driven approach to consider varying object complexity and guide large view-set spatial transform optimisations. By aligning large numbers of partial, arbitrary-pose views we evaluate this strategy quantitatively on large view-set range sensor data where we find that we can improve registration accuracy over existing methods and contribute increased registration robustness to the magnitude of coarse seed alignment. This allows large-scale registration on problem instances exhibiting varying object complexity with the added advantage of massive parallel efficiency.

Les travaux présentés dans cette thèse concernent les nouvelles techniques d'optimisation pour la résolution de certains problèmes importants issus de finance. Il s'agit des problèmes d'optimisation non convexe de grande dimension pour lesquels la recherche des bonnes méthodes de résolution est toujours d'actualité. Notre travail s'appuie principalement sur la programmation DC (Différence de fonctions Convexes) et DCA (DC Algorithmes). Cette démarche est motivée par la robustesse et la performance de la programmation DC et DCA comparée aux autres méthodes. La thèse est divisée en deux parties et est composée de sept chapitres. Dans la première partie intitulée ¡Méthodologie¡ nous présentons des outils théoriques et algorithmiques servant des références aux autres. Le premier chapitre concerne la programmation DC et DCA tandis que le deuxième porte sur les algorithmes par séparation et évaluation. Dans la deuxième partie nous développons la programmation DC et DCA pour la résolution des problèmes en finance. Nous commençons par une introduction à la gestion de portefeuille (le Chapitre 3). Le Chapitre 4 est dédié aux généralisations du modèle moyenne-variance (MV) de Markowitz, où nous étudions le modèle MV sous les contraintes de seuil d'achat, de seuil et de cardinalité. Le Chapitre 5 est consacré à la mesure de risque de baisse et les contraintes de cardinalité. Le Chapitre 6 porte sur le problème de choix de portefeuille avec les fonctions des coûts de transaction en escalier. L'investissement robuste en gestion de portefeuille sous les contraintes de cardinalité est développé dans le dernier chapitre. / The topics presented in this thesis are related to new optimization techniques for solving some challenging problems resulting from finance. They are large-scale non convex optimization problems for which finding efficient solving methods is currently the topic of numerous researches. Our work is based mainly on DC (Difference of Convex functions) programming and DCA (DC Algorithm). This approach is motivated by the robustness and efficiency of DC programming and DCA approaches in comparison to the other methods. The thesis is divided into two parts and consists of seven chapters. In the first part entitled Methodology ; we present theoretical tools and algorithms that we are going to use in the thesis. The first chapter is about DC programming and DCA and the second focuses on branch and bound algorithms. In the second part we develop DC programming and DCA for solving some problems in finance. We begin with an introduction to the modern portfolio theory (The Chapter 3). The Chapter 4 is dedicated to the generalizations of the mean variance (MV) model of Markowitz, where we study the MV model under the buy-in threshold constraints, threshold constraints, and cardinality constraints. The Chapter 5 is devoted to the portfolio selection problem under downside risk measure and cardinality constraints. The Chapter 6 deals with the portfolio optimization under step increasing transaction costs functions. Finally, the robust investment strategies with discrete asset choice constraints are developed in the last chapter.

Les infrastructures civiles sont généralement soumises à des facteurs externes pouvant agir sur leur durée de vie. Pour les ponts en béton armé, l’environnement agressif induit une pénétration des ions, comme les chlorures, dans le béton poreux entrainant la corrosion des armatures, qui est une cause principale de détérioration pour ce type de structures. Les effets du temps sont aussi à prendre en considération, ceux-ci se manifestent par le fluage et le retrait du béton, suite auxquels la performance de ces ouvrages est fortement influencée. Cependant dans ce type de problème, le caractère probabiliste est souvent dominant. Cela ne se limite pas au trafic routier qui génère des contraintes non-contrôlées dans les sections portantes mais concerne aussi beaucoup de variables impliquées dans le calcul. La théorie de fiabilité a toujours constitué le moyen le plus efficace pour traiter ce type de problèmes, vu qu’elle puisse fournir une idée sur la durée de vie sous forme d’une probabilité de défaillance ou d’un indice de fiabilité. Ce travail comporte quatre axes principaux. Une famille de 21 ponts en béton armé servira pour l’application. Concernant le chargement du trafic, il est simulé en se basant sur des données de pesage en marche provenant d’autoroutes en Europe. La théorie de fiabilité est ensuite utilisée pour le calcul des indices de fiabilité avec le temps. Les effets de corrosion, du fluage et du retrait en plus du chargement réaliste de trafic sont introduits dans le calcul. Enfin, une approche basée sur l’optimisation génétique est proposée afin d’actualiser les lois d’évolution de la rigidité en se basant sur des données simulées de la déflexion à long terme. / Civil infrastructures are generally subjected to external factors that can affect their lifetime. In case of reinforced concrete bridges, the aggressive environment induces, for example, the penetration of ions such as chloride, into the porous concrete leading to the corrosion of reinforcement bars. This constitutes the main cause of deterioration for this kind of structure. Time effects are also to be taken into account, for example creep and shrinkage that strongly influence the performance of the structure. However, in this type of problems, the probabilistic nature is often dominant. This is not limited to the traffic loading which generates uncontrolled stresses, but also concerns most of the variables involved in the calculation. Reliability theory has always been the most appropriate way to deal with this kind of problems, since it can provide an idea about the structure lifetime in the form of failure probability or reliability index. This work has four main axes. A set of 21 reinforced concrete bridges will be used for the application. Regarding the traffic loading applied on the bridges, it is simulated according to weigh-in-motion data recorded in European motorways. Subsequently, the reliability theory is used to calculate the time-dependent reliability indices for the bridge set. The effects of corrosion, shrinkage and creep as well as the realistic traffic loading are introduced in the calculation. Finally, a new approach based on genetic optimization is proposed to update the evolution law of the global rigidity based on simulated data for long term deflection.

Ph. D. (Mechanical Engineering), Faculty of Engineering, University of the Witwatersrand, 1986