Computer models of the geometry of the real world have a tendency to assume that the shapes and positions of objects can be described exactly. However, real surfaces are subject to irregularities such as bumps and undulations and so do not have perfect, mathematically definable forms. Engineers recognise this fact and so assign tolerance specifications to their designs. This thesis develops a representation of geometric tolerance and uncertainty in assemblies of rigid parts. Geometric tolerances are defined by tolerance zones which are regions in which the real surface must lie. Parts in an assembly can slop about and so their positions are uncertain. Toleranced parts and assemblies of toleranced parts are represented by networks of tolerance zones and datums. Each arc in the network represents a relationship implied by the tolerance specification or by a contact between the parts. It is shown how all geometric constraints can be converted to an algebraic form. Useful results can be obtained from the network of tolerance zones and datums. For example it is possible to determine whether the parts of an assembly can be guaranteed to fit together. It is also possible to determine the maximum slop that could occur in the assembly assuming that the parts satisfy the tolerance specification. Two applications of this work are (1) tolerance checking during design and (2) analysis of uncertainty build-up in a robot assembly plan. I n the former, a designer could check a proposed tolerance specification to make sure that certain design requirements are satisfied. In the latter, knowledge of manufacturing tolerances of parts being manipulated can be used to determine the constraints on the positions of the parts when they are in contact with other parts.

Eyes allow us to see and gather information about the environment. Eyes mainly act as an input organ as they collect light, but they also can be considered an output organ as they indicate the subject's gaze direction. Using the orientation of the head and the position of the eyes, it is possible to estimate the gaze path of an individual. Gaze estimation is a fast growing technology that track a person's eyes and head movements to "pin point" where the subject is looking at on a computer screen. The gaze direction is described as a person's line of sight. The gaze point, also known as the focus point, is defined as the intersection of the line of sight with the screen. Gaze tracking has an infinite number of applications such as monitoring driver alertness or helping track a person's eyes with a psychological disorder that cannot communicate his/her issues. Gaze tracking is also used as a human-machine interface for disabled people that have lost total control of their limbs. Another application of gaze estimation is marketing. Companies use the information given by the gaze estimation system from their customers to design their advertisements and products. / Electrical and Computer Engineering

A fim de se compreender como varia a diversidade de pteridófitas em função do aumento da elevação do terreno e quais os potenciais mecanismos responsáveis pelas mudanças na riqueza e na abundância de espécies ao longo do gradiente de altitude, foram estudadas as vertentes leste-nordeste de três montanhas do complexo costeiro da Serra do Mar, no Estado do Paraná Serra da Graciosa, Pico do Marumbi e Serra da Prata. As amostragens foram conduzidas em 10 parcelas de 10m x 60m, ao longo do gradiente florestal altitudinal de cada montanha. Os sítios de amostragem foram distribuídos em intervalos aproximados de 200 m em elevação, desde localidades próximas à linha de costa (áreas de Restinga arbórea e de Floresta Ombrófila Densa de Terras Baixas, entre 0-10 m de altitude) até os pontos mais altos das serras de (1.500 m.s.n.m., aproximadamente). Considerando todos os sítios, foram registradas 166 espécies, distribuídas em 61 gêneros e 21 famílias. Enquanto Hymenophyllaceae, Lycopodiaceae e as gramitidóides são observadas em altitudes mais elevadas, Polypodiaceae, Cyatheaceae, Thelypteridaceae, Lomariopsidaceae e Schizaeceae tendem a ocorrer em localidades mais baixas. Os resultados indicaram que existe um forte efeito da altitude sobre a determinação da riqueza de espécies, tanto em escala local (cada montanha, individualmente) quanto em escala regional (conjunto das três montanhas): a riqueza interpolada e a observada variaram segundo uma curva em forma de sino, ao longo dos gradientes, atingindo um pico a 800-1.000 m.s.n.m.. Análises de regressão múltipla evidenciaram que os principais fatores abióticos capazes de explicar o padrão de riqueza encontrado foram, em ordem decrescente, as restrições geométricas verificadas nos extremos do gradiente (modelo nulo baseado no efeito do domínio central MDE), a estrutura da floresta e a constituição físico-química do solo, para =0,05. Essas três variáveis, juntas, foram capazes de explicar 46,7% a 95,4% da variação da riqueza de espécies, dependendo da escala em questão. A riqueza interpolada foi mais bem amplamente explicada pelo MDE, enquanto que a riqueza observada foi explicada, primordialmente, pelos solos e pela estrutura florestal (valores resumidos segundo os primeiros eixos de análises não-métricas de escalas multidimensionais NMDS). A abundância, por sua vez, variou apenas no gradiente de altitude da Serra da Prata, apresentando relações positivas com a complexidade estrutural da floresta. Conforme vem sendo discutido na literatura para diversos grupos biológicos, os MDE mostraram-se os principais fatores determinantes da riqueza de espécies, atribuindo um forte peso à estocasticidade na explicação de padrões de distribuição das espécies. / In order to better understand how diversity of pteridophytes varies in function of the terrain elevation and what are the potential mechanisms driving species richness and abundance changes, the eastern-northeastern slopes of three mountains at Serra do Mar, State of Paraná, Brazil Serra da Graciosa, Marumbi Peak and Serra da Prata were studied. The surveys were done in 10 plots of 10m x 60m along forested altitudinal gradient at each mountain. Sites were distributed on 200 m-elevation intervals, from near sea level (forests on sandbanks Restinga and Lowland Rain Forest, between 0-10 m-elevation) up to the tops of mountains (1,500 m a.s.l., approximately). Considering all sites combined, we found 166 species of pteridophytes from 61 genera and 21 families. While Hymenophyllaceae, Lycopodiaceae, and grammitids are mainly observed at high elevations, Polypodiaceae, Cyatheaceae, Thelypteridaceae, Lomariopsidaceae, and Schizaceae tend to occur at lower places of the mountains. Results showed a strong altitudinal effect over the pteridophyte species richness for both local and regional scales (the three mountains separately or treated as a set): both interpolated and observed species richness had described a hump-shaped pattern along all gradients, peaking at 800-1,000 m a.s.l. Multiple regression analysis provided evidences that the main factors able to explain richness pattern were, in decreasing order, the geometric constraints noticed in the ends of the gradient (Mid-Domain Effect - MDE), the forest structure, and the physiochemical constitution of the soil, for =0.05. These three variables together explained 46.7% to 95.4% of species richness variation, depending on the scale. Interpolated richness was better explained by MDE, while the observed richness was firstly explained by soils and forest structure (summarized by the first dimensions of the non-metric multidimensional scaling analysis NMDS). Moreover, the abundance varied only in the altitudinal gradient at Serra da Prata, where a positive relationship to the structural complexity of the forest was remarked. According to the present results and to data found in the current literature for many taxonomic groups, MDE has been the most important factor determining the species richness. Thus, sthocasticity can get an original play in species distribution patterns.

A fim de se compreender como varia a diversidade de pteridófitas em função do aumento da elevação do terreno e quais os potenciais mecanismos responsáveis pelas mudanças na riqueza e na abundância de espécies ao longo do gradiente de altitude, foram estudadas as vertentes leste-nordeste de três montanhas do complexo costeiro da Serra do Mar, no Estado do Paraná Serra da Graciosa, Pico do Marumbi e Serra da Prata. As amostragens foram conduzidas em 10 parcelas de 10m x 60m, ao longo do gradiente florestal altitudinal de cada montanha. Os sítios de amostragem foram distribuídos em intervalos aproximados de 200 m em elevação, desde localidades próximas à linha de costa (áreas de Restinga arbórea e de Floresta Ombrófila Densa de Terras Baixas, entre 0-10 m de altitude) até os pontos mais altos das serras de (1.500 m.s.n.m., aproximadamente). Considerando todos os sítios, foram registradas 166 espécies, distribuídas em 61 gêneros e 21 famílias. Enquanto Hymenophyllaceae, Lycopodiaceae e as gramitidóides são observadas em altitudes mais elevadas, Polypodiaceae, Cyatheaceae, Thelypteridaceae, Lomariopsidaceae e Schizaeceae tendem a ocorrer em localidades mais baixas. Os resultados indicaram que existe um forte efeito da altitude sobre a determinação da riqueza de espécies, tanto em escala local (cada montanha, individualmente) quanto em escala regional (conjunto das três montanhas): a riqueza interpolada e a observada variaram segundo uma curva em forma de sino, ao longo dos gradientes, atingindo um pico a 800-1.000 m.s.n.m.. Análises de regressão múltipla evidenciaram que os principais fatores abióticos capazes de explicar o padrão de riqueza encontrado foram, em ordem decrescente, as restrições geométricas verificadas nos extremos do gradiente (modelo nulo baseado no efeito do domínio central MDE), a estrutura da floresta e a constituição físico-química do solo, para =0,05. Essas três variáveis, juntas, foram capazes de explicar 46,7% a 95,4% da variação da riqueza de espécies, dependendo da escala em questão. A riqueza interpolada foi mais bem amplamente explicada pelo MDE, enquanto que a riqueza observada foi explicada, primordialmente, pelos solos e pela estrutura florestal (valores resumidos segundo os primeiros eixos de análises não-métricas de escalas multidimensionais NMDS). A abundância, por sua vez, variou apenas no gradiente de altitude da Serra da Prata, apresentando relações positivas com a complexidade estrutural da floresta. Conforme vem sendo discutido na literatura para diversos grupos biológicos, os MDE mostraram-se os principais fatores determinantes da riqueza de espécies, atribuindo um forte peso à estocasticidade na explicação de padrões de distribuição das espécies. / In order to better understand how diversity of pteridophytes varies in function of the terrain elevation and what are the potential mechanisms driving species richness and abundance changes, the eastern-northeastern slopes of three mountains at Serra do Mar, State of Paraná, Brazil Serra da Graciosa, Marumbi Peak and Serra da Prata were studied. The surveys were done in 10 plots of 10m x 60m along forested altitudinal gradient at each mountain. Sites were distributed on 200 m-elevation intervals, from near sea level (forests on sandbanks Restinga and Lowland Rain Forest, between 0-10 m-elevation) up to the tops of mountains (1,500 m a.s.l., approximately). Considering all sites combined, we found 166 species of pteridophytes from 61 genera and 21 families. While Hymenophyllaceae, Lycopodiaceae, and grammitids are mainly observed at high elevations, Polypodiaceae, Cyatheaceae, Thelypteridaceae, Lomariopsidaceae, and Schizaceae tend to occur at lower places of the mountains. Results showed a strong altitudinal effect over the pteridophyte species richness for both local and regional scales (the three mountains separately or treated as a set): both interpolated and observed species richness had described a hump-shaped pattern along all gradients, peaking at 800-1,000 m a.s.l. Multiple regression analysis provided evidences that the main factors able to explain richness pattern were, in decreasing order, the geometric constraints noticed in the ends of the gradient (Mid-Domain Effect - MDE), the forest structure, and the physiochemical constitution of the soil, for =0.05. These three variables together explained 46.7% to 95.4% of species richness variation, depending on the scale. Interpolated richness was better explained by MDE, while the observed richness was firstly explained by soils and forest structure (summarized by the first dimensions of the non-metric multidimensional scaling analysis NMDS). Moreover, the abundance varied only in the altitudinal gradient at Serra da Prata, where a positive relationship to the structural complexity of the forest was remarked. According to the present results and to data found in the current literature for many taxonomic groups, MDE has been the most important factor determining the species richness. Thus, sthocasticity can get an original play in species distribution patterns.

Pour les véhicules intelligents autonomes ou semi-autonomes, la perception constitue la première tâche fondamentale à accomplir avant la décision et l’action. Grâce à l’analyse des données vidéo, Lidar et radar, elle fournit une représentation spécifique de l’environnement et de son état, à travers l’extraction de propriétés clés issues des données des capteurs. Comparé à d’autres modalités de perception telles que le GPS, les capteurs inertiels ou les capteurs de distance (Lidar, radar, ultrasons), les caméras offrent la plus grande quantité d’informations. Grâce à leur polyvalence, les caméras permettent aux systèmes intelligents d’extraire à la fois des informations contextuelles de haut niveau et de reconstruire des informations géométriques de la scène observée et ce, à haute vitesse et à faible coût. De plus, la technologie de détection passive des caméras permet une faible consommation d’énergie et facilite leur miniaturisation. L’utilisation des caméras n’est toutefois pas triviale et pose un certain nombre de questions théoriques liées à la façon dont ce capteur perçoit son environnement. Dans cette thèse, nous proposons un système de détection d’objets mobiles basé seule- ment sur l’analyse d’images. En effet, dans les environnements observés par un véhicule intelligent, les objets en mouvement représentent des obstacles avec un risque de collision élevé, et ils doivent être détectés de manière fiable et robuste. Nous abordons le problème de la détection d’objets mobiles à partir de l’extraction du contexte local reposant sur une segmentation de la route. Après transformation de l’image couleur en une image invariante à l’illumination, les ombres peuvent alors être supprimées réduisant ainsi leur influence négative sur la détection d’obstacles. Ainsi, à partir d’une sélection automatique de pixels appartenant à la route, une région d’intérêt où les objets en mouvement peuvent apparaître avec un risque de collision élevé, est extraite. Dans cette zone, les pixels appartenant à des objets mobiles sont ensuite identifiés à l’aide d’une approche plan+parallaxe. À cette fin, les pixels potentiellement mobiles et liés à l’effet de parallaxe sont détectés par une méthode de soustraction du fond de l’image; puis trois contraintes géométriques différentes: la contrainte épipolaire, la contrainte de cohérence structurelle et le tenseur trifocal, sont appliquées à ces pixels pour filtrer ceux issus de l’effet de parallaxe. Des équations de vraisemblance sont aussi proposées afin de combiner les différents contraintes d’une manière complémentaire et efficace. Lorsque la stéréovision est disponible, la segmentation de la route et la détection d’obstacles peuvent être affinées en utilisant une segmentation spécifique de la carte de disparité. De plus, dans ce cas, un algorithme de suivi robuste combinant les informations de l’image et la profondeur des pixels a été proposé. Ainsi, si l’une des deux caméras ne fonctionne plus, le système peut donc revenir dans un mode de fonctionnement monoculaire ce qui constitue une propriété importante pour la fiabilité et l’intégrité du système de perception. Les différents algorithmes proposés ont été testés sur des bases de données d’images publiques en réalisant une évaluation par rapport aux approches de l’état de l’art et en se comparant à des données de vérité terrain. Les résultats obtenus sont prometteurs et montrent que les méthodes proposées sont efficaces et robustes pour différents scénarios routiers et les détections s’avèrent fiables notamment dans des situations ambiguës. / For autonomous or semi-autonomous intelligent vehicles, perception constitutes the first fundamental task to be performed before decision and action/control. Through the analysis of video, Lidar and radar data, it provides a specific representation of the environment and of its state, by extracting key properties from sensor data with time integration of sensor information. Compared to other perception modalities such as GPS, inertial or range sensors (Lidar, radar, ultrasonic), the cameras offer the greatest amount of information. Thanks to their versatility, cameras allow intelligent systems to achieve both high-level contextual and low-level geometrical information about the observed scene, and this is at high speed and low cost. Furthermore, the passive sensing technology of cameras enables low energy consumption and facilitates small size system integration. The use of cameras is however, not trivial and poses a number of theoretical issues related to how this sensor perceives its environmen. In this thesis, we propose a vision-only system for moving object detection. Indeed,within natural and constrained environments observed by an intelligent vehicle, moving objects represent high risk collision obstacles, and have to be handled robustly. We approach the problem of detecting moving objects by first extracting the local contextusing a color-based road segmentation. After transforming the color image into illuminant invariant image, shadows as well as their negative influence on the detection process can be removed. Hence, according to the feature automatically selected onthe road, a region of interest (ROI), where the moving objects can appear with a high collision risk, is extracted. Within this area, the moving pixels are then identified usin ga plane+parallax approach. To this end, the potential moving and parallax pixels a redetected using a background subtraction method; then three different geometrical constraints : the epipolar constraint, the structural consistency constraint and the trifocaltensor are applied to such potential pixels to filter out parallax ones. Likelihood equations are also introduced to combine the constraints in a complementary and effectiveway. When stereo vision is available, the road segmentation and on-road obstacles detection can be refined by means of the disparity map with geometrical cues. Moreover, in this case, a robust tracking algorithm combining image and depth information has been proposed. If one of the two cameras fails, the system can therefore come back to a monocular operation mode, which is an important feature for perception system reliability and integrity. The different proposed algorithms have been tested on public images data set with anevaluation against state-of-the-art approaches and ground-truth data. The obtained results are promising and show that the proposed methods are effective and robust on the different traffic scenarios and can achieve reliable detections in ambiguous situations.

Suivant le domaine où on les sollicite, les solutions d’un système de contraintes géométriques (SCG) peuvent être : – formelles et exactes : elles prennent par exemple la forme d’un plan de construction produisant toutes les solutions, obtenu en appliquant des règles dérivées de lemmes de géométrie. Beaucoup de SCG, surtout en 3D, résistent à cette approche ; – numériques et approchées : elles sont les solutions d’un système d’équations construit à partir des contraintes et trouvées grâce à des méthodes numériques efficaces quand elles ne recherchent qu’une solution. De par la nature des problèmes traités, chercher toutes les solutions conduit à une complexité exponentielle. Les méthodes par continuation, ou homotopie, permettent d’obtenir toutes les solutions d’un système d’équations polynomiales. Leur application à des SCG est coûteuse et difficilement sujette aux raisonnements permis par l’origine géométrique du problème car elles opèrent hors de l’espace des figures géométriques. Notre travail a pour objet la spécialisation d’une méthode par continuation à des SCG. La géométrie simplifie et justifie sa mise en œuvre dans l’espace des figures, ou des raisonnements géométriques sont possibles. On aborde également les cas ou l’ensemble de solutions d’un problème contient des éléments isolés et des continuums. Des solutions proches d’une esquisse fournie par un utilisateur sont d’abord trouvées. La recherche d’autres solutions, malgré sa complexité exponentielle, est rendue envisageable par une approche itérative. Une nouvelle méthode de décomposition est proposée pour maîtriser le coût de la résolution. / Depending on the required application field, the solutions of a geometric constraints system (GCS) are either : – symbolic and exact such as construction plans, providing all the solutions, obtained by applying geometric rules. Many problems, mostly in a 3D context, resist to this approach ; – or numerical and approximated : they are the solutions of a system of equations built from the constraints, provided by generical numerical methods that are efficient when only one solution is sought. However, searching all the solutions leads to an exponential computation cost, due to the nature of problems. Continuation methods, also called homotopic methods, find all the solutions of a polynomial system. Using them to solve systems of equations associated to systems of constraints is nevertheless costly. Moreover, combining them with geometric reasoning is a challenge, because they act in a projective complex space and not in the realizations space. The aim of this work is to specialize a continuation method to GCS. Geometry is exploited to simplify and justify its adaptation in the space of realizations, so allowing geometric reasoning. Cases where the connected components of the solution space of a problem have heterogeneous dimensions are addressed. The method discussed here provides in a first step solutions that are similar to a sketch drawn by the user. Then a procedure is proposed to search new solutions. Its iterative nature seems to make the exponential complexity of this task bearable. A new decomposition method is proposed, that restrains the resolution cost.

En chirurgie mini-invasive guidée par l’image, une planification préopératoire précise des trajectoires des outils chirurgicaux est un facteur clé pour une intervention réussie. Cependant, une planification efficace est une tâche difficile, qui peut être considérablement améliorée en considérant différents facteurs contributifs tels que les déformations biomécaniques intra-opératoires, ou en introduisant de nouvelles techniques d'optimisation. Dans ce travail, nous nous concentrons sur deux aspects. Le premier aspect porte sur l'intégration de la déformation intra-opératoire dans le processus de planification de trajectoire. Nos méthodes combinent des techniques d'optimisation géométrique à base de simulations biomécaniques. Elles sont caractérisées par un certain niveau de généralité, et ont été expérimentées sur deux types d’interventions chirurgicales: les procédures percutanées pour l'ablation de tumeurs hépatiques, et la stimulation cérébrale profonde en neurochirurgie. Deuxièmement, nous étudions, mettons en œuvre, et comparons plusieurs approches d'optimisation en utilisant des méthodes qualitatives et quantitatives, et nous présentons une méthode efficace d'optimisation évolutionnaire multicritères à base de Pareto qui permet de trouver des solutions optimales qui ne sont pas accessibles par les méthodes existantes. / In image-guided minimally invasive surgery, a precise preoperative planning of the surgical tools trajectory is a key factor to a successful intervention. However, an efficient planning is a challenging task, which can be significantly improved when considering different contributing factors such as biomechanical intra-operative deformations, or novel optimization techniques. In this work, we focus on two aspects. The first aspect addresses integrating intra-operative deformation to the path planning process. Our methods combine geometric-based optimization techniques with physics-based simulations. They are characterized with a certain level of generality, and are experimented on two different surgical procedures: percutaneous procedures for hepatic tumor ablation, and in neurosurgery for Deep Brain Stimulation (DBS). Secondly, we investigate, implement, and compare many optimization approaches using qualitative and quantitative methods, and present an efficient evolutionary Pareto-based multi-criteria optimization method which can find optimal solutions that are not reachable via the current state of the art methods.

Cette thèse est consacrée à l'optimisation de la topologie et de la forme de systèmesmultiphysiques motivés par des applications de l'industrie aéronautique. Nouscalculons les dérivées de forme de fonctions de coût arbitraires pour un modèlefluide, thermique et mécanique faiblement couplé. Nous développons ensuite unalgorithme de type gradient adapté à la résolution de problèmes d'optimisation deformes sous contraintes qui ne requiert par de réglage de paramètres nonphysiques. Nous introduisons ensuite une méthode variationnelle qui permet decalculer des intégrales le long de rayons sur un maillage par la résolution d'unproblème variationnel qui ne requiert pas la détermination explicite de ces lignessur la discrétisation spatiale. Cette méthode nous a ainsi permis d'imposer unecontrainte de non-mélange de phases pour une application à l'optimisationd'échangeurs de chaleur bi-tubes. Tous ces ingrédients ont été employés pour traiterune variété de cas tests d'optimisation de formes pour des systèmes multi-physiques2-d ou 3-d. Nous avons considéré des problèmes à une seule, deux ou bien troisphysiques couplées en 2-d, et des problèmes de tailles relativement élevées en 3-dpour la mécanique, la conduction thermique, l'optimisation de profils aérodynamiques,et de la forme de systèmes en interaction fluide-structure. Un dernier chapitred'ouverture est consacré à l'étude de modèles homogénéisées d'ordres élevés pour lessystèmes elliptiques perforés. Ces équations d'ordres élevés englobent les troisrégimes homogénéisés classiques associés à divers rapports d'échelles pour la tailledes obstacles. Elles pourraient permettre, dans de futurs travaux, de développer denouvelles méthodes d'optimisation pour les systèmes fluides caractérisés par desmotifs multi-échelles, ainsi que couramment rencontré dans la conception deséchangeurs thermiques industriels. / This work is devoted to shape and topology optimization of multiphysics systemsmotivated by aeronautic industrial applications. Shape derivatives of arbitraryobjective functionals are computed for a weakly coupled thermal fluid-structuremodel. A novel gradient flow type algorithm is then developed for solving genericconstrained shape optimization problems without the need for tuning non-physicalmetaparameters. Motivated by the need for enforcing non-mixing constraints in thedesign of liquid-liquid heat exchangers, a variational method is developed in orderto simplify the numerical evaluation of geometric constraints: it allows to computeline integrals on a mesh by solving a variational problem without requiring theexplicit knowledge of these lines on the spatial discretization. All theseingredients allowed us to implement a variety of 2-d and 3-d multiphysics shapeoptimization test cases: from single, double or three physics problems in 2-d, tomoderately large-scale 3-d test cases for structural design, thermal conduction,aerodynamic design and a fluid-structure interacting system. A final opening chapterderives high order homogenized equations for perforated elliptic systems. These highorder equations encompass the three classical regimes of homogenized modelsassociated with different obstacle's size scalings. They could allow, in futureworks, to develop new topology optimization methods for fluid systems characterizedby multi-scale patterns as commonly encountered in industrial heat exchanger designs.

Estimating depth and detection of object instances in 3D space is fundamental in autonomous navigation, localization, and mapping, robotic object manipulation, and augmented reality. RGB-D images and LiDAR point clouds are the most illustrative formats of depth information. However, depth sensors offer many shortcomings, such as low effective spatial resolutions and capturing of a scene from a single perspective. The thesis focuses on reproducing denser and comprehensive 3D scene structure for given monocular RGB images using depth and 3D object detection. The first contribution of this thesis is the pipeline for the depth estimation based on an unsupervised learning framework. This thesis proposes two architectures to analyze structure from motion and 3D geometric constraint methods. The proposed architectures trained and evaluated using only RGB images and no ground truth depth data. The architecture proposed in this thesis achieved better results than the state-of-the-art methods. The second contribution of this thesis is the application of the estimated depth map, which includes two algorithms: point cloud generation and collision avoidance. The predicted depth map and RGB image are used to generate the point cloud data using the proposed point cloud algorithm. The collision avoidance algorithm predicts the possibility of collision and provides the collision warning message based on decoding the color in the estimated depth map. This algorithm design is adaptable to different color map with slight changes and perceives collision information in the sequence of frames. Our third contribution is a two-stage pipeline to detect the 3D objects from a monocular image. The first stage pipeline used to detect the 2D objects and crop the patch of the image and the same provided as the input to the second stage. In the second stage, the 3D regression network train to estimate the 3D bounding boxes to the target objects. There are two architectures proposed for this 3D regression network model. This approach achieves better average precision than state-of-theart for truncation of 15% or fully visible objects and lowers but comparable results for truncation more than 30% or partly/fully occluded objects.

The aim of this thesis is to present new results concerning duality in scalar optimization. We show how the theory can be applied to optimization problems arising in the theory of risk measures, portfolio optimization and machine learning. First we give some notations and preliminaries we need within the thesis. After that we recall how the well-known Lagrange dual problem can be derived by using the general perturbation theory and give some generalized interior point regularity conditions used in the literature. Using these facts we consider some special scalar optimization problems having a composed objective function and geometric (and cone) constraints. We derive their duals, give strong duality results and optimality condition using some regularity conditions. Thus we complete and/or extend some results in the literature especially by using the mentioned regularity conditions, which are weaker than the classical ones. We further consider a scalar optimization problem having single chance constraints and a convex objective function. We also derive its dual, give a strong duality result and further consider a special case of this problem. Thus we show how the conjugate duality theory can be used for stochastic programming problems and extend some results given in the literature. In the third chapter of this thesis we consider convex risk and deviation measures. We present some more general measures than the ones given in the literature and derive formulas for their conjugate functions. Using these we calculate some dual representation formulas for the risk and deviation measures and correct some formulas in the literature. Finally we proof some subdifferential formulas for measures and risk functions by using the facts above. The generalized deviation measures we introduced in the previous chapter can be used to formulate some portfolio optimization problems we consider in the fourth chapter. Their duals, strong duality results and optimality conditions are derived by using the general theory and the conjugate functions, respectively, given in the second and third chapter. Analogous calculations are done for a portfolio optimization problem having single chance constraints using the general theory given in the second chapter. Thus we give an application of the duality theory in the well-developed field of portfolio optimization. We close this thesis by considering a general Support Vector Machines problem and derive its dual using the conjugate duality theory. We give a strong duality result and necessary as well as sufficient optimality conditions. By considering different cost functions we get problems for Support Vector Regression and Support Vector Classification. We extend the results given in the literature by dropping the assumption of invertibility of the kernel matrix. We use a cost function that generalizes the well-known Vapnik's ε-insensitive loss and consider the optimization problems that arise by using this. We show how the general theory can be applied for a real data set, especially we predict the concrete compressive strength by using a special Support Vector Regression problem.