Neste trabalho apresenta-se o desenvolvimento e avaliação de um sistema de reconstrução 3D por luz estruturada. O sistema denominado de Scan3DSL é baseado em uma câmara digital de pequeno formato e um projetor de padrões. O modelo matemático para a reconstrução 3D é baseado na equação paramétrica da reta formada pelo raio de luz projetado combinado com as equações de colinearidade. Uma estratégia de codificação de padrões foi desenvolvida para permitir o reconhecimento dos padrões projetados em um processo automático. Uma metodologia de calibração permite a determinação dos vetores diretores de cada padrão projetado e as coordenadas do centro de perspectiva do projetor de padrões. O processo de calibração é realizado com a aquisição de múltiplas imagens em um plano de calibração com tomadas em diferentes orientações e posições. Um conjunto de algoritmos de processamento de imagens foi implementado para propiciar a localização precisa dos padrões e de algumas feições, como o centro de massa e quinas. Para avaliar a precisão e as potencialidades da metodologia, um protótipo foi construído, integrando uma única câmara e um projetor de padrões. Experimentos mostram que um modelo de superfície pode ser obtido em um tempo total de processamento inferior a 10 segundos, e com erro absoluto em profundidade em torno de 0,2 mm. Evidencia-se com isso a potencialidade de uso em várias aplicações. / The purpose of this work is to present a structured light system developed. The system named Scan3DSL is based on off-the-shelf digital cameras and a projector of patterns. The mathematical model for 3D reconstruction is based on the parametric equation of the projected straight line combined with the collinearity equations. A pattern codification strategy was developed to allow fully automatic pattern recognition. A calibration methodology enables the determination of the direction vector of each pattern and the coordinates of the perspective centre of the pattern projector. The calibration processes are carried out with the acquisition of several images of a flat surface from different distances and orientations. Several processes were combined to provide a reliable solution for patterns location. In order to assess the accuracy and the potential of the methodology, a prototype was built integrating in a single mount a projector of patterns and a digital camera. The experiments using reconstructed surfaces with real data indicated a relative accuracy of 0.2 mm in depth could be achieved, in a processing time less than 10 seconds.

Le sujet de cette thèse est l'étude d'idéaux monomiaux de l'anneau de polynômes S qui ont une résolution linéaire. D'après un résultat remarquable de Bayer et Stilman et en utilisant la polarisation, la classification des idéaux monomiaux ayant une résolution linéaire est équivalente à la classification des idéaux monomiaux libres de carrés ayant une résolution linéaire. Pour cette raison dans cette thèse nous considérons seulement le cas d'idéaux monomiaux libres de carrés. De plus, le théorème de Eagon-Reiner établit une dualité entre les idéaux monomiaux libres de carrés ayant une résolution linéaire et les idéaux monomiaux libres de carrés Cohen-Macaulay, ce qui montre que le problème de classification des idéaux monomiaux libres de carrés ayant une résolution linéaire est très difficile. Nous rappelons que les idéaux monomiaux libres de carrés sont en correspondance biunivoque avec les complexes simpliciaux d'une part, et d'autre part avec les clutters. Ces correspondances nous motivent pour utiliser les propriétés combinatoires des complexes simpliciaux et des clutters pour obtenir des résultats algébriques. La classification des idéaux monomiaux libres de carrés ayant une résolution linéaire engendrés en degré 2 a été faite par Froberg en 1990. Froberg a observé que l'idéal des circuits d'un graphe G a une résolution 2-linéaire si et seulement si G est un graphe de cordes, i.e. il n'a pas de cycles minimaux de longueur plus grande que 4. Dans [Em, ThVt, VtV, W] les auteurs ont partiellement généralisé les résultats de Froberg à des idéaux engendrés en degré >2. Ils ont introduit plusieurs définitions de clutters de cordes et démontré que les idéaux de circuits correspondant ont une résolution linéaire. Nous pouvons voir les cycles du point de vue topologique, comme la triangulation d'une courbe fermée, dans cette thèse nous utiliserons cette idée pour étudier des clutters associés à des triangulation de pseudo-manifolds en vue d'obtenir une généralisation partielle des résultats de Froberg à des idéaux engendrés en degré >2. Nous comparons notre travail à ceux de [Em, ThVt, VtV, W]. Nous présentons nos résultats dans le chapitres 4 et 5. / In this thesis, we study square-free monomial ideals of the polynomial ring S which have a linear resolution. By remarkable result of Bayer and Stilman [BS] and the technique of polarization, classification of ideals with linear resolution is equivalent to classification of square-free monomial ideals with linear resolution. For this reason, we consider only square-free monomial ideals in S. However, classification of square-free monomial ideals with linear resolution seems to be so difficult because by Eagon-Reiner Theorem [ER], this is equivalent to classification of Cohen-Macaulay ideals. It is worth to note that, square-free monomial ideals in S are in one-to-one correspondence to Stanley-Reisener ideals of simplicial complexes on one hand and the circuit ideal of clutters from another hand. This correspondence motivated mathematicians to use the combinatorial and geometrical properties of these objects in order to get the desired algebraic results. Classification of square-free monomial ideals with 2-linear resolution, was successfully done by Froberg [Fr] in 1990. Froberg observed that the circuit ideal of a graph G has a 2-linear resolution if and only if G is chordal, that is, G does not have an induced cycle of length > 3. In [Em, ThVt, VtV, W] the authors have partially generalized the Fr¨oberg's theorem for degree greater than 2. They have introduced several definitions of chordal clutters and proved that, their corresponding circuit ideals have linear resolutions. Viewing cycles as geometrical objects (triangulation of closed curves), in this thesis we try to generalize the concept of cycles to triangulation of pseudo-manifolds and get a partial generalization of Froberg's theorem for higher dimensional hypergraphs. All the results in Chapters 4 and 5 and some results in Chapter 3 are devoted to be the original results.

Neste trabalho apresenta-se o desenvolvimento e avaliação de um sistema de reconstrução 3D por luz estruturada. O sistema denominado de Scan3DSL é baseado em uma câmara digital de pequeno formato e um projetor de padrões. O modelo matemático para a reconstrução 3D é baseado na equação paramétrica da reta formada pelo raio de luz projetado combinado com as equações de colinearidade. Uma estratégia de codificação de padrões foi desenvolvida para permitir o reconhecimento dos padrões projetados em um processo automático. Uma metodologia de calibração permite a determinação dos vetores diretores de cada padrão projetado e as coordenadas do centro de perspectiva do projetor de padrões. O processo de calibração é realizado com a aquisição de múltiplas imagens em um plano de calibração com tomadas em diferentes orientações e posições. Um conjunto de algoritmos de processamento de imagens foi implementado para propiciar a localização precisa dos padrões e de algumas feições, como o centro de massa e quinas. Para avaliar a precisão e as potencialidades da metodologia, um protótipo foi construído, integrando uma única câmara e um projetor de padrões. Experimentos mostram que um modelo de superfície pode ser obtido em um tempo total de processamento inferior a 10 segundos, e com erro absoluto em profundidade em torno de 0,2 mm. Evidencia-se com isso a potencialidade de uso em várias aplicações. / The purpose of this work is to present a structured light system developed. The system named Scan3DSL is based on off-the-shelf digital cameras and a projector of patterns. The mathematical model for 3D reconstruction is based on the parametric equation of the projected straight line combined with the collinearity equations. A pattern codification strategy was developed to allow fully automatic pattern recognition. A calibration methodology enables the determination of the direction vector of each pattern and the coordinates of the perspective centre of the pattern projector. The calibration processes are carried out with the acquisition of several images of a flat surface from different distances and orientations. Several processes were combined to provide a reliable solution for patterns location. In order to assess the accuracy and the potential of the methodology, a prototype was built integrating in a single mount a projector of patterns and a digital camera. The experiments using reconstructed surfaces with real data indicated a relative accuracy of 0.2 mm in depth could be achieved, in a processing time less than 10 seconds.

Neste trabalho apresenta-se o desenvolvimento e avaliação de um sistema de reconstrução 3D por luz estruturada. O sistema denominado de Scan3DSL é baseado em uma câmara digital de pequeno formato e um projetor de padrões. O modelo matemático para a reconstrução 3D é baseado na equação paramétrica da reta formada pelo raio de luz projetado combinado com as equações de colinearidade. Uma estratégia de codificação de padrões foi desenvolvida para permitir o reconhecimento dos padrões projetados em um processo automático. Uma metodologia de calibração permite a determinação dos vetores diretores de cada padrão projetado e as coordenadas do centro de perspectiva do projetor de padrões. O processo de calibração é realizado com a aquisição de múltiplas imagens em um plano de calibração com tomadas em diferentes orientações e posições. Um conjunto de algoritmos de processamento de imagens foi implementado para propiciar a localização precisa dos padrões e de algumas feições, como o centro de massa e quinas. Para avaliar a precisão e as potencialidades da metodologia, um protótipo foi construído, integrando uma única câmara e um projetor de padrões. Experimentos mostram que um modelo de superfície pode ser obtido em um tempo total de processamento inferior a 10 segundos, e com erro absoluto em profundidade em torno de 0,2 mm. Evidencia-se com isso a potencialidade de uso em várias aplicações. / The purpose of this work is to present a structured light system developed. The system named Scan3DSL is based on off-the-shelf digital cameras and a projector of patterns. The mathematical model for 3D reconstruction is based on the parametric equation of the projected straight line combined with the collinearity equations. A pattern codification strategy was developed to allow fully automatic pattern recognition. A calibration methodology enables the determination of the direction vector of each pattern and the coordinates of the perspective centre of the pattern projector. The calibration processes are carried out with the acquisition of several images of a flat surface from different distances and orientations. Several processes were combined to provide a reliable solution for patterns location. In order to assess the accuracy and the potential of the methodology, a prototype was built integrating in a single mount a projector of patterns and a digital camera. The experiments using reconstructed surfaces with real data indicated a relative accuracy of 0.2 mm in depth could be achieved, in a processing time less than 10 seconds.

Le présent travail développe une approche sociocognitive de la Perspective Temporelle Future (PTF), tel que ce construit est mesuré par l’échelle ZTPI (Zimbardo Time Perspective Inventory, Zimbardo & Boyd, 1999). L’objectif de cette thèse est d’analyser la normativité de ce construit et d’explorer les dimensions liées à l’expérience du temps psychologique futur. Une démarche de triangulation a été menée dans une double perspective : produire une analyse multi-niveaux de la normativité associée à la PTF et développer une réflexion théorico-méthodologique concernant la mesure de ce construit. Une première série d’études expérimentales mobilisant l’approche sociocognitive des normes sociales (Dubois, 2003) démontre une valorisation importante de la PTF dans des contextes évaluatifs. Une seconde série d’études utilisant une méthodologie mixte (paradigmes des juges et construits socio-représentationnels) analyse les dynamiques normatives de la PTF dans des situations socialement marquées (i.e. contexte de santé). Enfin, une recherche socio-représentationnelle par entretien étudie l’expérience du temps psychologique futur en tant que forme d’expérience sociale (Jodelet, 2006). En envisageant la PTF sous différentes perspectives sociocognitives, ces travaux apportent une contribution au domaine de recherche du rapport au temps (mesure de la PTF et fonctionnements idéologiques). D’autre part, ce travail pose les bases d’une approche sociocognitive de la PTF en tant que norme sociale. / The present work develops a sociocognitive approach of Future Time Perspective (FTP), as this construct is measured by the ZTPI scale (Zimbardo Time Perspective Inventory, Zimbardo & Boyd, 1999). The aim of this thesis is the analysis of this construct’s normativity and the exploration of the dimensions related to future psychological time experience. A triangulation approach has been conducted in a double perspective: its aim is to produce a multi-level analysis of normativity associated to FTP as well as to develop a theoretical and methodological thought on this construct’s measurement. A first series of experimental studies using the sociocognitive approach to social norms (Dubois, 2003) reveals an important value of FTP in evaluative contexts. A second series of studies using mixt methodology (judge paradigms and socio-representational constructs) analyses FTP’s normative dynamics in socially relevant situations (i.e. health context). Finally, a socio-representational research with interviews focuses on future psychological time experience as a form of social experience (Jodelet, 2006). Considering FTP under several sociocognitive perspectives, this thesis contributes towards the research field on relation to time (FTP measurement and ideological logics). This work lays also the foundation of a sociocognitive approach of FTP as a social norm.

Cette thèse consiste en la conception d'un système d'acquisition et d'un algorithme de traitement d'image. Le but de ce travail est la détection de contaminants dans un contexte de contrôle qualité, particulièrement dans l'industrie pharmaceutique. Les contaminants sont des colonies de micro-organismes se développant sur membrane micro-poreuse. Nous avons choisi d'utiliser la mesure tridimensionnelle de surface pour réaliser l'acquisition des données, ce qui n'a jamais été fait pour des données micro-biologiques. Notre apport a de plus consisté à remplacer l'éclairage laser généralement utilisé par un dispositif à LED permettant de réduire le bruit dans les données. Cela permet de diminuer la durée d'incubation des tests de 14 jours à moins de 5. Concernant l'algorithme, nous avons analysé les données de hauteur en combinant une méthode de détection de données aberrantes et un séparateur à vaste marge. La difficulté de la détection réside dans la variété des signaux correspondant aux colonies, et également dans la présence d'artefacts semblables aux colonies. Nous sommes capables de détecter correctement la présence ou l'absence de contaminants dans 98% des cas. / An acquisition system and its algorithm are designed. Their purpose is contaminants detection as quality control in pharmaceutical industry. Contaminants are colonies of micro-organisms growing on micro-porous membrane. We use 3D surface measurement, which has never been done in a microbiological context. In addition, our contribution is to use an LED based lighting instead of a laser. It leads to an important noise reduction. It allows to decrease micro-organisms incubation period from 14 days in current method to 5 days or less. The height map from the system are processed with an outlier detection method combined to a support vector machine. Colonies show varying and various signals, and artifacts are present in the data. Nevertheless, we have been able to detect with success the presence or absence of contaminants with a rate of 98%.

Dans cette thèse, nous exploitons les outils de la théorie des probabilités et de la géométrie stochastique pour analyser des algorithmes opérant sur les tessellations. Ce travail est divisé entre deux thèmes principaux, le premier traite de la navigation dans une tessellation de Delaunay et dans son dual, le diagramme de Voronoï avec des implications pour les algorithmes de localisation spatiales et de routage dans les réseaux en ligne. Nous proposons deux nouveaux algorithmes de navigation dans la triangulation de Delaunay, que nous appelons Pivot Walk et Cone Walk. Pour Cone Walk, nous fournissons une analyse en moyenne détaillée avec des bornes explicites sur les propriétés de la pire marche possible effectuée par l'algorithme sur une triangulation de Delaunay aléatoire d'une région convexe bornée. C'est un progrès significatif car dans l'algorithme Cone Walk, les probabilités d'utiliser un triangle ou un autre au cours de la marche présentent des dépendances complexes, dépendances inexistantes dans d'autres marches. La deuxième partie de ce travail concerne l'étude des propriétés extrémales de tessellations aléatoires. En particulier, nous dérivons les premiers et derniers statistiques d'ordre pour les boules inscrites dans les cellules d'un arrangement de droites Poissonnien; ce résultat a des implications par exemple pour le hachage respectant la localité. Comme corollaire, nous montrons que les cellules minimisant l'aire sont des triangles. / In this thesis, we leverage the tools of probability theory and stochastic geometry to investigate the behavior of algorithms on geometric tessellations of space. This work is split between two main themes, the first of which is focused on the problem of navigating the Delaunay tessellation and its geometric dual, the Voronoi diagram. We explore the applications of this problem to point location using walking algorithms and the study of online routing in networks. We then propose and investigate two new algorithms which navigate the Delaunay triangulation, which we call Pivot Walk and Cone Walk. For Cone Walk, we provide a detailed average-case analysis, giving explicit bounds on the properties of the worst possible path taken by the algorithm on a random Delaunay triangulation in a bounded convex region. This analysis is a significant departure from similar results that have been obtained, due to the difficulty of dealing with the complex dependence structure of localized navigation algorithms on the Delaunay triangulation. The second part of this work is concerned with the study of extremal properties of random tessellations. In particular, we derive the first and last order-statistics for the inballs of the cells in a Poisson line tessellation. This result has implications for algorithms involving line tessellations, such as locality sensitive hashing. As a corollary, we show that the cells minimizing the area are triangles.

Perçu comme un système adaptatif complexe, l’espace public pourrait être examiné par le biais de la complexité. Dans cette thèse, nous discutons du cas d'un parc urbain, Horch Beyrouth, visant à mettre en valeur les apports épistémologiques et méthodologiques de l'approche de la complexité dans les études urbaines. Malgré que Horch Beyrouth représente jusqu'à 70% des espaces verts de Beyrouth, il a été en grande partie fermé au public depuis la fin de la guerre civile libanaise en 1990. Entouré de trois quartiers culturellement hétérogènes, le parc triangulaire incarne à la fois la multiplicité et l'exclusion urbaine. L’approche de la complexité offre non seulement un lexique scientifique transdisciplinaire, mais également des outils de modélisation interdisciplinaires. Pour illustrer ces outils, nous avons utilisé la triangulation systémique pour le diagnostic urbain de Horch Beyrouth. Il s’agit d’un outil qui reconnaît l’inscription des problèmes complexes dans des continuums structurels, fonctionnels et dynamiques, établissant des relations entre eux et projetant des interactions entre le système et son environnement. Nous avons également présenté l'outil de la méthodologie des systèmes souples pour une gouvernance interactive basée sur des représentations non linéaires de la réalité urbaine. Cette approche nous a fourni de nouvelles idées. Premièrement, aborder les villes, ainsi que les entités urbaines comme Horch Beyrouth, en tant que systèmes complexes, pourrait diverger notre perception des solutions linéaires fragmentées vers des processus évolutifs adaptifs. Deuxièmement, le chaos n’est pas à craindre. En fait, en se situant au bord du chaos les systèmes complexes s’adaptent et co-évoluent, ainsi la créativité se catalyse et le changement émerge. Enfin et surtout, un espace public ne doit pas être conçu, mais encouragé à émerger. Il serait donc préférable d’induire son auto-organisation que d'essayer de la contrôler. Ainsi, un changement d'attitude est nécessaire : le rôle des acteurs urbains, architectes et urbanistes, devrait se réorienter pour rechercher la dynamique sous-jacente d’un système urbain, établir ses propriétés émergentes, pour ultérieurement, déterminer et induire ses opportunités synergiques. / Perceived as a complex adaptive system, public space could be examined through the means of complexity. In this thesis, we discuss the case of an urban park, Horch Beirut, aiming to showcase the contributions of the complexity approach to urban studies, both epistemological and methodological ones. Horsh Beirut makes up to 70% of green spaces in Beirut, but has been mostly closed to the public since the end of the Lebanese civil war in 1990. Surrounded by three culturally heterogeneous neighborhoods, the triangular park embodies both urban multiplicity and exclusion. The complexity approach not only offers a transdiciplinary scientific lexicon but also interdisciplinary modeling tools. To showcase these tools, we apply Systemic Triangulation for the urban diagnosis of Horch Beirut. This tool acknowledges the inscription of complex problems in structural, functional and dynamic continuums, establishing the relationships between them, and projecting interactions between the system and its environment. We also propose the Soft Systems Methodology tool for an interactive governance based on non-linear representations of urban reality. The complexity approach has provided us some new insights. First, addressing cities, and urban entities like Horsh Beirut, as complex systems could diverge our perception of fragmented linear solutions towards adaptive evolutionary processes. Secondly, chaos is not to be feared. In fact, by being on the edge of chaos complex systems adapt and co-evolve, consequently creativity is catalyzed and change emerges. Finally, and most importantly, a public space should not be designed, but encouraged to emerge. It would be better to induce its self-organization than to try to control it. Thus, a change of attitude is necessary: the role of urban actors, architects and urban planners, should be reoriented towards seeking the underlying dynamics of an urban system, establishing its emerging properties, and subsequently, determining and inducing its synergistic opportunities.

Les artistes apprécient les images vectorielles car elles sont compactes et facilement manipulables. Cependant, beaucoup d’artistes expriment leur créativité en dessinant, en peignant ou encore en prenant des photographies. Digitaliser ces contenus produit des images rasterisées. L’objectif de cette thèse est de convertir des images rasterisées en images vectorielles qui sont facilement manipulables. Nous avons formulé le problème de vectorisation comme un problème de minimisation d’énergie que nous avons défini par deux termes. Le premier terme, plutôt classique, mesure la fidélité de l’image vectorielle générée avec l’image rasterisée d’origine. La nouveauté principale est le second terme qui mesure la simplicité de l’image vectorielle générée. Le terme de simplicité est global et contient des variables discrètes, ce qui rend sa minimisation difficile. Nous avons proposé deux algorithmes de vectorisation : un pour la vectorisation de croquis et un autre pour la vectorisation multicouches d’images couleurs. Ces deux algorithmes commencent par extraire des primitives géométriques (un squelette pour les croquis et une segmentation pour les images couleurs) qu’ils assemblent ensuite pour former l’image vectorielle. Dans la dernière partie de la thèse, nous proposons un nouvel algorithme qui est capable de vectoriser des croquis sans étapes préliminaires : on extrait et assemble les primitives simultanément. Nous montrons le potentiel de ce nouvel algorithme pour une variété de problèmes de vision par ordinateur comme l’extraction de réseaux linéiques, l’extraction d’objets et la compression d’images. / Artists appreciate vector graphics for their compactness and editability. However many artists express their creativity by sketching, painting or taking photographs. Digitizing these images produces raster graphics. The goal of this thesis is to convert raster graphics into vector graphics that are easy to edit. We cast image vectorization as an energy minimization problem. Our energy is a combination of two terms. The first term measures the fidelity of the vector graphics to the input raster graphics. This term is a standard term for image reconstruction problems. The main novelty is the second term which measures the simplicity of the vector graphics. The simplicity term is global and involves discrete unknowns which makes its minimization challenging. We propose two stochastic optimizations for this formulation: one for the line drawing vectorization problem and another one for the color image vectorization problem. These optimizations start by extracting geometric primitives (skeleton for sketches and segmentation for color images) and then assembling these primitives together to form the vector graphics. In the last chapter we propose a generic optimization method for the problem of geometric shape extraction. This new algorithm does not require any preprocessing step. We show its efficiency in a variety of vision problems including line network extraction, object contouring and image compression.

Mobile robotics has been very discussed and wide spread topic recently.   This due to the development in the computer technology that allows us to create   better and more sophisticated robots. The goal of this effort is to create robots   that will be able to autonomously move in the chosen environment. To achieve this goal,   it is necessary for the robot to create the map of its environment, where   the motion planning will occur. Nowadays, the probabilistic algorithms based   on the SLAM algorithm are considered standard in the mapping in these times.   This Phd. thesis deals with the proposal of the motion planning of the robot with   stereocamera placed on the pan-and-tilt unit. The motion planning is designed with   regard to the use of algorithms, which will look for the significant features   in the pair of the images. With the use of the triangulation the map, or a model will be created.     The benefits of this work can be divided into three parts. In the first one the way   of marking the free area, where the robot will plan its motion, is described. The second part   describes the motion planning of the robot in this free area. It takes into account   the properties of the SLAM algorithm and it tries to plan the exploration in order to create   the most precise map. The motion of the pan-and-tilt unit is described in the third part.   It takes advantage of the fact that the robot can observe places that are in the different   directions than the robot moves. This allows us to observe much bigger space without   losing the information about the precision of the movements.