Esta memoria para optar al grado de doctor por la Universidad de Alicante, en el área de Matemática Aplicada, se divide en ocho capítulos. En los cuatro primeros se lleva a cabo una revisión del problema de la rotación de la Tierra rígida y elástica, en formalismo hamiltoniano, y se introducen algunas alternativas originales a la construcción de ciertos elementos de la teoría. En los otros cuatro se presentan nuevas contribuciones al estudio analítico de los movimientos de precesión y nutación de la Tierra deformable. Estas se pueden agrupar en dos categorías: la obtención de fórmulas que describen el movimiento de rotación del eje de figura, que completan las existentes hasta la fecha, y la extensión del formalismo para hacerlo compatible con modelos reológicos de la Tierra más generales.

Ventilation imaging using 4D-CT is a convenient and cost effective functional imaging methodology which might be of value in radiotherapy treatment planning to spare functional lung volumes. To calculate ventilation imaging from 4D-CT we must use deformable image registration (DIR). This study validates the DIR methods and investigates the dependence of calculated ventilation on DIR methods and ventilation algorithms. The first hypothesis is if ventilation algorithms are robust then they will be insensitive to the precise DIR used provided the DIR is accurate. The second hypothesis is that the change in Houndsfield Unit (HU) method is less dependent on the DIR used and depends more on the CT image quality due to the inherent noise of HUs in normal CT imaging. DIR of the normal end expiration and inspiration phases of the 4D-CT images was used to correlate the voxels between the two respiratory phases. All DIR algorithms were validated using a 4D pixel-based and point-validated breathing thorax model, consisting of a 4D-CT image data set along with associated landmarks. Three different DIR algorithms, Optical Flow (OF), Diffeomorphic Demons (DD) and Diffeomorphic Morphons (DM), were retrospectively applied to the same group of 10 esophagus and 10 lung cancer cases all of which had associated 4D-CT image sets that encompassed the entire lung volume. Three different ventilation calculation algorithms were compared (Jacobian, ΔV, and HU) using the Dice similarity coefficient comparison. In the validation of the DIR algorithms, the average target registration errors with one standard deviation for the DIR algorithms were 1.6 ± 0.7 mm, maximum 3.1 mm for OF, 1.3 ± 0.6 mm, maximum 3.3 mm for DM, 1.3 ± 0.6 mm, maximum 2.8 mm for DD, indicating registration errors were within 2 voxels. Dependence of ventilation images on the DIR was greater for the ΔV and the Jacobian methods than for the HU method. The Dice similarity coefficient for 20% of low ventilation volume for ΔV was 0.33 ± 0.03 between OF and DM, 0.44 ± 0.05 between OF and DD and 0.51 ± 0.04 between DM and DD. The similarity comparisons for Jacobian was 0.32 ± 0.03, 0.44 ± 0.05 and 0.51 ± 0.04 respectively, and for HU 0.53 ± 0.03, 0.56 ± 0.03 and 0.76 ± 0.04 respectively. Dependence of ventilation images on the ventilation method used showed good agreement between the ΔV and Jacobian methods but differences between these two and the HU method were significantly greater. Dice similarity coefficient for using OF as DIR was 0.86 ± 0.01 between ΔV and Jacobian, 0.28 ± 0.04 between ΔV and HU and 0.28 ± 0.04 between Jacobian and HU respectively. When using DM or DD as DIR, similar values were obtained when comparing the different ventilation calculation methods. The similarity values for 20% of the high ventilation volume were close to those found for the 20% low ventilation volume. Mean target registration error for all three DIR methods was within one voxel suggesting that the registration done by either of the methods is quite accurate. Ventilation calculation from 4D-CT demonstrates some degree of dependency on the DIR algorithm employed. Similarities between ΔV and Jacobian are higher than between ΔV and HU and Jacobian and HU. This shows that ΔV and Jacobian are very similar, but HU is a very different ventilation calculation method.

The need for efficient interference detection frequently arises in computer graphics, robotics, virtual prototyping, surgery simulation, computer games, and visualization. To prevent bodies passing directly through each other, the simulation system must be able to track touching or intersecting geometric primitives. In interactive simulations, in which millions of geometric primitives may be involved, highly efficient collision detection algorithms are necessary. For these reasons, new adaptive collision detection algorithms for rigid and different types of deformable polygon meshes are proposed in this thesis. The solutions are based on adaptive bounding volume hierarchies. For deformable body simulation, different refit and reconstruction schemes to efficiently update the hierarchies as the models deform are presented. These methods permit the models to change their entire shape at every time step of the simulation. The types of deformable models considered are (i) polygon meshes that are deformed by arbitrary vertex repositioning, but with the mesh topology preserved, (ii) models deformed by linear morphing of a fixed number of reference meshes, and (iii) models undergoing completely unstructured relative motion among the geometric primitives. For rigid body simulation, a novel type of bounding volume, the slab cut ball, is introduced, which improves the culling efficiency of the data structure significantly at a low storage cost. Furthermore, a solution for even tighter fitting heterogeneous hierarchies is outlined, including novel intersection tests between spheres and boxes as well as ellipsoids and boxes. The results from the practical experiments indicate that significant speedups can be achieved by using these new methods for collision queries as well as for ray shooting in complex deforming scenes.

L'objectif fondamental de cette thèse est de développer et de mettre en oeuvre un outil interactif desimulation des techniques de micromanipulation biologiques de cellules. Au moyen de cet outil, l'opérateurpourra se former, s'entraîner et améliorer sa maîtrise en développant une gestuelle proche de celle exécutéeen réalité. La conception d'un tel environnement de simulation en temps-réel nécessite de trouver uncompromis entre le réalisme des modèles de comportement biomécanique utilisés, la précision et la stabilitédes algorithmes des méthodes de résolution et de rendu haptique utilisées ainsi que la vitesse de calcul. Lamodélisation mécanique retenue repose sur l'utilisation du modèle hyperélastique de St Venant-Kirchhoff etune formulation dynamique explicite éléments-finis du type masses-tenseurs. Le bien-fondé de cettemodélisation est vérifié sur des essais de microindentation par Microscopie à Force Atomique (AFM) decellules souches embryonnaires de souris et de microinjection d'ovocytes. Nous avons développé etimplémenté des modèles d'interaction en temps-réel qui s'articulent autour de la détection et la gestionrapide des collisions entre outil/cellule.La synthèse du rendu haptique fourni à l'opérateur est également proposée par l'intermédiaire d'un couplagevirtuel. Pour chaque application, nous avons justifié nos choix méthodologiques et Algorithmiques qui sontguidés par les contraintes de "réalisme+précision" "temps-réel". Les différents modèles proposés ont étéintégrés dans le simulateur SIMIC que nous avons développé pendant cette thèse. Ce dernier est dédié à lasimulation interactive pour l'aide à l'apprentissage du geste de microinjection et de nanoindentationcellulaire. / The fundamental objective of this thesis is to develop and implementing an interactive simulation techniquesfor micromanipulation biological cells. Using this tool, the operator can form, train and improve its control bydeveloping a gesture similar to that performed in reality. The design of such a simulation environment in realtime requires a compromise between the realism of biomechanical models used the accuracy and stability ofalgorithms and solution methods used haptic rendering and computational speed. Modeling Mechanicalrestraint involves the use of hyperelastic model of St Venant-Kirchhoff formulation and explicit dynamic finiteelement-type mass tensors. The validity of this model is tested on microindentation tests by Atomic ForceMicroscopy (AFM) of mouse embryonic stem cells and microinjection of oocytes. We have developed andimplemented models of real-time interaction that revolve around the detection and management of rapidcollisions between tool / cell.The synthesis of the haptic feedback provided to the operator is also available through a virtual coupling. Foreach application, we have justified our methodological choices and Algorithms that are guided by theconstraints of realism + precision "" real time ". The various proposed models have been integrated into thesimulator SIMIC that we developed during this thesis. This is dedicated to interactive simulation to supportlearning of gesture microinjection and cell nanoindentation.

Dans cette thèse nous avons contribué à la commande floue de deux types de robots mobiles : deux robots de type unicycle (Khepera II et fauteuil roulant). Ensuite, nous avons utilisé une architecture de pilotage réactive permettant d’intégrer la commande floue ainsi qu’un algorithme d’évitement d’obstacles réactif utilisant la théorie de Zones de Déformation Virtuelles (ZDV). Des résultats de simulation et expérimentales ont permis de valider l’approche développée. / In this thesis we contributed on developing a fuzzy control of two types of mobile robots : two unicycle robots (Khepera II and wheelchair). Then, we used a reactive pilotingarchitecture insuring the integration of both the fuzzy controller and an obstacle avoidance algorithm using the deformable virtual zones theory (DVZ). Simulation and experimental results validate the developed approach.

Considerações de informação perceptual têm ganhado espaço rapidamente em pesquisas referentes a representação, análise e exibição de malhas. Estudos com usuários, eye tracking e outras técnicas são capazes de fornecer informações cada vez mais úteis para sistemas voltados a usuário, que formam a maioria das aplicações em computação gráfica. Neste trabalho nós expandimos sobre o conceito de Saliência de Malhas — uma medida automática de importância visual para malhas de triângulos baseada em modelos de atenção humana em baixo nível — melhorando, extendendo e realizando integração com diferentes aplicações. Nós extendemos o conceito de Saliência de Malhas para englobar objetos deformáveis, mostrando como um mapa de saliência em nível de vértice pode ser construído capturando corretamente regiões de alta importância perceptual através de um conjunto de poses ou deformações. Nós definimos saliência multi-pose como um agregado multi-escala de valores de curvatura sobre uma vizinhança localmente estável, em conjunto com deformações desta vizinhança em múltiplas poses. Nós substituímos distância Euclideana por geodésica, assim fornecendo melhores estimativas de vizinhança local. Resultados mostram que saliência multi-pose gera resultados visualmente mais interessantes em simplificações quando comparado à saliência em uma única pose. Nós também aplicamos saliência de malhas ao problema de segmentação e rendering dependente de ponto de vista, introduzindo uma técnica para segmentação que particiona um objeto em um conjunto de clusters, cada um englobando um grupo de características localmente interessantes. Saliência de malhas é incorporada em um framework para clustering propagativo, guiando seleção de pontos de partida para clusters e custos de propagação de faces, levando a uma convergência de clusters ao redor de características perceptualmente importantes. Nós comparamos nossa técnica com diferentes métodos automáticos para segmentação, mostrando que ela fornece segmentação melhor ou comparável sem necessidade de intervenção do usuário. Uma vez que o algoritmo de segmentação proposto é especialmente aplicável a rendering multi-resolução, nós ilustramos uma aplicação do mesmo através de um sistema de rendering baseado em ponto de vista guiado por saliência, alcançando melhorias consideráveis em framerate com muito pouca perda de qualidade visual. / Considerations on perceptual information are quickly gaining importance in mesh representation, analysis and display research. User studies, eye tracking and other techniques are able to provide ever more useful insights for many user-centric systems, which form the bulk of computer graphics applications. In this work we build upon the concept of Mesh Saliency — an automatic measure of visual importance for triangle meshes based on models of low-level human visual attention—improving, extending and integrating it with different applications. We extend the concept of Mesh Saliency to encompass deformable objects, showing how a vertex-level saliency map can be constructed that accurately captures the regions of high perceptual importance over a range of mesh poses or deformations. We define multipose saliency as a multi-scale aggregate of curvature values over a locally stable vertex neighborhood together with deformations over multiple poses. We replace the use of the Euclidean distance by geodesic distance thereby providing superior estimates of the local neighborhood. Results show that multi-pose saliency generates more visually appealing mesh simplifications when compared to a single-pose mesh saliency. We also apply Mesh Saliency to the problem of mesh segmentation and view-dependent rendering, introducing a technique for segmentation that partitions an object into a set of face clusters, each encompassing a group of locally interesting features. Mesh Saliency is incorporated in a propagative mesh clustering framework, guiding cluster seed selection and triangle propagation costs and leading to a convergence of face clusters around perceptually important features. We compare our technique with different fully automatic segmentation algorithms, showing that it provides similar or better segmentation without the need for user input. Since the proposed clustering algorithm is specially suitable for multi-resolution rendering, we illustrate application of our clustering results through a saliency-guided view-dependent rendering system, achieving significant framerate increases with little loss of visual detail.

As imagens são sinais que possuem muita informação. Os objetos representados em ima- gens podem sofrer deformações fazendo com que suas características mudem, o que difi- culta o reconhecimento do objeto. A chave para o sucesso de um sistema de reconheci- mento de padrões em imagens é escolher adequadamente a sua abordagem e um modelo para as feições presentes nas imagens. Uma das dificuldades é extrair e selecionar as feições que são mais discriminantes entre as diferentes classes usadas para modelar um objeto. Os modelos ativos de formas (Active Shape Models ASM) adaptam-se às defor- mações de um objeto. O objeto a ser modelado, pode ser representado com um modelo de pontos distribuídos (Point Distribution Models PDM). O PDM consiste de pontos de interesse ou marcadores, que permitem a extração de feições em localizações específicas do objeto. Após tratar a incerteza da localização e oclusão dos marcadores é possível ex- trair as feições mais representativas, obtendo-se um desempenho alto em termos da taxa de reconhecimento. Nesta tese são introduzidas novas formas para extrair e selecionar feições com modelos ativos de formas, que melhoram a taxa de classificação onde há objetos deformáveis. Esta tese é inovadora no sentido de aperfeiçoar o uso de ASMs na classificação de faces humanas, e na sua aplicação no monitoramento visual de outros tipos de objetos deformáveis. / Images are signals that have a lot of information. The objects depicted in images may suf- fer deformations causing changes in their characteristics, which hinders the recognition of the object. The key to the success of a system of pattern recognition in images is to choose properly your approach and a model for the features in the images. One difficulty is to extract and select the features that are most discriminating between different classes used to model an object. The Active Shape Models (ASM) adapt to deformations of an object. The object to be modeled can be represented with a Points Distribution Model (PDM). The PDM consists of points of interest or landmarks that allow the extraction of features in specific locations of the object. After treating the uncertainty of the location and occlu- sion of the landmarks it is possible to extract the most representative features, obtaining a high performance in terms of recognition rate. This thesis introduces new ways to extract and select features with ASMs, which improve the classification rate where deformable objects are present. This thesis is innovative in the sense that improves the use of ASMs in the classification of human faces, and that can be applied in visual monitoring of other types of deformable objects.

Ce travail de thèse a été réalisé dans le cadre de la coopération entre l’Université de Technologie de Compiègne (UTC) et le Centre Technique des Industries Mécaniques (CETIM). Nous présentons un système de détection de personnes pour l’aide à la conduite dans les engins de chantier. Une partie du travail a été dédiée à l’analyse du contexte de l’application, ce qui a permis de proposer un système de perception composé d’une caméra monoculaire fisheye et d’un Lidar. L’utilisation des caméras fisheye donne l’avantage d’un champ de vision très large avec en contrepartie, la nécessité de gérer les fortes distorsions dans l’étape de détection. A notre connaissance, il n’y a pas eu de recherches dédiées au problème de la détection de personnes dans les images fisheye. Pour cette raison, nous nous sommes concentrés sur l’étude et la quantification de l’impact des distorsions radiales sur l’apparence des personnes dans les images et nous avons proposé des approches adaptatives pour gérer ces spécificités. Nos propositions se sont inspirées de deux approches de l’état de l’art pour la détection des personnes : les histogrammes de gradient orientés (HOG) et le modèle des parties déformables (DPM). Tout d’abord, en enrichissant la base d’apprentissage avec des imagettes fisheye artificielles, nous avons pu montrer que les classificateurs peuvent prendre en compte les distorsions dans la phase d’apprentissage. Cependant, adapter les échantillons d’entrée, n’est pas la solution optimale pour traiter le problème de déformation de l’apparence des personnes dans les images. Nous avons alors décidé d’adapter l’approche de DPM pour prendre explicitement en compte le modèle de distorsions. Il est apparu que les modèles déformables peuvent être modifiés pour s’adapter aux fortes distorsions des images fisheye, mais ceci avec un coût de calculatoire supérieur. Dans cette thèse, nous présentons également une approche de fusion Lidar/camera fisheye. Une architecture de fusion séquentielle est utilisée et permet de réduire les fausses détections et le coût calculatoire de manière importante. Un jeu de données en environnement de chantier a été construit et différentes expériences ont été réalisées pour évaluer les performances du système. Les résultats sont prometteurs, à la fois en terme de vitesse de traitement et de performance de détection. / This thesis has been carried out in the framework of the cooperation between the Compiègne University of Technology (UTC) and the Technical Centre for Mechanical Industries (CETIM). In this work, we present a vision-based multi-sensors people detection system for safety on heavy machines. A perception system composed of a monocular fisheye camera and a Lidar is proposed. The use of fisheye cameras provides an advantage of a wide field-of-view but yields the problem of handling the strong distortions in the detection stage.To the best of our knowledge, no research works have been dedicated to people detection in fisheye images. For that reason, we focus on investigating and quantifying the strong radial distortions impacts on people appearance and proposing adaptive approaches to handle that specificity. Our propositions are inspired by the two state-of-the-art people detection approaches : the Histogram of Oriented Gradient (HOG) and the Deformable Parts Model (DPM). First, by enriching the training data set, we prove that the classifier can take into account the distortions. However, fitting the training samples to the model, is not the best solution to handle the deformation of people appearance. We then decided to adapt the DPM approach to handle properly the problem. It turned out that the deformable models can be modified to be even better adapted to the strong distortions of the fisheye images. Still, such approach has adrawback of the high computation cost and complexity. In this thesis, we also present a framework that allows the fusion of the Lidar modality to enhance the vision-based people detection algorithm. A sequential Lidar-based fusion architecture is used, which addresses directly the problem of reducing the false detections and computation cost in vision-based-only system. A heavy machine dataset have been also built and different experiments have been carried out to evaluate the performances of the system. The results are promising, both in term of processing speed and performances.

Considerações de informação perceptual têm ganhado espaço rapidamente em pesquisas referentes a representação, análise e exibição de malhas. Estudos com usuários, eye tracking e outras técnicas são capazes de fornecer informações cada vez mais úteis para sistemas voltados a usuário, que formam a maioria das aplicações em computação gráfica. Neste trabalho nós expandimos sobre o conceito de Saliência de Malhas — uma medida automática de importância visual para malhas de triângulos baseada em modelos de atenção humana em baixo nível — melhorando, extendendo e realizando integração com diferentes aplicações. Nós extendemos o conceito de Saliência de Malhas para englobar objetos deformáveis, mostrando como um mapa de saliência em nível de vértice pode ser construído capturando corretamente regiões de alta importância perceptual através de um conjunto de poses ou deformações. Nós definimos saliência multi-pose como um agregado multi-escala de valores de curvatura sobre uma vizinhança localmente estável, em conjunto com deformações desta vizinhança em múltiplas poses. Nós substituímos distância Euclideana por geodésica, assim fornecendo melhores estimativas de vizinhança local. Resultados mostram que saliência multi-pose gera resultados visualmente mais interessantes em simplificações quando comparado à saliência em uma única pose. Nós também aplicamos saliência de malhas ao problema de segmentação e rendering dependente de ponto de vista, introduzindo uma técnica para segmentação que particiona um objeto em um conjunto de clusters, cada um englobando um grupo de características localmente interessantes. Saliência de malhas é incorporada em um framework para clustering propagativo, guiando seleção de pontos de partida para clusters e custos de propagação de faces, levando a uma convergência de clusters ao redor de características perceptualmente importantes. Nós comparamos nossa técnica com diferentes métodos automáticos para segmentação, mostrando que ela fornece segmentação melhor ou comparável sem necessidade de intervenção do usuário. Uma vez que o algoritmo de segmentação proposto é especialmente aplicável a rendering multi-resolução, nós ilustramos uma aplicação do mesmo através de um sistema de rendering baseado em ponto de vista guiado por saliência, alcançando melhorias consideráveis em framerate com muito pouca perda de qualidade visual. / Considerations on perceptual information are quickly gaining importance in mesh representation, analysis and display research. User studies, eye tracking and other techniques are able to provide ever more useful insights for many user-centric systems, which form the bulk of computer graphics applications. In this work we build upon the concept of Mesh Saliency — an automatic measure of visual importance for triangle meshes based on models of low-level human visual attention—improving, extending and integrating it with different applications. We extend the concept of Mesh Saliency to encompass deformable objects, showing how a vertex-level saliency map can be constructed that accurately captures the regions of high perceptual importance over a range of mesh poses or deformations. We define multipose saliency as a multi-scale aggregate of curvature values over a locally stable vertex neighborhood together with deformations over multiple poses. We replace the use of the Euclidean distance by geodesic distance thereby providing superior estimates of the local neighborhood. Results show that multi-pose saliency generates more visually appealing mesh simplifications when compared to a single-pose mesh saliency. We also apply Mesh Saliency to the problem of mesh segmentation and view-dependent rendering, introducing a technique for segmentation that partitions an object into a set of face clusters, each encompassing a group of locally interesting features. Mesh Saliency is incorporated in a propagative mesh clustering framework, guiding cluster seed selection and triangle propagation costs and leading to a convergence of face clusters around perceptually important features. We compare our technique with different fully automatic segmentation algorithms, showing that it provides similar or better segmentation without the need for user input. Since the proposed clustering algorithm is specially suitable for multi-resolution rendering, we illustrate application of our clustering results through a saliency-guided view-dependent rendering system, achieving significant framerate increases with little loss of visual detail.

As imagens são sinais que possuem muita informação. Os objetos representados em ima- gens podem sofrer deformações fazendo com que suas características mudem, o que difi- culta o reconhecimento do objeto. A chave para o sucesso de um sistema de reconheci- mento de padrões em imagens é escolher adequadamente a sua abordagem e um modelo para as feições presentes nas imagens. Uma das dificuldades é extrair e selecionar as feições que são mais discriminantes entre as diferentes classes usadas para modelar um objeto. Os modelos ativos de formas (Active Shape Models ASM) adaptam-se às defor- mações de um objeto. O objeto a ser modelado, pode ser representado com um modelo de pontos distribuídos (Point Distribution Models PDM). O PDM consiste de pontos de interesse ou marcadores, que permitem a extração de feições em localizações específicas do objeto. Após tratar a incerteza da localização e oclusão dos marcadores é possível ex- trair as feições mais representativas, obtendo-se um desempenho alto em termos da taxa de reconhecimento. Nesta tese são introduzidas novas formas para extrair e selecionar feições com modelos ativos de formas, que melhoram a taxa de classificação onde há objetos deformáveis. Esta tese é inovadora no sentido de aperfeiçoar o uso de ASMs na classificação de faces humanas, e na sua aplicação no monitoramento visual de outros tipos de objetos deformáveis. / Images are signals that have a lot of information. The objects depicted in images may suf- fer deformations causing changes in their characteristics, which hinders the recognition of the object. The key to the success of a system of pattern recognition in images is to choose properly your approach and a model for the features in the images. One difficulty is to extract and select the features that are most discriminating between different classes used to model an object. The Active Shape Models (ASM) adapt to deformations of an object. The object to be modeled can be represented with a Points Distribution Model (PDM). The PDM consists of points of interest or landmarks that allow the extraction of features in specific locations of the object. After treating the uncertainty of the location and occlu- sion of the landmarks it is possible to extract the most representative features, obtaining a high performance in terms of recognition rate. This thesis introduces new ways to extract and select features with ASMs, which improve the classification rate where deformable objects are present. This thesis is innovative in the sense that improves the use of ASMs in the classification of human faces, and that can be applied in visual monitoring of other types of deformable objects.