In this thesis we address the problem of digitizing the motion of three-dimensional shapes that move and deform in time. These shapes are observed from several points of view with cameras that record the scene's evolution as videos. Using available reconstruction methods, these videos can be converted into a sequence of three-dimensional snapshots that capture the appearance and shape of the objects in the scene. The focus of this thesis is to complement appearance and shape with information on the motion and deformation of objects. In other words, we want to measure the trajectory of every point on the observed surfaces. This is a challenging problem because the captured videos are only sequences of images, and the reconstructed shapes are built independently from each other. While the human brain excels at recreating the illusion of motion from these snapshots, using them to automatically measure motion is still largely an open problem. The majority of prior works on the subject has focused on tracking the performance of one human actor, and used the strong prior knowledge on the articulated nature of human motion to handle the ambiguity and noise inherent to visual data. In contrast, the presented developments consist of generic methods that allow to digitize scenes involving several humans and deformable objects of arbitrary nature. To perform surface tracking as generically as possible, we formulate the problem as the geometric registration of surfaces and deform a reference mesh to fit a sequence of independently reconstructed meshes. We introduce a set of algorithms and numerical tools that integrate into a pipeline whose output is an animated mesh. Our first contribution consists of a generic mesh deformation model and numerical optimization framework that divides the tracked surface into a collection of patches, organizes these patches in a deformation graph and emulates elastic behavior with respect to the reference pose. As a second contribution, we present a probabilistic formulation of deformable surface registration that embeds the inference in an Expectation-Maximization framework that explicitly accounts for the noise and in the acquisition. As a third contribution, we look at how prior knowledge can be used when tracking articulated objects, and compare different deformation model with skeletal-based tracking. The studies reported by this thesis are supported by extensive experiments on various 4D datasets. They show that in spite of weaker assumption on the nature of the tracked objects, the presented ideas allow to process complex scenes involving several arbitrary objects, while robustly handling missing data and relatively large reconstruction artifacts.

Cette thèse traite du suivi temporel de surfaces déformables. Ces surfaces sont observées depuis plusieurs points de vue par des caméras qui capturent l'évolution de la scène et l'enregistrent sous la forme de vidéos. Du fait des progrès récents en reconstruction multi-vue, cet ensemble de vidéos peut être converti en une série de clichés tridimensionnels qui capturent l'apparence et la forme des objets dans la scène. Le problème au coeur des travaux rapportés par cette thèse est de complémenter les informations d'apparence et de forme avec des informations sur les mouvements et les déformations des objets. En d'autres mots, il s'agit de mesurer la trajectoire de chacun des points sur les surfaces observées. Ceci est un problème difficile car les vidéos capturées ne sont que des séquences d'images, et car les formes reconstruites à chaque instant le sont indépendemment les unes des autres. Si le cerveau humain excelle à recréer l'illusion de mouvement à partir de ces clichés, leur utilisation pour la mesure automatisée du mouvement reste une question largement ouverte. La majorité des précédents travaux sur le sujet se sont focalisés sur la capture du mouvement humain et ont bénéficié de la nature articulée de ce mouvement qui pouvait être utilisé comme a-priori dans les calculs. La spécificité des développements présentés ici réside dans la généricité des méthodes qui permettent de capturer des scènes dynamiques plus complexes contenant plusieurs acteurs et différents objets déformables de nature inconnue a priori. Pour suivre les surfaces de la façon la plus générique possible, nous formulons le problème comme celui de l'alignement géométrique de surfaces, et déformons un maillage de référence pour l'aligner avec les maillages indépendemment reconstruits de la séquence. Nous présentons un ensemble d'algorithmes et d'outils numériques intégrés dans une chaîne de traitements dont le résultat est un maillage animé. Notre première contribution est une méthode de déformation de maillage qui divise la surface en une collection de morceaux élémentaires de surfaces que nous nommons patches. Ces patches sont organisés dans un graphe de déformation, et une force est appliquée sur cette structure pour émuler une déformation élastique par rapport à la pose de référence. Comme seconde contribution, nous présentons une formulation probabiliste de l'alignement de surfaces déformables qui modélise explicitement le bruit dans le processus d'acquisition. Pour finir, nous étudions dans quelle mesure les a-prioris sur la nature articulée du mouvement peuvent aider, et comparons différents modèles de déformation à une méthode de suivi de squelette. Les développements rapportés par cette thèse sont validés par de nombreuses expériences sur une variété de séquences. Ces résultats montrent qu'en dépit d'a-prioris moins forts sur les surfaces suivies, les idées présentées permettent de traiter des scènes complexes contenant de multiples objets tout en se comportant de façon robuste vis-a-vis de données fragmentaires et d'erreurs de reconstruction. / In this thesis we address the problem of digitizing the motion of three-dimensional shapes that move and deform in time. These shapes are observed from several points of view with cameras that record the scene's evolution as videos. Using available reconstruction methods, these videos can be converted into a sequence of three-dimensional snapshots that capture the appearance and shape of the objects in the scene. The focus of this thesis is to complement appearance and shape with information on the motion and deformation of objects. In other words, we want to measure the trajectory of every point on the observed surfaces. This is a challenging problem because the captured videos are only sequences of images, and the reconstructed shapes are built independently from each other. While the human brain excels at recreating the illusion of motion from these snapshots, using them to automatically measure motion is still largely an open problem. The majority of prior works on the subject has focused on tracking the performance of one human actor, and used the strong prior knowledge on the articulated nature of human motion to handle the ambiguity and noise inherent to visual data. In contrast, the presented developments consist of generic methods that allow to digitize scenes involving several humans and deformable objects of arbitrary nature. To perform surface tracking as generically as possible, we formulate the problem as the geometric registration of surfaces and deform a reference mesh to fit a sequence of independently reconstructed meshes. We introduce a set of algorithms and numerical tools that integrate into a pipeline whose output is an animated mesh. Our first contribution consists of a generic mesh deformation model and numerical optimization framework that divides the tracked surface into a collection of patches, organizes these patches in a deformation graph and emulates elastic behavior with respect to the reference pose. As a second contribution, we present a probabilistic formulation of deformable surface registration that embeds the inference in an Expectation-Maximization framework that explicitly accounts for the noise and in the acquisition. As a third contribution, we look at how prior knowledge can be used when tracking articulated objects, and compare different deformation model with skeletal-based tracking. The studies reported by this thesis are supported by extensive experiments on various 4D datasets. They show that in spite of weaker assumption on the nature of the tracked objects, the presented ideas allow to process complex scenes involving several arbitrary objects, while robustly handling missing data and relatively large reconstruction artifacts.

[pt] Escoamentos de fluidos sobre paredes flexíveis se fazem presentes em diversos processos biológicos e industriais. A flexibilidade do sólido permite a propagação de ondas na interface, podendo levar o sistema a se tornar instável mesmo a baixos valores do número de Reynolds. Esta perda de estabilidade provoca uma alteração nas características hidrodinâmicas e na transferência de calor do processo. Os trabalhos disponíveis na literatura se concentram em torno de análise de estabilidade linear e experimentos de determinação de parâmetros críticos. Entretanto estas metodologias não são capazes de descrever o comportamento do sistema após sua desestabilização. Neste trabalho, o regime instável de um escoamento de Couette de um fluido Newtoniano sobre um sólido incompressível e impermeável de MooneyRivlin é estudado numericamente através da solução acoplada das equações de conservação de quantidade de movimento linear transiente de cada meio. O número de Reynolds foi escolhido pequeno o suficiente para afastar a possibilidade de que mecanismos inerciais se façam presentes. Diferentes razões de espessura líquido-sólido flexível foram utilizadas para se determinar os efeitos desta grandeza sobre o processo. O sistema de equações diferenciais foram integradas no espaço pelo método de Galerkinjelementos finitos, e no tempo por diferenças finitas. A necessidade de se utilizar passos de tempo variáveis exigiu o desenvolvimento de uma fórmula específica para a aproximação da derivada segunda presente no termo transiente do sólido. / [en] Fluid flow over flexible wall are present in several biological and industrial processes. The flexibility of the solid body permits the waves propagation along the interface, leading the system to become unstable even at low value of Reynolds number. This loss of stability induce some changes on the hydrodynamic characteristics and on the heat transfer of the process. Works available on literature are concentrated around linear stability analysis and experiments of determining critical parameters. Nevertheless these methodologies are not able of describing the system behavior after the desestabilization. In this work, the unstable regime of a Newtonian fluid Couette flow over an incompressible and impermeable Mooney-Rivlin solid is numerically studied by solving the coupled fluid and solid momentum equation. The Reynolds number has been chosen small enough to avoid the presence of inertial mechanisms. Different liquid-flexible solid thickness ratio were used to determine the effect of this parameter on the problem. The system of differential equations were integrated by Galerki s/finite elements method on space, and by finite differences on time. The necessity of using variables changeables time steps demanded the development of a specific equation to approximates the second material derivative present on the unsteady solid term.

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