<p>Mathematical models of classes of objects can significantly contribute to the analysis of digital images. A major problem in modelling is to establish suitable descriptions that cover not only a single object but also the variation that is usually present within a class of objects.</p><p>The objective of this thesis is to develop more general modelling strategies than commonly used today. In particular, the impact of the human factor in the model creation process should be minimised. It is presumed that the human ability of abstraction imposes undesired constraints on the description. In comparison, common approaches are discussed from the viewpoint of generality.</p><p>The technique considered introduces <i>appearance space </i>as a common framework to represent both shapes and images. In appearance space, an object is represented by a single point in a high-dimensional vector space. Accordingly, objects subject to variation appear as <i>nonlinear manifolds</i> in appearance space. These manifolds are often characterised by only a few intrinsic dimensions. A model of a class of objects is therefore considered equal to the mathematical description of this manifold.</p><p>The presence of nonlinearity motivates the use of artificial auto-associative neural networks in the modelling process. The network extracts nonlinear modes of variation from a number of training examples. The procedure is evaluated on both synthetic and natural data of shapes and images and shows promising results as a general approach to object modelling.</p>

Mathematical models of classes of objects can significantly contribute to the analysis of digital images. A major problem in modelling is to establish suitable descriptions that cover not only a single object but also the variation that is usually present within a class of objects. The objective of this thesis is to develop more general modelling strategies than commonly used today. In particular, the impact of the human factor in the model creation process should be minimised. It is presumed that the human ability of abstraction imposes undesired constraints on the description. In comparison, common approaches are discussed from the viewpoint of generality. The technique considered introduces appearance space as a common framework to represent both shapes and images. In appearance space, an object is represented by a single point in a high-dimensional vector space. Accordingly, objects subject to variation appear as nonlinear manifolds in appearance space. These manifolds are often characterised by only a few intrinsic dimensions. A model of a class of objects is therefore considered equal to the mathematical description of this manifold. The presence of nonlinearity motivates the use of artificial auto-associative neural networks in the modelling process. The network extracts nonlinear modes of variation from a number of training examples. The procedure is evaluated on both synthetic and natural data of shapes and images and shows promising results as a general approach to object modelling.

La modélisation 3d automatique d'un environnement à partir d'images est un sujet toujours d'actualité en vision par ordinateur. Ce problème se résout en général en trois temps : déplacer une caméra dans la scène pour prendre la séquence d'images, reconstruire la géométrie, et utiliser une méthode de stéréo dense pour obtenir une surface de la scène. La seconde étape met en correspondances des points d'intérêts dans les images puis estime simultanément les poses de la caméra et un nuage épars de points 3d de la scène correspondant aux points d'intérêts. La troisième étape utilise l'information sur l'ensemble des pixels pour reconstruire une surface de la scène, par exemple en estimant un nuage de points dense.Ici nous proposons de traiter le problème en calculant directement une surface à partir du nuage épars de points et de son information de visibilité fournis par l'estimation de la géométrie. Les avantages sont des faibles complexités en temps et en espace, ce qui est utile par exemple pour obtenir des modèles compacts de grands environnements comme une ville. Pour cela, nous présentons une méthode de reconstruction de surface du type sculpture dans une triangulation de Delaunay 3d des points reconstruits. L'information de visibilité est utilisée pour classer les tétraèdres en espace vide ou matière. Puis une surface est extraite de sorte à séparer au mieux ces tétraèdres à l'aide d'une méthode gloutonne et d'une minorité de points de Steiner. On impose sur la surface la contrainte de 2-variété pour permettre des traitements ultérieurs classiques tels que lissage, raffinement par optimisation de photo-consistance ... Cette méthode a ensuite été étendue au cas incrémental : à chaque nouvelle image clef sélectionnée dans une vidéo, de nouveaux points 3d et une nouvelle pose sont estimés, puis la surface est mise à jour. La complexité en temps est étudiée dans les deux cas (incrémental ou non). Dans les expériences, nous utilisons une caméra catadioptrique bas coût et obtenons des modèles 3d texturés pour des environnements complets incluant bâtiments, sol, végétation ... Un inconvénient de nos méthodes est que la reconstruction des éléments fins de la scène n'est pas correcte, par exemple les branches des arbres et les pylônes électriques. / The automatic 3d modeling of an environment using images is still an active topic in Computer Vision. Standard methods have three steps : moving a camera in the environment to take an image sequence, reconstructing the geometry of the environment, and applying a dense stereo method to obtain a surface model of the environment. In the second step, interest points are detected and matched in images, then camera poses and a sparse cloud of 3d points corresponding to the interest points are simultaneously estimated. In the third step, all pixels of images are used to reconstruct a surface of the environment, e.g. by estimating a dense cloud of 3d points. Here we propose to generate a surface directly from the sparse point cloud and its visibility information provided by the geometry reconstruction step. The advantages are low time and space complexities ; this is useful e.g. for obtaining compact models of large and complete environments like a city. To do so, a surface reconstruction method by sculpting 3d Delaunay triangulation of the reconstructed points is proposed.The visibility information is used to classify the tetrahedra in free-space and matter. Then a surface is extracted thanks to a greedy method and a minority of Steiner points. The 2-manifold constraint is enforced on the surface to allow standard surface post-processing such as denoising, refinement by photo-consistency optimization ... This method is also extended to the incremental case : each time a new key-frame is selected in the input video, new 3d points and camera pose are estimated, then the reconstructed surface is updated.We study the time complexity in both cases (incremental or not). In experiments, a low-cost catadioptric camera is used to generate textured 3d models for complete environments including buildings, ground, vegetation ... A drawback of our methods is that thin scene components cannot be correctly reconstructed, e.g. tree branches and electric posts.