This dissertation describes the design and implementation of a system that has been designed to extract 3D information from pairs of 2D images. System input consists of two images taken by an ordinary digital camera. System output is a full 3D model extracted from 2D images. There are no assumptions about the positions of the cameras during the time when the images are being taken, but the scene must not undergo any modifications. The process of extracting 3D information from 2D images consists of three basic steps. First, point matching is performed. The main contribution of this step is the introduction of an approach to matching image segments in the context of an approximation space. The second step copes with the problem of estimating external camera parameters. The proposed solution to this problem uses 3D geometry rather than the fundamental matrix widely used in 2D to 3D conversion. In the proposed approach (DirectGS), the distances between reprojected rays for all image points are minimised. The contribution of the approach considered in this step is a definition of an optimal search space for solving the 2D to 3D conversion problem and introduction of an efficient algorithm that minimises reprojection error. In the third step, the problem of dense matching is considered. The contribution of this step is the introduction of a proposed approach to dense matching of 3D object structures that utilises the presence of points on lines in 3D space. The theory and experiments developed for this dissertation demonstrate the usefulness of the proposed system in the process of digitizing 3D information. The main advantage of the proposed approach is its low cost, simplicity in use for an untrained user and the high precision of reconstructed objects. / October 2007

This dissertation describes the design and implementation of a system that has been designed to extract 3D information from pairs of 2D images. System input consists of two images taken by an ordinary digital camera. System output is a full 3D model extracted from 2D images. There are no assumptions about the positions of the cameras during the time when the images are being taken, but the scene must not undergo any modifications. The process of extracting 3D information from 2D images consists of three basic steps. First, point matching is performed. The main contribution of this step is the introduction of an approach to matching image segments in the context of an approximation space. The second step copes with the problem of estimating external camera parameters. The proposed solution to this problem uses 3D geometry rather than the fundamental matrix widely used in 2D to 3D conversion. In the proposed approach (DirectGS), the distances between reprojected rays for all image points are minimised. The contribution of the approach considered in this step is a definition of an optimal search space for solving the 2D to 3D conversion problem and introduction of an efficient algorithm that minimises reprojection error. In the third step, the problem of dense matching is considered. The contribution of this step is the introduction of a proposed approach to dense matching of 3D object structures that utilises the presence of points on lines in 3D space. The theory and experiments developed for this dissertation demonstrate the usefulness of the proposed system in the process of digitizing 3D information. The main advantage of the proposed approach is its low cost, simplicity in use for an untrained user and the high precision of reconstructed objects.

This dissertation describes the design and implementation of a system that has been designed to extract 3D information from pairs of 2D images. System input consists of two images taken by an ordinary digital camera. System output is a full 3D model extracted from 2D images. There are no assumptions about the positions of the cameras during the time when the images are being taken, but the scene must not undergo any modifications. The process of extracting 3D information from 2D images consists of three basic steps. First, point matching is performed. The main contribution of this step is the introduction of an approach to matching image segments in the context of an approximation space. The second step copes with the problem of estimating external camera parameters. The proposed solution to this problem uses 3D geometry rather than the fundamental matrix widely used in 2D to 3D conversion. In the proposed approach (DirectGS), the distances between reprojected rays for all image points are minimised. The contribution of the approach considered in this step is a definition of an optimal search space for solving the 2D to 3D conversion problem and introduction of an efficient algorithm that minimises reprojection error. In the third step, the problem of dense matching is considered. The contribution of this step is the introduction of a proposed approach to dense matching of 3D object structures that utilises the presence of points on lines in 3D space. The theory and experiments developed for this dissertation demonstrate the usefulness of the proposed system in the process of digitizing 3D information. The main advantage of the proposed approach is its low cost, simplicity in use for an untrained user and the high precision of reconstructed objects.

Analyse de la forme 3D est un sujet de recherche extrêmement actif dans les deux l'infographie et vision par ordinateur. Dans la vision par ordinateur, l'acquisition de formes et de modélisation 3D sont généralement le résultat du traitement des données complexes et des méthodes d'analyse de données. Il existe de nombreuses situations concrètes où une forme visuelle est modélisé par un nuage de points observés avec une variété de capteurs 2D et 3D. Contrairement aux données graphiques, les données sensorielles ne sont pas, dans le cas général, uniformément répartie sur toute la surface des objets observés et ils sont souvent corrompus par le bruit du capteur, les valeurs aberrantes, les propriétés de surface (diffusion, spécularités, couleur, etc), l'auto occlusions, les conditions d'éclairage variables. Par ailleurs, le même objet que l'on observe par différents capteurs, à partir de points de vue légèrement différents, ou à des moments différents cas peuvent donner la répartition des points tout à fait différentes, des niveaux de bruit et, plus particulièrement, les différences topologiques, par exemple, la fusion des mains. Dans cette thèse, nous présentons une représentation de multi-échelle des formes articulés et concevoir de nouvelles méthodes d'analyse de forme, en gardant à l'esprit les défis posés par les données de forme visuelle. En particulier, nous analysons en détail le cadre de diffusion de chaleur pour représentation multi-échelle de formes 3D et proposer des solutions pour la segmentation et d'enregistrement en utilisant les méthodes spectrales graphique et divers algorithmes d'apprentissage automatique, à savoir, le modèle de mélange gaussien (GMM) et le Espérance-Maximisation (EM). Nous présentons d'abord l'arrière-plan mathématique sur la géométrie différentielle et l'isomorphisme graphique suivie par l'introduction de la représentation spectrale de formes 3D articulés. Ensuite, nous présentons une nouvelle méthode non supervisée pour la segmentation de la forme 3D par l'analyse des vecteurs propres Laplacien de graphe. Nous décrivons ensuite une solution semi-supervisé pour la segmentation de forme basée sur un nouveau paradigme d'apprendre, d'aligner et de transférer. Ensuite, nous étendre la représentation de forme 3D à une configuration multi-échelle en décrivant le noyau de la chaleur cadre. Enfin, nous présentons une méthode d'appariement dense grâce à la représentation multi-échelle de la chaleur du noyau qui peut gérer les changements topologiques dans des formes visuelles et de conclure par une discussion détaillée et l'orientation future des travaux. / 3D shape analysis is an extremely active research topic in both computer graphics and computer vision. In computer vision, 3D shape acquisition and modeling are generally the result of complex data processing and data analysis methods. There are many practical situations where a visual shape is modeled by a point cloud observed with a variety of 2D and 3D sensors. Unlike the graphical data, the sensory data are not, in the general case, uniformly distributed across the surfaces of the observed objects and they are often corrupted by sensor noise, outliers, surface properties (scattering, specularities, color, etc.), self occlusions, varying lighting conditions. Moreover, the same object that is observed by different sensors, from slightly different viewpoints, or at different time instances may yield completely different point distributions, noise levels and, most notably, topological differences, e.g., merging of hands. In this thesis we outline single and multi-scale representation of articulated 3D shapes and devise new shape analysis methods, keeping in mind the challenges posed by visual shape data. In particular, we discuss in detail the heat diffusion framework for multi-scale shape representation and propose solutions for shape segmentation and dense shape registration using the spectral graph methods and various other machine learning algorithms, namely, the Gaussian Mixture Model (GMM) and the Expectation Maximization (EM). We first introduce the mathematical background on differential geometry and graph isomorphism followed by the introduction of pose-invariant spectral embedding representation of 3D articulated shapes. Next we present a novel unsupervised method for visual shape segmentation by analyzing the Laplacian eigenvectors. We then outline a semi-supervised solution for shape segmentation based upon a new learn, align and transfer paradigm. Next we extend the shape representation to a multi-scale setup by outlining the heat-kernel framework. Finally, we present a topologically-robust dense shape matching method using the multi-scale heat kernel representation and conclude with a detailed discussion and future direction of work.