This paper describes a new method for lens distortion calibration using only point correspondences in multiple views, without the need to know either the 3D location of the points or the camera locations. The standard lens distortion model is a model of the deviations of a real camera from the ideal pinhole or projective camera model.Given multiple views of a set of corresponding points taken by ideal pinhole cameras there exist epipolar and trilinear constraints among pairs and triplets of these views. In practice, due to noise in the feature detection and due to lens distortion these constraints do not hold exactly and we get some error. The calibration is a search for the lens distortion parameters that minimize this error. Using simulation and experimental results with real images we explore the properties of this method. We describe the use of this method with the standard lens distortion model, radial and decentering, but it could also be used with any other parametric distortion models. Finally we demonstrate that lens distortion calibration improves the accuracy of 3D reconstruction.

A novel approach for watermarking of 3D models is introduced, for which data is embedded into 3D models, whereas extracted from their projected 2D visual or 2D-plus-depth representations. Such a watermarking system is valuable, since most of the 3D content is being consumed as 2D visual data. Apart from the efficiency of embedding data into 3D models before generation of arbitrary 2D projections, in some use cases, such as free viewpoint video or computer games, 2D content has to be rendered at the client, where watermarking is less secure. In order to achieve this aim, 3D-2D perspective projection invariants, as well as 3D projective invariants are used and utilization of such invariants enables the method to be independent of the viewpoint from which 2D representations are generated. The first method proposed employs a perspective projection invariant to extract hidden data from an arbitrary 2D view of a watermarked 3D model. Data is encoded in the relative positions of six interest points, selection of which requires minimal criteria. Two main problems for such a watermarking system are identified as noise sensitivity of the invariant and repeatability of the interest point detection. By optimizing an objective function considering this sensitivity, the optimal 3D interest point displacements are obtained. Performance of the proposed system is evaluated through simulations on polygonal 3D mesh models and the results strongly indicate that perspective invariant-based watermarking is feasible. As an extenstion for 2D plus depth representation of 3D models, data embedded in 3D models is also detected by combining information in 2D views and range data by utilizing another projective invariant. Finally, the problem of repeatable interest point detection that remain detectable after data embedding, is also examined and a novel method to identify such repeatable interest points is presented. The proposed methods indicate a new direction in watermarking research.

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Cette thèse porte sur différentes problématiques liées à la détection, l'ajustement et l'identification de structures elliptiques en images. Nous plaçons la détection de primitives géométriques dans le cadre statistique des méthodes a contrario afin d'obtenir un détecteur de segments de droites et d'arcs circulaires/elliptiques sans paramètres et capable de contrôler le nombre de fausses détections. Pour améliorer la précision des primitives détectées, une technique analytique simple d'ajustement de coniques est proposée ; elle combine la distance algébrique et l'orientation du gradient. L'identification d'une configuration de cercles coplanaires en images par une signature discriminante demande normalement la rectification Euclidienne du plan contenant les cercles. Nous proposons une technique efficace de calcul de la signature qui s'affranchit de l'étape de rectification ; elle est fondée exclusivement sur des propriétés invariantes du plan projectif, devenant elle même projectivement invariante / This thesis deals with different aspects concerning the detection, fitting, and identification of elliptical features in digital images. We put the geometric feature detection in the a contrario statistical framework in order to obtain a combined parameter-free line segment, circular/elliptical arc detector, which controls the number of false detections. To improve the accuracy of the detected features, especially in cases of occluded circles/ellipses, a simple closed-form technique for conic fitting is introduced, which merges efficiently the algebraic distance with the gradient orientation. Identifying a configuration of coplanar circles in images through a discriminant signature usually requires the Euclidean reconstruction of the plane containing the circles. We propose an efficient signature computation method that bypasses the Euclidean reconstruction; it relies exclusively on invariant properties of the projective plane, being thus itself invariant under perspective

In this thesis, a number of novel watermarking techniques for different 3D representations are presented. A novel watermarking method is proposed for the mono-view video, which might be interpreted as the basic implicit representation of 3D scenes. The proposed method solves the common flickering problem in the existing video watermarking schemes by means of adjusting the watermark strength with respect to temporal contrast thresholds of human visual system (HVS), which define the maximum invisible distortions in the temporal direction. The experimental results indicate that the proposed method gives better results in both objective and subjective measures, compared to some recognized methods in the literature. The watermarking techniques for the geometry and image based representations of 3D scenes, denoted as 3D watermarking, are examined and classified into three groups, as 3D-3D, 3D-2D and 2D-2D watermarking, in which the pair of symbols identifies whether the watermark is embedded-detected in a 3D model or a 2D projection of it. A detailed literature survey on 3D-3D watermarking is presented that mainly focuses on protection of the intellectual property rights of the 3D geometrical representations. This analysis points out the specific problems in 3D-3D geometry watermarking , such as the lack of a unique 3D scene representation, standardization for the coding schemes and benchmarking tools on 3D geometry watermarking. For 2D-2D watermarking category, the copyright problem for the emerging free-view televisions (FTV) is introduced. The proposed watermarking method for this original problem embeds watermarks into each view of the multi-view video by utilizing the spatial sensitivity of HVS. The hidden signal in a selected virtual view is detected by computing the normalized correlation between the selected view and a generated pattern, namely rendered watermark, which is obtained by applying the same rendering operations which has occurred on the selected view to the original watermark. An algorithm for the estimation of the virtual camera position and rotation is also developed based on the projective planar relations between image planes. The simulation results show the applicability of the method to the FTV systems. Finally, the thesis also presents a novel 3D-2D watermarking method, in which a watermark is embedded into 3-D representation of the object and detected from a 2-D projection (image) of the same model. A novel solution based on projective invariants is proposed which modifies the cross ratio of the five coplanar points on the 3D model according to the watermark bit and extracts the embedded bit from the 2D projections of the model by computing the cross-ratio. After presenting the applicability of the algorithm via simulations, the future directions for this novel problem for 3D watermarking are addressed.