Common cameras with a dynamic range of two orders cannot reproduce typical outdoor scenes with a radiance range of over five orders. Most high dynamic range (HDR) imaging techniques reconstruct the whole dynamic range from exposure bracketed low dynamic range (LDR) images. But the camera must be kept steady with no or small motion, which is not practical in many cases. Thus, we develop a more efficient framework for omnidirectional HDR imaging with a moving camera. The proposed framework is composed of three major stages: geometric calibration and rotational alignment, multi-view stereo correspondence and HDR composition. First, camera poses are determined and omnidirectional images are rotationally aligned. Second, the aligned images are fed into a spherical vision toolkit to find disparity maps. Third, enhanced disparity maps are used to warp differently exposed neighboring images to a target view and an HDR radiance map is obtained by fusing the registered images in radiance. We develop disparity-based forward and backward image warping algorithms for spherical stereo vision and implement them in GPU. We also explore some techniques for disparity map enhancement including a superpixel technique and a color model for outdoor scenes. We examine different factors such as exposure increment step size, sequence ordering, and the baseline between views. We demonstrate the success with indoor and outdoor scenes and compare our results with two state-of-the-art HDR imaging methods. The proposed HDR framework allows us to capture HDR radiance maps, disparity maps and an omnidirectional field of view, which has many applications such as HDR view synthesis and virtual navigation.

Dans cette thèse, nous traiterons du problème de la détection et du suivi 3D de personnes dans des séquences d'images omnidirectionnelles, dans le but de réaliser des applications permettant l'estimation de pose 3D. Ceci nécessite, la mise en place d'un suivi stable et précis de la personne dans un environnement réel. Dans le cadre de cette étude, on utilisera une caméra catadioptrique composée d'un miroir sphérique et d'une caméra perspective. Ce type de capteur est couramment utilisé dans la vision par ordinateur et la robotique. Son principal avantage est son large champ de vision qui lui permet d'acquérir une vue à 360 degrés de la scène avec un seul capteur et en une seule image. Cependant, ce capteur va engendrer des distorsions importantes dans les images, ne permettant pas une application directe des méthodes classiquement utilisées en vision perspective. Cette thèse traite de deux approches de suivi développées durant cette thèse, qui permettent de tenir compte de ces distorsions. Elles illustrent le cheminement suivi par nos travaux, nous permettant de passer de la détection de personne à l'estimation 3D de sa pose. La première étape de nos travaux a consisté à mettre en place un algorithme de détection de personnes dans les images omnidirectionnelles. Nous avons proposé d'étendre l'approche conventionnelle pour la détection humaine en image perspective, basée sur l'Histogramme Orientés du Gradient (HOG), pour l'adapter à des images sphériques. Notre approche utilise les variétés riemanniennes afin d'adapter le calcul du gradient dans le cas des images omnidirectionnelles. Elle utilise aussi le gradient sphérique pour le cas les images sphériques afin de générer notre descripteur d'image omnidirectionnelle. Par la suite, nous nous sommes concentrés sur la mise en place d'un système de suivi 3D de personnes avec des caméras omnidirectionnelles. Nous avons fait le choix de faire du suivi 3D basé sur un modèle de la personne avec 30 degrés de liberté car nous nous sommes imposés comme contrainte l'utilisation d'une seule caméra catadioptrique. / In this thesis we will handle the problem of 3D people detection and tracking in omnidirectional images sequences, in order to realize applications allowing3D pose estimation, we investigate the problem of 3D people detection and tracking in omnidirectional images sequences. This requires a stable and accurate monitoring of the person in a real environment. In order to achieve this, we will use a catadioptric camera composed of a spherical mirror and a perspective camera. This type of sensor is commonly used in computer vision and robotics. Its main advantage is its wide field of vision, which allows it to acquire a 360-degree view of the scene with a single sensor and in a single image. However, this kind of sensor generally generates significant distortions in the images, not allowing a direct application of the methods conventionally used in perspective vision. Our thesis contains a description of two monitoring approaches that take into account these distortions. These methods show the progress of our work during these three years, allowing us to move from person detection to the 3Destimation of its pose. The first step of this work consisted in setting up a person detection algorithm in the omnidirectional images. We proposed to extend the conventional approach for human detection in perspective image, based on the Gradient-Oriented Histogram (HOG), in order to adjust it to spherical images. Our approach uses the Riemannian varieties to adapt the gradient calculation for omnidirectional images as well as the spherical gradient for spherical images to generate our omnidirectional image descriptor.

Despite the immense advances of science and medicine in recent years, several aspects regarding the physiology and the anatomy of the human brain are yet to be discovered and understood. A particularly challenging area in the study of human brain anatomy is that of brain connectivity, which describes the intricate means by which different regions of the brain interact with each other. The study of brain connectivity is deeply dependent on understanding the organization of white matter. The latter is predominantly comprised of bundles of myelinated axons, which serve as connecting pathways between approximately 10¹¹ neurons in the brain. Consequently, the delineation of fine anatomical details of white matter represents a highly challenging objective, and it is still an active area of research in the fields of neuroimaging and neuroscience, in general. Recent advances in medical imaging have resulted in a quantum leap in our understanding of brain anatomy and functionality. In particular, the advent of diffusion magnetic resonance imaging (dMRI) has provided researchers with a non-invasive means to infer information about the connectivity of the human brain. In a nutshell, dMRI is a set of imaging tools which aim at quantifying the process of water diffusion within the human brain to delineate the complex structural configurations of the white matter. Among the existing tools of dMRI high angular resolution diffusion imaging (HARDI) offers a desirable trade-off between its reconstruction accuracy and practical feasibility. In particular, HARDI excels in its ability to delineate complex directional patterns of the neural pathways throughout the brain, while remaining feasible for many clinical applications. Unfortunately, HARDI presents a fundamental trade-off between its ability to discriminate crossings of neural fiber tracts (i.e., its angular resolution) and the signal-to-noise ratio (SNR) of its associated images. Consequently, given that the angular resolution is of fundamental importance in the context of dMRI reconstruction, there is a need for effective algorithms for de-noising HARDI data. In this regard, the most effective de-noising approaches have been observed to be those which exploit both the angular and the spatial-domain regularity of HARDI signals. Accordingly, in this thesis, we propose a formulation of the problem of reconstruction of HARDI signals which incorporates regularization assumptions on both their angular and their spatial domains, while leading to a particularly simple numerical implementation. Experimental evidence suggests that the resulting cross-domain regularization procedure outperforms many other state of the art HARDI de-noising methods. Moreover, the proposed implementation of the algorithm supersedes the original reconstruction problem by a sequence of efficient filters which can be executed in parallel, suggesting its computational advantages over alternative implementations.

Despite the immense advances of science and medicine in recent years, several aspects regarding the physiology and the anatomy of the human brain are yet to be discovered and understood. A particularly challenging area in the study of human brain anatomy is that of brain connectivity, which describes the intricate means by which different regions of the brain interact with each other. The study of brain connectivity is deeply dependent on understanding the organization of white matter. The latter is predominantly comprised of bundles of myelinated axons, which serve as connecting pathways between approximately 10¹¹ neurons in the brain. Consequently, the delineation of fine anatomical details of white matter represents a highly challenging objective, and it is still an active area of research in the fields of neuroimaging and neuroscience, in general. Recent advances in medical imaging have resulted in a quantum leap in our understanding of brain anatomy and functionality. In particular, the advent of diffusion magnetic resonance imaging (dMRI) has provided researchers with a non-invasive means to infer information about the connectivity of the human brain. In a nutshell, dMRI is a set of imaging tools which aim at quantifying the process of water diffusion within the human brain to delineate the complex structural configurations of the white matter. Among the existing tools of dMRI high angular resolution diffusion imaging (HARDI) offers a desirable trade-off between its reconstruction accuracy and practical feasibility. In particular, HARDI excels in its ability to delineate complex directional patterns of the neural pathways throughout the brain, while remaining feasible for many clinical applications. Unfortunately, HARDI presents a fundamental trade-off between its ability to discriminate crossings of neural fiber tracts (i.e., its angular resolution) and the signal-to-noise ratio (SNR) of its associated images. Consequently, given that the angular resolution is of fundamental importance in the context of dMRI reconstruction, there is a need for effective algorithms for de-noising HARDI data. In this regard, the most effective de-noising approaches have been observed to be those which exploit both the angular and the spatial-domain regularity of HARDI signals. Accordingly, in this thesis, we propose a formulation of the problem of reconstruction of HARDI signals which incorporates regularization assumptions on both their angular and their spatial domains, while leading to a particularly simple numerical implementation. Experimental evidence suggests that the resulting cross-domain regularization procedure outperforms many other state of the art HARDI de-noising methods. Moreover, the proposed implementation of the algorithm supersedes the original reconstruction problem by a sequence of efficient filters which can be executed in parallel, suggesting its computational advantages over alternative implementations.

In a Minkowski three dimensional space, whose metric is based on a strictly convex and centrally symmetric unit ball , we deal with ruled surfaces Φ in the sense of E. Kruppa. This means that we have to look for Minkowski analogues of the classical differential invariants of ruled surfaces in a Euclidean space. Here, at first – after an introduction to concepts of a Minkowski space, like semi-orthogonalities and a semi-inner-product based on the so-called cosine-Minkowski function - we construct an orthogonal 3D moving frame using Birkhoff’s left-orthogonality. This moving frame is canonically connected to ruled surfaces: beginning with the generator direction and the asymptotic plane of this generator g we complete this flag to a frame using the left-orthogonality defined by ; ( is described either by its supporting function or a parameter representation). The plane left-orthogonal to the asymptotic plane through generator g(t) is called Minkowski central plane and touches Φ in the striction point s(t) of g(t). Thus the moving frame defines the Minkowski striction curve S of the considered ruled surface Φ similar to the Euclidean case. The coefficients occurring in the Minkowski analogues to Frenet-Serret formulae of the moving frame of Φ in a Minkowski space are called “M-curvatures” and “M-torsions”. Here we essentially make use of the semi-inner product and the sine-Minkowski and cosine-Minkowski functions. Furthermore we define a covariant differentiation in a Minkowski 3-space using a new vector called “deformation vector” and locally measuring the deviation of the Minkowski space from a Euclidean space. With this covariant differentiation it is possible to declare an “M-geodesicc parallelity” and to show that the vector field of the generators of a skew ruled surface Φ is an M-geodesic parallel field along its Minkowski striction curve s. Finally we also define the Pirondini set of ruled surfaces to a given surface Φ. The surfaces of such a set have the M-striction curve and the strip of M-central planes in common

In a Minkowski three dimensional space, whose metric is based on a strictly convex and centrally symmetric unit ball , we deal with ruled surfaces Φ in the sense of E. Kruppa. This means that we have to look for Minkowski analogues of the classical differential invariants of ruled surfaces in a Euclidean space. Here, at first – after an introduction to concepts of a Minkowski space, like semi-orthogonalities and a semi-inner-product based on the so-called cosine-Minkowski function - we construct an orthogonal 3D moving frame using Birkhoff’s left-orthogonality. This moving frame is canonically connected to ruled surfaces: beginning with the generator direction and the asymptotic plane of this generator g we complete this flag to a frame using the left-orthogonality defined by ; ( is described either by its supporting function or a parameter representation). The plane left-orthogonal to the asymptotic plane through generator g(t) is called Minkowski central plane and touches Φ in the striction point s(t) of g(t). Thus the moving frame defines the Minkowski striction curve S of the considered ruled surface Φ similar to the Euclidean case. The coefficients occurring in the Minkowski analogues to Frenet-Serret formulae of the moving frame of Φ in a Minkowski space are called “M-curvatures” and “M-torsions”. Here we essentially make use of the semi-inner product and the sine-Minkowski and cosine-Minkowski functions. Furthermore we define a covariant differentiation in a Minkowski 3-space using a new vector called “deformation vector” and locally measuring the deviation of the Minkowski space from a Euclidean space. With this covariant differentiation it is possible to declare an “M-geodesicc parallelity” and to show that the vector field of the generators of a skew ruled surface Φ is an M-geodesic parallel field along its Minkowski striction curve s. Finally we also define the Pirondini set of ruled surfaces to a given surface Φ. The surfaces of such a set have the M-striction curve and the strip of M-central planes in common