L'analyse des structures curvilignes en 3 dimensions est un problème difficile en analyse d'images. En effet, ces structures sont fines, facilement corrompues par le bruit et présentent une géométrie complexe. Depuis plusieurs années, de nombreuses méthodes spécialement dédiées au traitement d'images contenant des structures curvilignes ont vu le jour. Ces méthodes concernent diverses applications en science des matériaux, télédétection ou encore en imagerie médicale. Malgré cela, l'analyse des structures curvilignes demeure une tâche complexe.Dans cette présentation nous parlerons de la caractérisation des structures curvilignes pour l'analyse d'images. Nous présenterons en premier lieu une nouvelle méthode appelée RORPO, à partir de laquelle deux caractéristiques peuvent être calculées. La première est une caractéristique d'intensité, qui préserve l'intensité des structures curvilignes tout en réduisant celle des autres structures. La deuxième est une caractéristique de direction, qui fournit en chaque point d'une image, la direction d'une structure curviligne potentielle.RORPO, contrairement à la plupart des méthodes de la littérature, est une méthode non locale, non linéaire et mieux adaptées à l'anisotropie intrinsèque des structures curvilignes. Cette méthode repose sur une notion récente de Morphologie Mathématique: les opérateurs par chemins.RORPO peut directement servir au filtrage d'images contenant des structures curvilignes, afin de spécifiquement les préserver, mais aussi de réduire le bruit. Mais les deux caractéristiques de RORPO peuvent aussi être utilisées comme information a priori sur les structure curvilignes, afin d'être intégrées dans une méthode plus complexe d'analyse d'image.Dans un deuxième temps, nous présenterons ainsi un terme de régularisation destiné à la segmentation variationnelle, utilisant les deux caractéristiques de RORPO.L'information apportée par ces deux caractéristiques permet de régulariser les structures curvilignes seulement dans la direction de leur axe principal. De cette manière, ces structures sont mieux préservées, et certaines structures curvilignes déconnectées par le bruit peuvent aussi être reconnectées.Des résultats en 2D et 3D de ces méthodes seront enfin présentées sur des images de vaisseaux sanguins provenant de diverses modalités / The analysis of curvilinear structures in 3D images is a complex and challenging task. Curvilinear structures are thin, easily corrupted by noise and present a complex geometry. Despite the numerous applications in material sciences, remote sensing and medical imaging and the large number of dedicated methods developed the last few years, the detection of such structures remains a difficult problem.In this thesis, we work on the characterization of curvilinear structures. We first propose a new framework called RORPO, to characterize such structures through two features: an intensity feature which preserves the intensity of curvilinear structures while decreasing the intensity of other structures, and a directional feature providing at each point, the direction of the curvilinear structure.RORPO, unlike classic other state of the art methods, is non-local and non-linear, which are desirable properties adapted to the intrinsic anisotropy of curvilinear structures. RORPO is based on recent advances in mathematical morphology: the path operators.We provide a full description of the structural and algorithmic details of RORPO, and we also conduct a quantitative comparative study of our features with three popular curvilinear structure analysis filters: the Frangi Vesselness, the Optimally Oriented Flux, and the Hybrid Diffusion with Continuous Switch.Besides the straightforward filtering application, both RORPO features are designed to be used as prior information to characterize curvilinear structures. We propose a regularization term for variational segmentation which embed these features. Classic regularization terms are not adapted to curvilinear structures and usually lead to the loss of most of the low-contrasted ones. We propose to only regularize curvilinear structures along their main axis thanks to both RORPO features. This directional regularization better preserves curvilinear structures but also reconnect parts of these structures which may have been disconnected by noise.We present results of the segmentation of retinal images with the Chan et al. model either with the classic total variation or our directional regularization term. This confirm that our regularization term is better suited for images with curvilinear structures

In modern society, cancer has become one of the most terrifying diseases because of its high and increasing death rate. The disease's deep impact demands extensive research to detect and eradicate it in all its forms. Breast cancer is one of the most common forms of cancer, and approximately one in nine women in the Western world will develop it over the course of their lives. Screening programmes have been shown to reduce the mortality rate, but they introduce an enormous amount of information that must be processed by radiologists on a daily basis. Computer Aided Diagnosis (CAD) systems aim to assist clinicians in their decision-making process, by acting as a second opinion and helping improve the detection and classification ratios by spotting very difficult and subtle cases. Although the field of cancer detection is rapidly developing and crosses over imaging modalities, X-ray mammography remains the principal tool to detect the first signs of breast cancer in population screening. The advantages and disadvantages of other imaging modalities for breast cancer detection are discussed along with the improvements and difficulties encountered in screening programmes. Remarkable achievements to date in breast CAD are equally presented. This thesis introduces original results for the detection of features from mammographic image analysis to improve the effectiveness of early cancer screening programmes. The detection of early signs of breast cancer is vital in managing such a fast developing disease with poor survival rates. Some of the earliest signs of cancer in the breast are the clusters of microcalcifications. The proposed method is based on image filtering comprising partial differential equations (PDE) for image enhancement. Subsequently, microcalcifications are segmented using characteristics of the human visual system, based on the superior qualities of the human eye to depict localised changes of intensity and appearance in an image. Parameters are set according to the image characteristics, which makes the method fully automated. The detection of breast masses in temporal mammographic pairs is also investigated as part of the development of a complete breast cancer detection tool. The design of this latter algorithm is based on the detection sequence used by radiologists in clinical routine. To support the classification of masses into benign or malignant, novel tumour features are introduced. Image normalisation is another key concept discussed in this thesis along with its benefits for cancer detection.