生活中在使用相機時，由於機器晃動或物體移動所造成的模糊影像時常可見。當影像模糊的成因是影像曝光時間內相機與拍攝物體相對線性移動時，則我們稱為線性動態模糊。理論上，模糊影像可以表示成原始影像與點擴散函數的旋積，本文的研究重點為點擴散函數中模糊參數的估計，雷登轉換將被運用在此問題上。我們首先介紹兩個現有方法，我們將探討這些方法中用來消除雜訊的步驟之適用性及必要性。另一方面，在模糊參數的估計過程中，我們在雷登轉換加入圓限制以及採用移動平均法。我們透過實驗證實，本篇提出的方法可以獲得更準確的估計結果以及更好的模糊影像還原效果。 / Nowadays, collecting a digital image becomes convenient and low-cost due to rapid progress in digital camera technology. Blurred images frequently appear because of camera shake or moving objects. There are several different types of blur. When the blur is caused by the linear motion between the object and the camera during the light exposure, it’s called a linear motion blur. Mathematically, a blurred image is expressed as a convolution of a point spread function and the original image. Our study considers Radon transform for the estimation of the point spread function. To improve the existing methods, a circle restriction and the moving average method are applied in the estimating procedure. Through intensive experiments, the proposed method is found enable to produce more accurate estimation and better performance in image restoration.

Les ``C-arm'' sont des systémes de radiologie interventionnelle fréquemment utilisés en salle d'opération ou au lit du patient. Des images 3D des structures anatomiques internes peuvent être calculées à partir de multiples radiographies acquises sur un ``C-arm mobile'' et isocentrique décrivant une trajectoire généralement circulaire autour du patient. Pour cela, la géométrie conique d'acquisition de chaque radiographie doit être précisément connue. Malheureusement, les C-arm se déforment en général au cours de la trajectoire. De plus leur motorisation engendre des oscillations non reproductibles. Ils doivent donc être calibrés au cours de l'acquisition. Ma thèse concerne la calibration intrinsèque d'un C-arm à partir de la détection de la projection du collimateur de la source dans les radiographies.Nous avons développé une méthode de détection de la projection des bords linéaires du collimateur. Elle surpasse les méthodes classiques comme le filtre de Canny sur données simulées ou réelles. La précision que nous obtenons sur l'angle et la position (phi,s) des droites est de l'ordre de: phi{RMS}=+/- 0.0045 degrees et s{RMS}=+/- 1.67 pixels. Nous avons évalué nos méthodes et les avons comparés à des méthodes classiques de calibration dans le cadre de la reconstruction 3D. / Mobile isocentric x-ray C-arm systems are an imaging tool used during a variety of interventional and image guided procedures. Three-dimensional images can be produced from multiple projection images of a patient or object as the C-arm rotates around the isocenter provided the C-arm geometry is known. Due to gravity affects and mechanical instabilities the C-arm source and detector geometry undergo significant non-ideal and possibly non reproducible deformation which requires a process of geometric calibration. This research investigates the use of the projection of the slightly closed x-ray tube collimator edges in the image field of view to provide the online intrinsic calibration of C-arm systems.A method of thick straight edge detection has been developed which outperforms the commonly used Canny filter edge detection technique in both simulation and real data investigations. This edge detection technique has exhibited excellent precision in detection of the edge angles and positions, (phi,s), in the presence of simulated C-arm deformation and image noise: phi{RMS} = +/- 0.0045 degrees and s{RMS} = +/- 1.67 pixels. Following this, the C-arm intrinsic calibration, by means of accurate edge detection, has been evaluated in the framework of 3D image reconstruction.

The focus of this thesis is variational image restoration techniques that involve novel non-smooth first-order gradient regularisers: Total Variation (TV) regularisation in image and data space for reconstruction of thin structures from PET data and regularisers given by an infimal-convolution of TV and $L^p$ seminorms for denoising images with piecewise affine structures. In the first part of this thesis, we present a novel variational model for PET reconstruction. During a PET scan, we encounter two different spaces: the sinogram space that consists of all the PET data collected from the detectors and the image space where the reconstruction of the unknown density is finally obtained. Unlike most of the state of the art reconstruction methods in which an appropriate regulariser is designed in the image space only, we introduce a new variational method incorporating regularisation in image and sinogram space. In particular, the corresponding minimisation problem is formed by a total variational regularisation on both the sinogram and the image and with a suitable weighted $L^2$ fidelity term, which serves as an approximation to the Poisson noise model for PET. We establish the well-posedness of this new model for functions of Bounded Variation (BV) and perform an error analysis through the notion of the Bregman distance. We examine analytically how TV regularisation on the sinogram affects the reconstructed image especially the boundaries of objects in the image. This analysis motivates the use of a combined regularisation principally for reconstructing images with thin structures. In the second part of this thesis we propose a first-order regulariser that is a combination of the total variation and $L^p$ seminorms with $1 < p \le \infty$. A well-posedness analysis is presented and a detailed study of the one dimensional model is performed by computing exact solutions for simple functions such as the step function and a piecewise affine function, for the regulariser with $p = 2$ and $p = 1$. We derive necessary and sufficient conditions for a pair in $BV \times L^p$ to be a solution for our proposed model and determine the structure of solutions dependent on the value of $p$. In the case $p = 2$, we show that the regulariser is equivalent to the Huber-type variant of total variation regularisation. Moreover, there is a certain class of one dimensional data functions for which the regularised solutions are equivalent to high-order regularisers such as the state of the art total generalised variation (TGV) model. The key assets of our regulariser are the elimination of the staircasing effect - a well-known disadvantage of total variation regularisation - the capability of obtaining piecewise affine structures for $p = 1$ and qualitatively comparable results to TGV. In addition, our first-order $TVL^p$ regulariser is capable of preserving spike-like structures that TGV is forced to smooth. The numerical solution of the proposed first-order model is in general computationally more efficient compared to high-order approaches.

Les Distributions de Partons Généralisées (GPDs) encodent les corrélations entre impulsion longitudinale et position transverse des partons dans les hadrons et permettent d'imager la structure du nucléon en 2+1 dimensions. Elles ont été étudiées théoriquement et expérimentalement pendant deux décennies et une nouvelle ère expérimentale débute actuellement (à Jefferson Lab et COMPASS, mais aussi à l'avenir à un collisionneur électron-ion) pour les extraire avec grande précision. La difficulté est que seul un accès expérimental indirect est possible, à travers divers canaux de diffusion exclusive et les observables associés. Cela implique de prendre nécessairement en compte les nombreuses contraintes théoriques si l'on veut concevoir des modèles fiables pour la phénoménologie. En particulier, deux contraintes cruciales sont les propriétés de "polynomialité" et de "positivité". L'approche de cette thèse consiste à tirer partie des deux propriétés en modélisant d'abord les fonctions d'onde sur le cône de lumière des premiers états de Fock du nucléon, permettant d'obtenir une GPD dans la région appelée DGLAP via overlap où le nombre de partons est conservé, puis l'étendre de manière covariante à la région ERBL, avec une inversion de transformée de Radon. In fine, le but est d'appliquer cette procédure à un modèle de quark-constituant pour GPDs de valence, ce qui permettrait de produire de manière inédite pour ce genre de modèle des résultats à comparer à l'expérience (sur le processus de diffusion Compton profondément virtuelle en l’occurrence). Pour atteindre cette objectif, on utilise la librairie PARTONS sous différentes hypothèses perturbatives. / Generalized Parton Distributions (GPDs) encode the correlations between longitudinal momentum and transverse position of partons inside hadrons and can give access to a picture of the nucleon structure in 2+1 dimensions. They have been studied theoretically and experimentally for almost two decades and a new experimental era is starting (at JLab and COMPASS currently, and in the future at an EIC) to extract them. The difficulty is that only an indirect experimental access is so far possible, through different exclusive channels and various observables. Therefore, one has to take into account the many theoretical constraints to be able to produce accurate models and rely on their phenomenology. Two important constraints are called the polynomiality and positivity properties. The approach of this thesis is to make use of both of them by first modeling low Fock states light-front wave-functions, which gives a GPD in the DGLAP region by a parton number conserved overlap, and then covariantly extending this GPD to the ERBL region, through an inverse radon transform. In fine, the goal is to apply this on a constituent quark-like model for valence GPDs, which would allow to produce a phenomenological output (on DVCS data for instance) from this kind of models, which was impossible before. We make use of the versatile PARTONS framework to achieve this under various perturbative QCD assumptions.

No description available.

Atributos visuais de textura e forma foram investigados para a recuperação baseada em conteúdo de imagens mamográficas (CBIR). Para a similaridade de imagens, foi considerada a estrutura de densidade mamária, representada principalmente pelos tecidos fibro-glandulares. A pesquisa consistiu de três etapas: (1) Preparação e processamento das imagens; (2) Extração e seleção de atributos visuais de textura e forma; (3) Implementação de um sistema de recuperação de imagem. A primeira etapa consistiu dos processos de retirada de ruído do fundo da imagem, segmentação da região da mama, detecção da região de músculo peitoral, localização do mamilo e da segmentação da região de tecidos fibro-glandulares. Utilizou-se a equação de Difusão Anisotrópica com filtro de Wiener para retirada e suavização de ruídos encontrados na imagem e preservação da borda da mama. Para a segmentação da região da mama, foram utilizadas as técnicas de limiarização de Princípio de Máxima Entropia, Método de Preservação de Momento, Método de Otsu, Método interativo de Ridler & Carvard, Método de Reddi e Método da Matriz de Co-ocorrência. A melhor imagem foi escolhida numa tarefa supervisionada. A detecção automática da região do músculo peitoral foi feita com a combinação do operador de Canny e a transformada de Radon como detector de linha. A posição do mamilo foi detectada com a transformada de Radon como detector de direção de densidade. A segmentação da região de tecidos fibro-glandulares foi feita também com as técnicas de limiarização do Princípio de Máxima Entropia, Método de Preservação de Momento, e Método de Otsu. Momentos Estatísticos extraídos do Histograma, Medida de Granulometria, Momentos Estatísticos extraídos do Domínio de Radon, Momento de Hu, e Textura de Haralick foram investigados como atributos de textura. Medida de Área, Circularidade e Razão de Diâmetro foram investigados como atributos de forma. A rede de Mapas Auto-Organizáveis de Kohonen foi utilizada como sistema de recuperação de imagem. Foram utilizadas, neste trabalho, 1080 imagens do projeto de Banco de Imagens do HCFMRP-USP, módulo Mamografia. O treinamento e teste foram feitos com a técnica de \"leaving-one-out\" e os melhores resultados obtidos foram: Taxa de precisão de 91,07% para a combinação dos cinco grupos de atributos de Forma, Estatísticos Extraídos do Histograma, Momento de Hu, Espectral no Domínio de Radon e de Medida de Granulometria; taxa de precisão e revocação do coeficiente de correlação médio representadas pela área sob a curva com valor de 0,02351 dos grupos de atributos de forma, de Textura de Haralick e Momento de Hu. Os resultados obtidos indicaram a relevância de nosso trabalho e seu potencial de utilização para a recuperação baseada em conteúdo de imagens mamográficas. / Visual texture based on texture and shape features were investigated for content-based mammographic images retrieval (CBIR). For similarity of images, the mammary density structures were considered, mainly represented by fibro-glandular tissues. This research consisted of three stages: (1) Images preparation and processing; (2) Extraction and selection of the visual features; (3) Implementation of a retrieval system. The first stage consisted of noisy removing from the image background, breast region segmentation, pectoral muscle region detection, nipple localization and the fibro-glandular tissues region segmentation. The equation of Anisotropic Diffusion was used with Wiener filter for noisy removing with the breast region edge preservation. For the breast region segmentation, the Thresholding techniques were used of Maximum Entropy Principle, Moment Preserving Method, Otsu Method, Ridler & Carvard Method, Reddi Method and Co-occurrence Matrix Method. The better image was chosen in a supervised task. The automatic pectoral muscle region detection was made with the Canny operator and Radon Transform combination as straight line detector. The nipple position was detected with the Radon Transform as density direction detector. The fibro-glandular tissues region was also defined with the thresholding techniques of the Maximum Entropy Principle, Moment Preserving Method, and Otsu Method. The Statistical Moments extracted from the Histogram, Measured of Granulometry, Statistical Moments extracted in Radon Domain, Moment of Hu, and Haralick Textures were investigated as texture features. Area, Circularity and Diameter Ratio were investigated as shape features. The Self-Organizing Maps of Kohonen was used as image retrieval system. One thousand and eighty images of the HCFMRP-USP Database Project, Mammography Module, were used in this work. The training and test processes were realized with the \"leaving-one-out\" technique and the best results obtained were: The precision rate of 91,07% for the combination of the five following features group: Shape, Statistical Moments extracted of the Histogram, Moment of Hu, Statistical Moments extracted in Radon Domain and Measure of Granulometry; precision and revocation rates of the average coefficient of correlation represented by the area under the curve with value of 0,02351 for the three following features group: Shape, Haralick Textures and Moment de Hu. The results obtained indicated the relevance of our work for the content-based mammographic images retrieval.

Atributos visuais de textura e forma foram investigados para a recuperação baseada em conteúdo de imagens mamográficas (CBIR). Para a similaridade de imagens, foi considerada a estrutura de densidade mamária, representada principalmente pelos tecidos fibro-glandulares. A pesquisa consistiu de três etapas: (1) Preparação e processamento das imagens; (2) Extração e seleção de atributos visuais de textura e forma; (3) Implementação de um sistema de recuperação de imagem. A primeira etapa consistiu dos processos de retirada de ruído do fundo da imagem, segmentação da região da mama, detecção da região de músculo peitoral, localização do mamilo e da segmentação da região de tecidos fibro-glandulares. Utilizou-se a equação de Difusão Anisotrópica com filtro de Wiener para retirada e suavização de ruídos encontrados na imagem e preservação da borda da mama. Para a segmentação da região da mama, foram utilizadas as técnicas de limiarização de Princípio de Máxima Entropia, Método de Preservação de Momento, Método de Otsu, Método interativo de Ridler & Carvard, Método de Reddi e Método da Matriz de Co-ocorrência. A melhor imagem foi escolhida numa tarefa supervisionada. A detecção automática da região do músculo peitoral foi feita com a combinação do operador de Canny e a transformada de Radon como detector de linha. A posição do mamilo foi detectada com a transformada de Radon como detector de direção de densidade. A segmentação da região de tecidos fibro-glandulares foi feita também com as técnicas de limiarização do Princípio de Máxima Entropia, Método de Preservação de Momento, e Método de Otsu. Momentos Estatísticos extraídos do Histograma, Medida de Granulometria, Momentos Estatísticos extraídos do Domínio de Radon, Momento de Hu, e Textura de Haralick foram investigados como atributos de textura. Medida de Área, Circularidade e Razão de Diâmetro foram investigados como atributos de forma. A rede de Mapas Auto-Organizáveis de Kohonen foi utilizada como sistema de recuperação de imagem. Foram utilizadas, neste trabalho, 1080 imagens do projeto de Banco de Imagens do HCFMRP-USP, módulo Mamografia. O treinamento e teste foram feitos com a técnica de \"leaving-one-out\" e os melhores resultados obtidos foram: Taxa de precisão de 91,07% para a combinação dos cinco grupos de atributos de Forma, Estatísticos Extraídos do Histograma, Momento de Hu, Espectral no Domínio de Radon e de Medida de Granulometria; taxa de precisão e revocação do coeficiente de correlação médio representadas pela área sob a curva com valor de 0,02351 dos grupos de atributos de forma, de Textura de Haralick e Momento de Hu. Os resultados obtidos indicaram a relevância de nosso trabalho e seu potencial de utilização para a recuperação baseada em conteúdo de imagens mamográficas. / Visual texture based on texture and shape features were investigated for content-based mammographic images retrieval (CBIR). For similarity of images, the mammary density structures were considered, mainly represented by fibro-glandular tissues. This research consisted of three stages: (1) Images preparation and processing; (2) Extraction and selection of the visual features; (3) Implementation of a retrieval system. The first stage consisted of noisy removing from the image background, breast region segmentation, pectoral muscle region detection, nipple localization and the fibro-glandular tissues region segmentation. The equation of Anisotropic Diffusion was used with Wiener filter for noisy removing with the breast region edge preservation. For the breast region segmentation, the Thresholding techniques were used of Maximum Entropy Principle, Moment Preserving Method, Otsu Method, Ridler & Carvard Method, Reddi Method and Co-occurrence Matrix Method. The better image was chosen in a supervised task. The automatic pectoral muscle region detection was made with the Canny operator and Radon Transform combination as straight line detector. The nipple position was detected with the Radon Transform as density direction detector. The fibro-glandular tissues region was also defined with the thresholding techniques of the Maximum Entropy Principle, Moment Preserving Method, and Otsu Method. The Statistical Moments extracted from the Histogram, Measured of Granulometry, Statistical Moments extracted in Radon Domain, Moment of Hu, and Haralick Textures were investigated as texture features. Area, Circularity and Diameter Ratio were investigated as shape features. The Self-Organizing Maps of Kohonen was used as image retrieval system. One thousand and eighty images of the HCFMRP-USP Database Project, Mammography Module, were used in this work. The training and test processes were realized with the \"leaving-one-out\" technique and the best results obtained were: The precision rate of 91,07% for the combination of the five following features group: Shape, Statistical Moments extracted of the Histogram, Moment of Hu, Statistical Moments extracted in Radon Domain and Measure of Granulometry; precision and revocation rates of the average coefficient of correlation represented by the area under the curve with value of 0,02351 for the three following features group: Shape, Haralick Textures and Moment de Hu. The results obtained indicated the relevance of our work for the content-based mammographic images retrieval.

Diffusion-weighted magnetic resonance imaging (MRI) has allowed unprecedented non-invasive mapping of brain neural connectivity in vivo by means of fiber tractography applications. Fiber tractography has emerged as a useful tool for mapping brain white matter connectivity prior to surgery or in an intraoperative setting. The advent of high angular resolution diffusion-weighted imaging (HARDI) techniques in MRI for fiber tractography has allowed mapping of fiber tracts in areas of complex white matter fiber crossings. Raw HARDI images, as a result of elevated diffusion-weighting, suffer from depressed signal-to-noise ratio (SNR) levels. The accuracy of fiber tractography is dependent on the performance of the various methods extracting dominant fiber orientations from the HARDI-measured noisy diffusivity profiles. These methods will be sensitive to and directly affected by the noise. In the first part of the thesis this issue is addressed by applying an objective and adaptive smoothing to the noisy HARDI data via generalized cross-validation (GCV) by means of the smoothing splines on the sphere method for estimating the smooth diffusivity profiles in three dimensional diffusion space. Subsequently, fiber orientation distribution functions (ODFs) that reveal dominant fiber orientations in fiber crossings are then reconstructed from the smoothed diffusivity profiles using the Funk-Radon transform. Previous ODF smoothing techniques have been subjective and non-adaptive to data SNR. The GCV-smoothed ODFs from our method are accurate and are smoothed without external intervention facilitating more precise fiber tractography. Diffusion-weighted MRI studies in amyotrophic lateral sclerosis (ALS) have revealed significant changes in diffusion parameters in ALS patient brains. With the need for early detection of possibly discrete upper motor neuron (UMN) degeneration signs in patients with early ALS, a HARDI study is applied in order to investigate diffusion-sensitive changes reflected in the diffusion tensor imaging (DTI) measures axial and radial diffusivity as well as the more commonly used measures fractional anisotropy (FA) and mean diffusivity (MD). The hypothesis is that there would be added utility in considering axial and radial diffusivities which directly reflect changes in the diffusion tensors in addition to FA and MD to aid in revealing neurodegenerative changes in ALS. In addition, applying adaptive smoothing via GCV to the HARDI data further facilitates the application of fiber tractography by automatically eliminating spurious noisy peaks in reconstructed ODFs that would mislead fiber tracking.

Cette étude est consacrée aux distributions de partons généralisées (GPDs, de l'anglais Generalised Parton Distributions). Dans un premier temps, les principales propriétés des GPDs sont rappelées. On insiste notamment sur les propriétés dites de support et sur la polynomialité. Cette dernière est automatiquement respectée lorsque l'on modélise les GPDs au travers des doubles distributions (DDs), les GPDs s'écrivant comme la transformée de Radon des DDs.Dans le cas scalaire, deux DDs, notées F et G, sont nécessaires pour décrire la GPD H. Du fait de la relation intégrale existant entre H d'un côté, et F et G de l'autre, F et G sont définies de manière ambiguë. Cette ambiguïté est exploitée dans le présent travail afin de développer une nouvelle paramétrisation phénoménologique. Utilisant l'Ansatz de Radyushkin, il est possible d'obtenir un modèle réaliste de GPD, et de le comparer aux données expérimentales disponibles. Dans le cas présent, deux types de modèles, l'un négligeant la GPD E, l'autre en tenant compte, sont comparés aux données de diffusion Compton profondément virtuelle (DVCS) de la collaboration Hall A au Jeffeson Laboratory (JLab). Dans le premier cas, on observe une plus grande flexibilité de la paramétrisation par rapport aux précédentes, ce qui permet une meilleure comparaison aux données sur les sections efficaces indépendantes de l'hélicité du faisceau. Dans le second cas, seule la GPD E est profondément modifiée. De ce fait la comparaison aux données change peu par rapport aux modèles précédents. Seules des données plus sensibles à E permettront de trancher entre les paramétrisations.Afin de dépasser les paramétrisations phénoménologiques, un premier pas a été fait vers la description dynamique des hadrons. En utilisant les équations de Dyson-Schwinger, il a été possible de calculer analytiquement la GPD de pion dans le cadre de l'approximation du diagramme triangle. La comparaison aux données expérimentales disponibles (facteur de forme et PDF) s'est révélée très bonne. Il est également possible de montrer que l'approximation du diagramme triangle permet de retrouver le théorème de pion mou. Néanmoins, ce premier modèle ne respecte pas l'ensemble des propriétés des GPDs. Elle viole la symétrie d'échange x, 1-x, et par conséquent des termes supplémentaires, précédemment négligés, sont pris en compte. On peut ainsi obtenir la densité de probabilité de trouver un quark portant une fraction d'impulsion x dans le plan transverse. Des perspectives de calculs sur le cône de lumière sont présentés dans le dernier chapitre. / This study is devoted to generalised parton distributions (GPDs). First, the main properties of GPDs are given to the reader. One can stress the so-called support properties and the polynomiality property. The latter is automatically fulfiled when modeling GPDs from double distributions (DDs), GPDs being considered as the Radon transform of DDs. In the scalar case, two DDs denoted by F and G are required to describe the GPD H. Due to the integral relation existing between H on one hand, and F and G on the other hand, F and G are not defnied unambiguously. This ambiguity is exploited in the present work in order to develop a new phenomenological parametrisation. Using the Radyushkin Ansatz, it is then possible get a realistic model of GPDs, and to compare it with available experimental data. In the present case, two types of models, one neglecting the GPD E, the other taking it into account are compared with the Jlab Hall A DVCS data. In the former cae, one can notice a better flexibility allowing to better reproduced the beam-helicity independent cross sections. In the latter one, only the GPD E is deeply modified, and thus the comparison with available data does not change significantly with respect to previous parametrisations. Only data more sensitive to E will allow one to selet the most relevant parametrisation.In order to go beyond phenomenological parametrisations, a first step has been done toward a dynamical description of hadron structure. Using the Dyson-Schwinger equations, it has been possible to compute analytically the pion GPD within the triangle diagram approximation. The comparison with available data (Form factor and PDF) appears to be very good. Nevertheless, this first model does not fulfil all the required properties. Especially the soft pion theorem, which corresponds to a specific kinematical limit. It has been shown in this work that this is due to the violation of the Axial-Vector Ward-Takahashi identity, and that the triangle approximation is sufficient to ensure the sof pion theorem. Still it violates the exchange symmetry x, 1-x, and thus additional terms, previously neglected, are taken into account. It is then possible to compute the probability density to find a quark at a given position in the transverse plan carrying a given momentum fraction. Finally, perspective on lightcone computations are given in the last chapter.