Os métodos incrementais pertencem a uma classe de métodos iterativos que divide o conjunto de dados em subconjuntos ordenados, e que atualiza a imagem ao processar cada subconjunto (sub-iterações). Isso acelera a convergência das reconstruções, e imagens de qualidade são obtidas em menos iterações. No entanto, a cada sub-iteração é necessário calcular os operadores de projeção e retroprojeção, resultando no custo computacional de ordem O(n3) para a reconstrução de imagens de dimensão × . Por outro lado, algumas alternativas baseadas na interpolação em uma grade regular no espaço de Fourier ou em transformadas rápidas não-uniformes, dentre outras ideias, foram desenvolvidas a fim de aliviar esse custo computacional. Além disso, diversas abordagens foram bem sucedidas em acelerar o cálculo das iterações de algoritmos clássicos, mas nenhuma havia sido utilizada em conjunto com os métodos incrementais. Neste trabalho é proposta uma nova abordagem em que a técnica de transformada rápida de Fourier não uniforme (NFFT) é utilizada nas sub-iterações de métodos incrementais com o objetivo de efetuar de forma eficiente os cálculos numericamente mais intensos: a projeção e a retroprojeção, resultando em métodos incrementais com complexidade O(n2 log n ). Os métodos propostos são aplicados à tomografia por radiação síncrotron e os resultados da pesquisa mostram um bom desempenho. / Incremental methods belong to a class of iterative methods that divide the data set into ordered subsets, and which update the image when processing each subset (sub-iterations). It accelerates the reconstruction convergence and quality images are obtained in fewer iterations. However, it is necessary to compute the projection and backprojection operators in each sub-iteration, resulting in the computational cost of O(n3) flops for × images. On the other hand, some alternatives based on interpolation over a regular grid on the Fourier space or on nonequispaced fast transforms, among other ideas, were developed in order to alleviate the computational cost. In addition, several approaches substantially speed up the computation of the iterations of classical algorithms, but the incremental methods had not been benefited from these techniques. In this work, a new approach is proposed in which the nonequispaced fast Fourier transform (NFTT) is used in each subiteration of incremental methods in order to perform the numerically intensive calculations efficiently: the projection and backprojection, resulting in incremental methods with complexity O(n2 log n ). The proposed methods are applied to the synchrotron radiation tomography and the results show a good performance.

La reconstruction tomographique à partir de données de projections est un problème inverse largement utilisé en imagerie médicale et de façon plus modeste pour le contrôle nondestructif. Avec un nombre suffisant de projections, les algorithmes analytiques permettentdes reconstructions rapides et précises. Toutefois, dans le cas d’un faible nombre de vues(imagerie faible dose) et/ou d’angle limité (contraintes spécifiques liées à l’installation), lesdonnées disponibles pour l’inversion ne sont pas complètes, le mauvais conditionnementdu problème s’accentue, et les résultats montrent des artefacts importants. Pour aborderces situations, une approche alternative consiste à discrétiser le problème de reconstruction,et à utiliser des algorithmes itératifs ou une formulation statistique du problème afinde calculer une estimation de l’objet inconnu. Ces méthodes sont classiquement basées surune discrétisation du volume en un ensemble de voxels, et fournissent des cartes 3D de ladensité de l’objet étudié. Les temps de calcul et la ressource mémoire de ces méthodesitératives sont leurs principaux points faibles. Par ailleurs, quelle que soit l’application, lesvolumes sont ensuite segmentés pour une analyse quantitative. Devant le large éventaild’outils de segmentation existant, basés sur différentes interprétations des contours et defonctionnelles à minimiser, les choix sont multiples et les résultats en dépendent.Ce travail de thèse présente une nouvelle approche de reconstruction simultanée àla segmentation des différents matériaux qui composent le volume. Le processus dereconstruction n’est plus basé sur une grille régulière de pixels (resp. voxels), mais sur unmaillage composé de triangles (resp. tétraèdres) non réguliers qui s’adaptent à la formede l’objet. Après une phase d’initialisation, la méthode se décompose en trois étapesprincipales que sont la reconstruction, la segmentation et l’adaptation du maillage, quialternent de façon itérative jusqu’à convergence. Des algorithmes itératifs de reconstructioncommunément utilisés avec une représentation conventionnelle de l’image ont étéadaptés et optimisés pour être exécutés sur des grilles irrégulières composées d’élémentstriangulaires ou tétraédriques. Pour l’étape de segmentation, deux méthodes basées surune approche paramétrique (snake) et l’autre sur une approche géométrique (level set)ont été mises en oeuvre afin de considérer des objets de différentes natures (mono- etmulti- matériaux). L’adaptation du maillage au contenu de l’image estimée est basée surles contours segmentés précédemment, pour affiner la maille au niveau des détails del’objet et la rendre plus grossière dans les zones contenant peu d’information. En finde processus, le résultat est une image classique de reconstruction tomographique enniveaux de gris, mais dont la représentation par un maillage adapté au contenu proposeidirectement une segmentation associée. Les résultats montrent que la partie adaptative dela méthode permet de représenter efficacement les objets et conduit à diminuer drastiquementla mémoire nécessaire au stockage. Dans ce contexte, une version 2D du calcul desopérateurs de reconstruction sur une architecture parallèle type GPU montre la faisabilitédu processus dans son ensemble. Une version optimisée des opérateurs 3D permet descalculs encore plus efficaces. / Tomography reconstruction from projections data is an inverse problem widely used inthe medical imaging field. With sufficiently large number of projections over the requiredangle, the FBP (filtered backprojection) algorithms allow fast and accurate reconstructions.However in the cases of limited views (lose dose imaging) and/or limited angle (specificconstrains of the setup), the data available for inversion are not complete, the problembecomes more ill-conditioned, and the results show significant artifacts. In these situations,an alternative approach of reconstruction, based on a discrete model of the problem,consists in using an iterative algorithm or a statistical modelisation of the problem to computean estimate of the unknown object. These methods are classicaly based on a volumediscretization into a set of voxels and provide 3D maps of densities. Computation time andmemory storage are their main disadvantages. Moreover, whatever the application, thevolumes are segmented for a quantitative analysis. Numerous methods of segmentationwith different interpretations of the contours and various minimized energy functionalare offered, and the results can depend on their use.This thesis presents a novel approach of tomographic reconstruction simultaneouslyto segmentation of the different materials of the object. The process of reconstruction isno more based on a regular grid of pixels (resp. voxel) but on a mesh composed of nonregular triangles (resp. tetraedra) adapted to the shape of the studied object. After aninitialization step, the method runs into three main steps: reconstruction, segmentationand adaptation of the mesh, that iteratively alternate until convergence. Iterative algorithmsof reconstruction used in a conventionnal way have been adapted and optimizedto be performed on irregular grids of triangular or tetraedric elements. For segmentation,two methods, one based on a parametric approach (snake) and the other on a geometricapproach (level set) have been implemented to consider mono and multi materials objects.The adaptation of the mesh to the content of the estimated image is based on the previoussegmented contours that makes the mesh progressively coarse from the edges to thelimits of the domain of reconstruction. At the end of the process, the result is a classicaltomographic image in gray levels, but whose representation by an adaptive mesh toits content provide a correspoonding segmentation. The results show that the methodprovides reliable reconstruction and leads to drastically decrease the memory storage. Inthis context, the operators of projection have been implemented on parallel archituecturecalled GPU. A first 2D version shows the feasability of the full process, and an optimizedversion of the 3D operators provides more efficent compoutations.

Os métodos incrementais pertencem a uma classe de métodos iterativos que divide o conjunto de dados em subconjuntos ordenados, e que atualiza a imagem ao processar cada subconjunto (sub-iterações). Isso acelera a convergência das reconstruções, e imagens de qualidade são obtidas em menos iterações. No entanto, a cada sub-iteração é necessário calcular os operadores de projeção e retroprojeção, resultando no custo computacional de ordem O(n3) para a reconstrução de imagens de dimensão × . Por outro lado, algumas alternativas baseadas na interpolação em uma grade regular no espaço de Fourier ou em transformadas rápidas não-uniformes, dentre outras ideias, foram desenvolvidas a fim de aliviar esse custo computacional. Além disso, diversas abordagens foram bem sucedidas em acelerar o cálculo das iterações de algoritmos clássicos, mas nenhuma havia sido utilizada em conjunto com os métodos incrementais. Neste trabalho é proposta uma nova abordagem em que a técnica de transformada rápida de Fourier não uniforme (NFFT) é utilizada nas sub-iterações de métodos incrementais com o objetivo de efetuar de forma eficiente os cálculos numericamente mais intensos: a projeção e a retroprojeção, resultando em métodos incrementais com complexidade O(n2 log n ). Os métodos propostos são aplicados à tomografia por radiação síncrotron e os resultados da pesquisa mostram um bom desempenho. / Incremental methods belong to a class of iterative methods that divide the data set into ordered subsets, and which update the image when processing each subset (sub-iterations). It accelerates the reconstruction convergence and quality images are obtained in fewer iterations. However, it is necessary to compute the projection and backprojection operators in each sub-iteration, resulting in the computational cost of O(n3) flops for × images. On the other hand, some alternatives based on interpolation over a regular grid on the Fourier space or on nonequispaced fast transforms, among other ideas, were developed in order to alleviate the computational cost. In addition, several approaches substantially speed up the computation of the iterations of classical algorithms, but the incremental methods had not been benefited from these techniques. In this work, a new approach is proposed in which the nonequispaced fast Fourier transform (NFTT) is used in each subiteration of incremental methods in order to perform the numerically intensive calculations efficiently: the projection and backprojection, resulting in incremental methods with complexity O(n2 log n ). The proposed methods are applied to the synchrotron radiation tomography and the results show a good performance.

Orientador: Denis Henrique Pinheiro Salvadeo / Resumo: Tomossíntese Mamária Digital (DBT) é uma técnica de imageamento radiográfico, com aquisição de projeções em ângulos limitados utilizando dose reduzida de radiação. Ela tem por objetivo reconstruir fatias tomográficas do interior da mama, possibilitando o diagnóstico precoce de possíveis lesões e aumentando, consequentemente, a probabilidade de cura do paciente. Contudo, devido ao fato de que DBT utiliza doses baixas de radiação, a imagem gerada contém mais ruído que a mamografia digital. Embora a qualidade do exame esteja diretamente relacionada com a dose utilizada, espera-se que a dose de radiação empregada no exame seja a mais baixa possível, mas ainda com qualidade suficiente para que o diagnóstico possa ser realizado, conforme o princípio As Low As Reasonably Achievable (ALARA). Uma das etapas importantes para se buscar o princípio ALARA é a reconstrução tomográfica, que consiste em um software que gera as fatias do interior da mama a partir de um conjunto de projeções 2D de DBT adquiridas. Por outro lado, técnicas de Aprendizado de Máquina, especialmente redes neurais com aprendizado profundo, que recentemente tem evoluído consideravelmente o estado da arte em diversos problemas de Visão Computacional e Processamento de Imagens, tem características adequadas para serem aplicadas também na etapa de reconstrução. Deste modo, este trabalho investigou uma arquitetura básica de rede neural artificial com aprendizado profundo que seja capaz de reconstruir imagens de DBT, espe... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Digital Breast Tomosynthesis (DBT) is a technique of radiographic imaging, with acquisition of projections at limited angles using reduced dose of radiation. It aims to reconstruct tomographic slices inside the breast, making possible the early diagnosis of possible lesions and, consequently, increasing the probability of cure of the patient. However, due to the fact that DBT uses low doses of radiation, the generated image contains more noise than digital mammography. Although the quality of the exam is directly related to the dose applied, the radiation dose used in the examination is expected to be as low as possible, but still keeping enough quality for the diagnosis to be made, as determined by the As Low As Reasonably Achievable (ALARA) principle. One of the important steps to achieve the ALARA principle is the tomographic reconstruction, which consists of a software that generates slices inside the breast from an acquired set of 2D DBT projections. On the other hand, Machine Learning techniques, especially neural networks with deep learning, that have recently evolved considerably the state-of-the-art in several problems in Computer Vision and Image Processing areas, it has suitable characteristics to be applied also in the reconstruction step. Thus, this work investigated a basic architecture of artificial neural network with deep learning that is capable to reconstruct DBT images, especially focused on noise reduction. Furthermore, considering an additional filtering... (Complete abstract click electronic access below) / Mestre

Positron Emission Tomography (PET) is pivotal in medical imaging but is prone to artifactsfrom physiological movements, notably respiration. These motion artifacts both degradeimage quality and compromise precise attenuation correction. To counteract this, gatingstrategies partition PET data in synchronization with respiratory cycles, ensuring each gatenearly represents a static phase. Additionally, a 3D deep learning image registration modelcan be used for inter-gate motion correction, maximizing the use of the full acquired data. Thisstudy aimed to implement and evaluate two gating strategies: an external device-based approachand a data-driven centroid-of-distribution (COD) trace algorithm, and assess their impact on theperformance of the registration model. Analysis of clinical data from four subjects indicated thatthe external device approach outperformed its data-driven counterpart, which faced challengesin real-patient settings. Post motion compensation, both methods achieved results comparableto state-of-the-art reconstructions, suggesting the deep learning model addressed some data-driven method limitations. However, the motion corrected outputs did not exhibit significantimprovements in image quality over state-of-the-art standards. / Positronemissionstomografi (PET) är fundamentalt inom medicinsk avbildning men påverkasav artefakter orsakade av fysiologiska rörelser, framför allt andning. Dessa artefakter påverkarbildkvaliteten negativt och försvårar korrekt attenueringskorrigering. För att motverka dettakan tekniker för rörelsekorrigering tillämpas. Dessa innefattar gating-tekniker där PET-dataförst synkroniseras med andningscykeln för att därefter segmenterateras i olika så kalladegater som representerar en specifick respiratorisk fas. Vidare kan en 3D djupinlärningsmodellanvändas för att korrigera för rörelserna mellan gaterna, vilket optimerar användningen av allinsamlad data. Denna studie implementerade och undersökte två gating-tekniker: en externenhetsbaserad metod och en datadriven ”centroid-of-distribution (COD)” spår-algoritm, samtanalyserade hur dessa tekniker påverkar prestandan av bildregistreringsmodellen. Utifrånanalysen av kliniska data från fyra patienter visade sig metoden med den externa enhetenvara överlägsen den datadrivna metoden, som hade svårigheter i verkliga patient-situationer.Trots detta visade bildregistreringsmodellen potential att delvis kompensera för den datadrivnametodens begränsningar, då resultatet från båda strategeierna var jämförbara med befintligaklinisk bildrekonstruktion. Dock kunde ingen markant förbättring i bildkvalitet urskiljas av derörelsekorrigerade bilderna jämfört med nuvarande toppstandard.

L'objectif de cette thèse était de quantifier le réseau lacuno-canaliculaire du tissu osseux à partir d’images 3D acquises en nano CT synchrotron de phase. Ceci a nécessité d’optimiser les processus d’acquisition et de reconstruction de phase, ainsi que de développer des méthodes efficaces de traitement d'images pour la segmentation et l’analyse 3D. Dans un premier temps, nous avons étudié et évalué différents algorithmes de reconstruction de phase. Nous avons étendu la méthode de Paganin pour plusieurs distances de propagation et l’avons évaluée et comparée à d’autres méthodes, théoriquement puis sur nos données expérimentales Nous avons développé une chaine d’analyse, incluant la segmentation des images et prenant en compte les gros volumes de données à traiter. Pour la segmentation des lacunes, nous avons choisi des méthodes telles que le filtre médian, le seuillage par hystérésis et l'analyse par composantes connexes. La segmentation des canalicules repose sur une méthode de croissance de région après rehaussement des structures tubulaires. Nous avons calculé des paramètres de porosité, des descripteurs morphologiques des lacunes ainsi que des nombres de canalicules par lacune. Par ailleurs, nous avons introduit des notions de paramètres locaux calculés dans le voisinage des lacunes. Nous avons obtenu des résultats sur des images acquises à différentes tailles de voxel (120nm, 50nm, 30nm) et avons également pu étudier l’impact de la taille de voxel sur les résultats. Finalement ces méthodes ont été utilisées pour analyser un ensemble de 27 échantillons acquis à 100 nm dans le cadre du projet ANR MULTIPS. Nous avons pu réaliser une analyse statistique pour étudier les différences liées au sexe et à l'âge. Nos travaux apportent de nouvelles données quantitatives sur le tissu osseux qui devraient contribuer à la recherche sur les mécanismes de fragilité osseuse en relation avec des maladies comme l’ostéoporose. / Osteoporosis is a bone fragility disease resulting in abnormalities in bone mass and density. In order to prevent osteoporotic fractures, it is important to have a better understanding of the processes involved in fracture at various scales. As the most abundant bone cells, osteocytes may act as orchestrators of bone remodeling which regulate the activities of both osteoclasts and osteoblasts. The osteocyte system is deeply embedded inside the bone matrix and also called lacuno-canalicular network (LCN). Although several imaging techniques have recently been proposed, the 3D observation and analysis of the LCN at high spatial resolution is still challenging. The aim of this work was to investigate and analyze the LCN in human cortical bone in three dimensions with an isotropic spatial resolution using magnified X-ray phase nano-CT. We performed image acquisition at different voxel sizes of 120 nm, 100 nm, 50 nm and 30 nm in the beamlines ID16A and ID16B of the European Synchrotron Radiation Facility (ESRF - European Synchrotron Radiation Facility - Grenoble). Our first study concerned phase retrieval, which is the first step of data processing and consists in solving a non-linear inverse problem. We proposed an extension of Paganin’s method suited to multi-distance acquisitions, which has been used to retrieve phase maps in our experiments. The method was compared theoretically and experimentally to the contrast transfer function (CTF) approach for homogeneous object. The analysis of the 3D reconstructed images requires first to segment the LCN, including both the segmentation of lacunae and of canaliculi. We developed a workflow based on median filter, hysteresis thresholding and morphology filters to segment lacunae. Concerning the segmentation of canaliculi, we made use of the vesselness enhancement to improve the visibility of line structures, the variational region growing to extract canaliculi and connected components analysis to remove residual noise. For the quantitative assessment of the LCN, we calculated morphological descriptors based on an automatic and efficient 3D analysis method developed in our group. For the lacunae, we calculated some parameters like the number of lacunae, the bone volume, the total volume of all lacunae, the lacunar volume density, the average lacunae volume, the average lacunae surface, the average length, width and depth of lacunae. For the canaliculi, we first computed the total volume of all the canaliculi and canalicular volume density. Moreover, we counted the number of canaliculi at different distances from the surface of each lacuna by an automatic method, which could be used to evaluate the ramification of canaliculi. We reported the statistical results obtained on the different groups and at different spatial resolutions, providing unique information about the organization of the LCN in human bone in three dimensions.

La tomographie d'émission monophotonique (TEMP) dédiée au petit animal est une technique d'imagerie nucléaire qui joue un rôle important en imagerie moléculaire. Les systèmes TEMP, à l'aide de collimateurs pinholes ou multi-pinholes, peuvent atteindre des résolutions spatiales submillimétriques et une haute sensibilité pour un petit champ de vue, ce qui est particulièrement attractif pour imager des souris. Une géométrie de collimation originale a été proposée, dans le cadre d'un projet, appelé SIGAHRS, piloté par la société Biospace. Ce collimateur présente des longueurs focales qui varient spatialement dans le plan transaxial et qui sont fixes dans le plan axial. Une haute résolution spatiale est recherchée au centre du champ de vue, avec un grand champ de vue et une haute sensibilité. Grâce aux simulations Monte Carlo, dont nous pouvons maîtriser tous les paramètres, nous avons étudié cette collimation originale que nous avons positionnée par rapport à un collimateur parallèle et un collimateur monofocal convergent. Afin de générer des données efficacement, nous avons développé un module multi-CPU/GPU qui utilise une technique de lancer de rayons dans le collimateur et qui nous a permis de gagner un facteur ~ 60 en temps de calcul, tout en conservant ~ 90 % du signal, pour l'isotope ⁹⁹^mTc (émettant à 140,5 keV), comparé à une simulation Monte Carlo classique. Cependant, cette approche néglige la pénétration septale et la diffusion dans le collimateur. Les données simulées ont ensuite été reconstruites avec l'algorithme OSEM. Nous avons développé quatre méthodes de projection (une projection simple (S-RT), une projection avec volume d'intersection (S-RT-IV), une projection avec calcul de l'angle solide (S-RT-SA) et une projection tenant compte de la profondeur d'interaction (S-RT-SA-D)). Nous avons aussi modélisé une PSF dans l'espace image, anisotrope et non-stationnaire, en nous inspirant de la littérature existante. Nous avons étudié le conditionnement de la matrice système pour chaque projecteur et collimateur, et nous avons comparé les images reconstruites pour chacun des collimateurs et pour chacun des projecteurs. Nous avons montré que le collimateur original proposé est le système le moins bien conditionné. Nous avons aussi montré que la modélisation de la PSF dans l'image ainsi que de la profondeur d'intéraction améliorent la qualité des images reconstruites ainsi que le recouvrement de contraste. Cependant, ces méthodes introduisent des artefacts de bord. Comparé aux systèmes existants, nous montrons que ce nouveau collimateur a un grand champ de vue (~ 70 mm dans le plan transaxial), avec une résolution de 1,0 mm dans le meilleur des cas, mais qu'il a une sensibilité relativement faible (1,32x10⁻² %). / Small animal single photon emission computed tomography (SPECT) is a nuclear medicine imaging technique that plays an important role in molecular imaging. SPECT systems using pinhole or multi-pinhole collimator can achieve submillimetric spatial resolution and high sensitivity in a small field of view, which is particularly appropriate for imaging mice. In our work, we studied a new collimator dedicated to small animal SPECT, in the context of a project called SIGAHRS, led by the Biospace company. In this collimator, focal lengths vary spatially in the transaxial plane and are fixed in the axial plane. This design aims at achieving high spatial resolution in the center of the field of view, with a large field of view and high sensitivity. Using Monte Carlo simulations, where all parameters can be controlled, we studied this new collimator geometry and compared it to a parallel collimator and a cone-beam collimator. To speed up the simulations, we developed a multi-CPU/GPU module that uses a technique of ray tracing. Using this approach, the acceleration factor was ~ 60 and we restored ~ 90 % of the signal for ⁹⁹^mTc (140.5 keV emission), compared to a classical Monte Carlo simulation. The 10 % difference is due to the fact that the multi-CPU/GPU module neglects the septal penetration and scatter in the collimator. We demonstrated that the data acquired with the new collimator could be reconstructed without artifact using an OSEM algorithm. We developed four forward projectors (simple projector (S-RT), projector accounting for the surface of the detecting pixel (S-RT-IV), projection modeling the solid angle (S-RT-SA) of the projection tube, and projector modeling the depth of interaction (S-RT-SA-D)). We also modeled the point spread function of the collimator in the image domain, using an anisotropic non-stationary function. To characterize the reconstruction, we studied the conditioning number of the system matrix for each projector and each collimator. We showed that the new collimator was more ill-conditioned than a parallel collimator or a cone-beam collimator. We showed that the image based PSF and the modeling of the depth of interaction improved the quality of the images, but edge artefacts were introduced when modeling the PSF in the image domain. Compared to existing systems, we showed that this new collimator has a large field of view (~ 70 mm in the transaxial plane) with a resolution of 1.0 mm in the best case but suffers from a relatively low sensitivity (1.32x10⁻² %).

Most applications in computer vision suffer from two major difficulties. The first is they are notoriously ridden with sub-optimal local minima. The second is that they typically require high computational cost to be solved robustly. The reason for these two drawbacks is that most problems in computer vision, even when well-defined, typically require finding a solution in a very large high-dimensional space. It is for these two reasons that multiscale methods are particularly well-suited to problems in computer vision. Multiscale methods, by way of looking at the coarse scale nature of a problem before considering the fine scale nature, often have the ability to avoid sub-optimal local minima and obtain a more globally optimal solution. In addition, multiscale methods typically enjoy reduced computational cost. This thesis applies novel multiscale active contour methods to several problems in computer vision, especially in simultaneous segmentation and reconstruction of tomography images. In addition, novel multiscale methods are applied to contour registration using minimal surfaces and to the computation of non-linear rotationally invariant optical flow. Finally, a methodology for fast robust image segmentation is presented that relies on a lower dimensional image basis derived from an image scale space. The specific advantages of using multiscale methods in each of these problems is highlighted in the various simulations throughout the thesis, particularly their ability to avoid sub-optimal local minima and their ability to solve the problems at a lower overall computational cost.

La cryo-microscopie électronique est une technique tomographique permettant de reconstituer la structure 3D d’un objet complexe en biologie à partir d’un jeu d’acquisitions. Ces images de l’objet complexe sont appelées les projections et sont acquises sous orientations inconnues. Un des avantages de la cryo-microscopie électronique est l’obtention d’un modèle 3D de très haute résolution de l’objet dans un état naturel. La procédure de reconstruction comporte plusieurs étapes telles que l’alignement, la classification des projections, l’estimation de leurs orientations et le raffinement des projections. Lors de ces étapes, la distance entre deux projections est fréquemment mesurée. Le travail réalisé au cours de cette thèse s’organise autour de la recherche théorique d’une distance entre des projections non-orientées avec comme objectif l’amélioration de la procédure de reconstruction tomographique en cryo-microscopie électronique. La contribution de ce travail de thèse est une méthode permettant d’estimer la différence angulaire entre deux projections dans les cas 2D et 3D. Notre méthode est basée sur la construction d’un graphe de voisinage dont les sommets sont les projections, dont les arêtes relient des projections voisines et sont pondérées par une approximation locale de la différence angulaire. Le calcul de ces poids repose sur les propriétés des moments de projection. Notre méthode est testée sur des images simulées de différentes résolutions et de différents niveaux du bruit. La comparaison avec des autres méthodes d’estimation de la différence angulaire est aussi réalisée. / Cryo-electron microscopy is a tomographic technique allowing to reconstruct a 3D model of complex structure in biology from a set of acquired images. These images are known as the tomographic projections and are taken at unknown directions. The advantage of the cryo-electron microscopy is the 3D reconstruction at very high resolution. The reconstruction procedure consists of many steps such as projection alignment, projection classification, orientation estimation and projection refinement. During these steps, the distance between two projections is frequently measured. The work in this thesis aims at studying the distances mesured between two unknown-direction projections with the objective of improving the reconstruction result in the cryo-electron microscopy. The contribution of this thesis is the developement of a method for estimating the angular difference between two projections in 2D and 3D. Our method is based on the construction of a neighborhood graph whose vertices are the projections, whose edges link the projection neighbors and are weighted by a local approximation of the angular difference. The calculation of the weights relies on the projection moment properties. The proposed method has been tested on simulated images with different resolutions and at different noise levels. The comparison with others estimation methods of angular difference has been realised.

No description available.