This thesis is devoted to dense deformable image registration/fusion using discrete methods. The main contribution of the thesis is a principled registration framework coupling iconic/geometric information through graph-based techniques. Such a formulation is derived from a pair-wise MRF view-point and solves both problems simultaneously while imposing consistency on their respective solutions. The proposed framework was used to cope with pair-wise image fusion (symmetric and asymmetric variants are proposed) as well as group-wise registration for population modeling. The main qualities of our framework lie in its computational efficiency and versatility. The discrete nature of the formulation renders the framework modular in terms of iconic similarity measures as well as landmark extraction and association techniques. Promising results using a standard benchmark database in optical flow estimation and 3D medical data demonstrate the potentials of our methods.

La présente thèse est consacrée au recalage et à la fusion d’images de façon dense et déformable via des méthodes d’optimisation discrète. La contribution majeure consiste en un principe de couplage entre recalage géométrique et iconique via l’utilisation de méthodes dites graphiques. Une telle formulation peut être obtenue à partir d’un Champ de Markov Aléatoire binaire et permet de résoudre les deux problèmes simultanément tout en imposant une cohérence à leurs solutions respectives. La méthodologie s’applique à la fusion de paires d’images (dans ses versions symétrique et asymétrique), ainsi qu’au recalage simultané de groupes d’images nécessaire à l’étude de populations. Les qualités principales de notre approche résident dans sa faible complexité algorithmique et sa versatilité. L’utilisation d’une formulation discrète assure une grande modularité concernant tant la mesure de similarité iconique que l’extraction et l’association de points d’intérêt. Les résultats prometteurs obtenus sur les bases de données de référence en flot optique et sur des données médicales tridimensionnelles démontrent tout le potentiel de notre méthodologie / This thesis is devoted to dense deformable image registration/fusion using discrete methods. The main contribution of the thesis is a principled registration framework coupling iconic/geometric information through graph-based techniques. Such a formulation is derived from a pair-wise MRF view-point and solves both problems simultaneously while imposing consistency on their respective solutions. The proposed framework was used to cope with pair-wise image fusion (symmetric and asymmetric variants are proposed) as well as group-wise registration for population modeling. The main qualities of our framework lie in its computational efficiency and versatility. The discrete nature of the formulation renders the framework modular in terms of iconic similarity measures as well as landmark extraction and association techniques. Promising results using a standard benchmark database in optical flow estimation and 3D medical data demonstrate the potentials of our methods.

This dissertation provides the foundations of computer-based automated phenotyping methods for analyzing 3D images of mouse embryos. A group-wise registration technique was utilized and optimized and computerized methods were employed for analysis of 3D MRI images of mouse embryos. The assumption that embryo anatomy is highly conserved among genetically identical specimens was verified. The group-wise registration approach was used to align a group of embryos from the 129S1/SvImJ (129Sv) strain as well as a group of C57BL/6J (C57) embryos. Finally, we shed some light on some of the morphological differences between the 129Sv and C57 strains using automated techniques.

This dissertation provides the foundations of computer-based automated phenotyping methods for analyzing 3D images of mouse embryos. A group-wise registration technique was utilized and optimized and computerized methods were employed for analysis of 3D MRI images of mouse embryos. The assumption that embryo anatomy is highly conserved among genetically identical specimens was verified. The group-wise registration approach was used to align a group of embryos from the 129S1/SvImJ (129Sv) strain as well as a group of C57BL/6J (C57) embryos. Finally, we shed some light on some of the morphological differences between the 129Sv and C57 strains using automated techniques.

La présente thèse propose des méthodes pour l'estimation du mouvement des organes d'un patient autravers de l'imagerie tomographique. Le but est la correction du mouvement spatio-temporel sur les imagesmédicales tomographiques. En tant que paradigme expérimental, nous considérons le problème de l'estimation dumouvement dans l'imagerie IRM de diffusion, une modalité d'imagerie sensible à la diffusion des molécules d'eaudans le corps. Le but de ces travaux de thèse est l'évaluation des patients atteints de lymphome, car l'eau diffusedifféremment dans les tissus biologiques sains et dans les lésions. L'effet de la diffusion de l'eau peut être mieuxreprésenté par une image paramétrique, grâce au coefficient de diffusion apparente (image à ADC), créé sur la based'une série d'images DWI du même patient (séquence d'images 3D), acquises au moment de la numérisation. Unetelle image paramétrique a la possibilité de devenir un biomarqueur d'imagerie d’IRM et de fournir aux médecinsdes informations complémentaires concernantl'image de FDG-PET qui est la méthode d'imagerie de base pour lelymphome et qui montre la quantité de glucose métabolisée.Nos principales contributions sont au nombre de trois. Tout d'abord, nous proposons une méthode de recalaged'image déformable en groupe spécialement conçue pour la correction de mouvement dans l’IRM de diffusion, carelle est guidée par un modèle physiologique décrivant le processus de diffusion qui se déroule lors de l'acquisitionde l'image. Notre méthode détermine une image à ADC de plus grande précision en termes de représentation dugradient de la diffusion des molécules d'eau par rapport à l` image correspondante obtenue par pratique couranteou par d'autres méthodes de recalage d'image non basé sur un modèle. Deuxièmement, nous montrons qu'enimposant des contraintes spatiales sur le calcul de l'image à ADC, les tumeurs de l'image peuvent être encore mieuxcaractérisées en les classant dans les différentes catégories liées à la maladie. Troisièmement, nous montronsqu'une corrélation entre DWI et FDG-PET doit exister en examinant la corrélation entre les caractéristiquesstatistiques extraites par l'image à ADC lisse découlant de notre méthode du recalage d’image déformable et lesscores de recommandation sur la malignité des lésions, donnés par des experts basés sur une évaluation des imagesFDG-PET correspondantes du patient. / This doctoral thesis develops methods to estimate patient's motion, voluntary and involuntary (organs'motion), in order to correct for motion in spatiotemporal tomographic medical images. As an experimentalparadigm we consider the problem of motion estimation in Diffusion-Weighted Magnetic Resonance Imaging (DWI),an imaging modality sensitive to the diffusion of water molecules in the body. DWI is used for the evaluation oflymphoma patients, since water diffuses differently in healthy tissues and in lesions. The effect of water diffusioncan be better depicted through a parametric map, the so-called apparent diffusion coefficient (ADC map), createdbased on a series of DW images of the same patient (3D image sequence), acquired in time during scanning. Such aparametric map has the potentiality to become an imaging biomarker in DWI and provide physicians withcomplementary information to current state-of-the-art FDG-PET imaging reflecting quantitatively glycosemetaboslism.Our contributions are three fold. First, we propose a group-wise deformable image registration methodespecially designed for motion correction in DWI, as it is guided by a physiological model describing the diffusionprocess taking place during image acquisition. Our method derives an ADC map of higher accuracy in terms ofdepicting the gradient of the water molecules' diffusion in comparison to the corresponding map derived bycommon practice or by other model-free group-wise image registration methods. Second, we show that by imposingspatial constraints on the computation of the ADC map, the tumours in the image can be even better characterized interms of classifying them into the different types of the disease. Third, we show that a correlation between DWI andFDG-PET should exist by examining the correlation between statistical features extracted by the smooth ADC mapderived by our deformable registration method, and recommendation scores on the malignancy of the lesions, givenby experts based on an evaluation of the corresponding FDG-PET images of the patient.

Diffusion Tensor MRI can be used to depict the anisotropy of tissue. Translation of this technique to moving objects such as the beating heart has recently become feasible, but remains a challenging task, often leading to high noise levels and limited accuracy. Ultimately, knowledge of the 3D fibre architecture of the myocardium invivo should allow for a better understanding of the cardiac function both in healthy and pathological situations. The main goal of the work presented in this thesis is to overcome the difficulties that such technology presents, by introducing a combination of image processing and analysis approaches. In particular, the characteristic ellipsoidal shape of the left ventricular chamber is used to introduce a shape-based prolate spheroidal coordinate frame that allows for comprehensive, robust and dedicated analysis of diffusion tensor data within the myocardial wall. It is shown that the description of this information is more compact in this coordinate frame. Furthermore, it is demonstrated that the acquisition limitations can be overcome by introducing an approximation scheme based on this coordinate frame. These techniques are tested on ex-vivo datasets to assess their fidelity and sensitivity. Finally, these techniques are applied in-vivo on a group of healthy volunteers, where 2D DTI slices of the LV were acquired at end diastole and end systole, using cardiac dedicated diffusion MR acquisition. Results demonstrate the advantages of using curvilinear coordinates both for the analysis and the approximation of cardiac DTI information. Resulting in-vivo fibre architectures were found to agree with previously reported studies on ex-vivo specimens. The outcome of this work can open the door for clinical applications and cardiac electrophysiology modelling, and improve the understanding of the left ventricular structure and dynamics.