This thesis describes extensions to 2D and 3D model-based segmentation algorithms for the analysis of ultrasound images and sequences. Starting from a common 2D+t "track-to-last" algorithm, it is shown that the typical method of searching for boundary candidates perpendicular to the model contour is unnecessary if, for each boundary candidate, its corresponding position on the model contour is optimised jointly with the model contour geometry. With this observation, two 2D+t segmentation algorithms, which accurately recover boundary displacements and are capable of segmenting arbitrarily long sequences, are formulated and validated. Generalising to 3D, subdivision surfaces are shown to be natural choices for continuous model surfaces, and the algorithms necessary for joint optimisation of the correspondences and model surface geometry are described. Three applications of 3D model-based segmentation for ultrasound image analysis are subsequently presented and assessed: skull segmentation for fetal brain image analysis; face segmentation for shape analysis, and single-frame left ventricle (LV) segmentation from echocardiography images for volume measurement. A framework to perform model-based segmentation of multiple 3D sequences - while jointly optimising an underlying linear basis shape model - is subsequently presented for the challenging application of right ventricle (RV) segmentation from 3D+t echocardiography sequences. Finally, an algorithm to automatically select boundary candidates independent of a model surface estimate is described and presented for the task of LV segmentation. Although motivated by challenges in ultrasound image analysis, the conceptual contributions of this thesis are general and applicable to model-based segmentation problems in many domains. Moreover, the components are modular, enabling straightforward construction of application-specific formulations for new clinical problems as they arise in the future.

De nombreux scanners laser permettent d'obtenir la surface 3D a partir d'un objet. Néanmoins, la surface reconstruite est souvent lisse, ce qui est du au débruitage interne du scanner et aux décalages entre les scans. Cette these utilise des scans haute precision et choisit de ne pas perdre ni alterer les echantillons initiaux au cours du traitement afin de les visualiser. C'est en effet la seule façon de decouvrir les imperfections (trous, decalages de scans). De plus, comme les donnees haute precision capturent meme le plus leger detail, tout debruitage ou sous-echantillonnage peut amener a perdre ces details.La these s'attache a prouver que l'on peut trianguler le nuage de point initial en ne perdant presque aucun echantillon. Le probleme de la visualisation exacte sur des donnees de plus de 35 millions de points et de 300 scans differents est ainsi resolu. Deux problemes majeurs sont traites: le premier est l'orientation du nuage de point brut complet et la creation d'un maillage. Le second est la correction des petits decalages entre les scans qui peuvent creer un tres fort aliasing et compromettre la visualisation de la surface. Le second developpement de la these est une decomposition des nuages de points en hautes/basses frequences. Ainsi, des methodes classiques pour l'analyse d'image, l'arbre des ensembles de niveau et la representation MSER, sont etendues aux maillages, ce qui donne une methode intrinseque de segmentation de maillages. Une analyse mathematiques d'operateurs differentiels discrets, proposes dans la litterature et operant sur des nuages de points est realisee. En considerant les developpements asymptotiques de ces operateurs sur une surface reguliere, ces operateurs peuvent etre classifies. Cette analyse amene au developpement d'un operateur discret consistant avec Ie mouvement par courbure moyenne (l'equation de la chaleur intrinseque) definissant ainsi un espace-echelle numerique simple et remarquablement robuste. Cet espace-echelle permet de resoudre de maniere unifiee tous les problemes mentionnes auparavant (orientation et triangulation du nuage de points, fusion de scans, segmentation de maillages) qui sont ordinairement traites avec des techniques distinctes. / Many laser devices acquire directly 3D objects and reconstruct their surface. Nevertheless, the final reconstructed surface is usually smoothed out as a result of the scanner internal de-noising process and the offsets between different scans. This thesis, working on results from high precision scans, adopts the somewhat extreme conservative position, not to loose or alter any raw sample throughout the whole processing pipeline, and to attempt to visualize them. Indeed, it is the only way to discover all surface imperfections (holes, offsets). Furthermore, since high precision data can capture the slightest surface variation, any smoothing and any sub-sampling can incur in the loss of textural detail.The thesis attempts to prove that one can triangulate the raw point cloud with almost no sample loss. It solves the exact visualization problem on large data sets of up to 35 million points made of 300 different scan sweeps and more. Two major problems are addressed. The first one is the orientation of the complete raw point set, an the building of a high precision mesh. The second one is the correction of the tiny scan misalignments which can cause strong high frequency aliasing and hamper completely a direct visualization.The second development of the thesis is a general low-high frequency decomposition algorithm for any point cloud. Thus classic image analysis tools, the level set tree and the MSER representations, are extended to meshes, yielding an intrinsic mesh segmentation method.The underlying mathematical development focuses on an analysis of a half dozen discrete differential operators acting on raw point clouds which have been proposed in the literature. By considering the asymptotic behavior of these operators on a smooth surface, a classification by their underlying curvature operators is obtained.This analysis leads to the development of a discrete operator consistent with the mean curvature motion (the intrinsic heat equation) defining a remarkably simple and robust numerical scale space. By this scale space all of the above mentioned problems (point set orientation, raw point set triangulation, scan merging, segmentation), usually addressed by separated techniques, are solved in a unified framework.