Abstract: Cardiovascular Diseases, specially those affecting the Left Ventricle (LV), are the leading cause of death in developed countries with approximately a 30% of all global deaths. In order to address this public health concern, physicians focus on diagnosis and therapy planning. On one hand, early and accurate detection of Regional Wall Motion Abnormalities (RWMA) significantly contributes to a quick diagnosis and prevents the patient to reach more severe stages. On the other hand, a thouroughly knowledge of the normal gross anatomy of the LV, as well as, the distribution of its muscular fibers is crucial for designing specific interventions and therapies (such as pacemaker implanction). Statistical models obtained from the analysis of different imaging modalities allow the computation of the normal ranges of variation within a given population. Normality models are a valuable tool for the definition of objective criterions quantifying the degree of (anomalous) deviation of the LV function and anatomy for a given subject. The creation of statistical models involve addressing three main issues: extraction of data from images, definition of a common domain for comparison of data across patients and designing appropriate statistical analysis schemes. In this PhD thesis we present generic image processing tools for the creation of statistical models of the LV anatomy and function. On one hand, we use differential geometry concepts to define a computational framework (the Normalized Parametric Domain, NPD) suitable for the comparison and fusion of several clinical scores obtained over the LV. On the other hand, we present a variational approach (the Harmonic Phase Flow, HPF) for the estimation of myocardial motion that provides dense and continuous vector fields without overestimating motion at injured areas. These tools are used for the creation of statistical models. Regarding anatomy, we obtain an atlas jointly modelling, both, LV gross anatomy and fiber architecture. Regarding function, we compute normality patterns of scores characterizing the (global and local) LV function and explore, for the first time, the configuration of local scores better suited for RWMA detection.

Abstract: L’evolució tecnològica en el tractament de les imatges mèdiques permet reconstruir, amb el software apropiat, imatges tridimensionals de les estructures cardiovasculars i dotar-les de moviment. Les imatges 4D resultants faciliten l’estudi de la fisiopatologia de la insuficiència cardíaca en base als transtorns de l’activació electromecànica ventricular, el que pot ser d’interès en el procés de selecció de pacients candidats a teràpies de resincronització. Presentem els resultats preliminars de la reconstrucció 4D del ventricle esquerre (VE) a partir de les seqüències de tagging miocàrdic del VE.

Abstract: Medical imaging is very useful in the assessment and treatment of many diseases. To deal with the great amount of data provided by imaging scanners and extract quantitative information that physicians can interpret, many analysis algorithms have been developed. Any process of analysis always consists of a first step of segmenting some particular structure. In medical imaging, structures are not always well defined and suffer from noise artifacts thus, ordinary segmentation methods are not well suited. The ones that seem to give better results are those based on deformable models. Nevertheless, despite their capability of mixing image features together with smoothness constraints that may compensate for image irregularities, these are naturally local methods, i. e., each node of the active contour evolve taking into account information about its neighbors and some other weak constraints about flexibility and smoothness, but not about the global shape that they should find. Due to the fact that structures to be segmented are the same for all cases but with some inter and intra-patient variation, the incorporation of a priori knowledge about shape in the segmentation method will provide robustness to it. Active Shape Models is an algorithm based on the creation of a shape model called Point Distribution Model. It performs a segmentation using only shapes similar than those previously learned from a training set that capture most of the variation presented by the structure. This algorithm works by updating shape nodes along a normal segment which often can be too restrictive. For this reason we propose a generalization of this algorithm that we call Generalized Active Shape Models and fully integrates the a priori knowledge given by the Point Distribution Model with deformable models or any other appropriate segmentation method. Two different applications to cardiac imaging of this generalized method are developed and promising results are shown.

Abstract: Medical imaging feeds research in many computer vision and image processing fields: image filtering, segmentation, shape recovery, registration, retrieval and pattern matching. Because of their low contrast changes and large variety of artifacts and noise, medical imaging processing techniques relying on an analysis of the geometry of image level sets rather than on intensity values result in more robust treatment. From the starting point of treatment of intravascular images, this PhD thesis ad- dresses the design of differential image operators based on geometric principles for a robust shape modelling and restoration. Among all fields applying shape recovery, we approach filtering and segmentation of image objects. For a successful use in real images, the segmentation process should go through three stages: noise removing, shape modelling and shape recovery. This PhD addresses all three topics, but for the sake of algorithms as automated as possible, techniques for image processing will be designed to satisfy three main principles: a) convergence of the iterative schemes to non-trivial states avoiding image degeneration to a constant image and representing smooth models of the originals; b) smooth asymptotic behav- ior ensuring stabilization of the iterative process; c) fixed parameter values ensuring equal (domain free) performance of the algorithms whatever initial images/shapes. Our geometric approach to the generic equations that model the different processes approached enables defining techniques satisfying all the former requirements. First, we introduce a new curvature-based geometric flow for image filtering achieving a good compromise between noise removing and resemblance to original images. Sec- ond, we describe a new family of diffusion operators that restrict their scope to image level curves and serve to restore smooth closed models from unconnected sets of points. Finally, we design a regularization of snake (distance) maps that ensures its smooth convergence towards any closed shape. Experiments show that performance of the techniques proposed overpasses that of state-of-the-art algorithms.