Abstract: Tagged magnetic resonance is a very usefull and unique tool that provides a complete local and global knowledge of the left ventricle (LV) motion. In this article we introduce a method capable of tracking and segmenting the LV. Spectral methods are applied in order to obtain the so called HARP images which encode information about movement and are the base for LV point-tracking. For segmentation we use Active Shapes (ASM) that model LV shape variation in order to overcome possible local misplacements of the boundary. We finally show experiments on both synthetic and real data which appear to be very promising.

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: 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.

Abstract: Cardiovascular diseases are a leading cause of death in developed countries. Most of them are caused by arterial (specially coronary) diseases, mainly caused by plaque accumulation. Such pathology narrows blood flow (stenosis) and affects artery bio- mechanical elastic properties (atherosclerosis). In the last decades, IntraVascular UltraSound (IVUS) has become a usual imaging technique for the diagnosis and follow up of arterial diseases. IVUS is a catheter-based imaging technique which shows a sequence of cross sections of the artery under study. Inspection of a single image gives information about the percentage of stenosis. Meanwhile, inspection of longitudinal views provides information about artery bio-mechanical properties, which can prevent a fatal outcome of the cardiovascular disease. On one hand, dynamics of arteries (due to heart pumping among others) is a major artifact for exploring tissue bio-mechanical properties. On the other one, manual stenosis measurements require a manual tracing of vessel borders, which is a time-consuming task and might suffer from inter-observer variations. This PhD thesis proposes several image processing tools for exploring vessel dy- namics and structures. We present a physics-based model to extract, analyze and correct vessel in-plane rigid dynamics and to retrieve cardiac phase. Furthermore, we introduce a deterministic-statistical method for automatic vessel borders detection. In particular, we address adventitia layer segmentation. An accurate validation pro- tocol to ensure reliable clinical applicability of the methods is a crucial step in any proposal of an algorithm. In this thesis we take special care in designing a valida- tion protocol for each approach proposed and we contribute to the in vivo dynamics validation with a quantitative and objective score to measure the amount of motion suppressed.