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: Regional scores (e.g. strain, perfusion) of the Left Ventricle (LV) functionality are playing an increasing role in the diagnosis of cardiac diseases. A main limitation is the lack of normality models for complementary scores oriented to assessment of the LV integrity. This paper introduces an original framework based on a parametrization of the LV domain, which allows comparison across subjects of local physiological measures of different nature. We compute regional normality patterns in a feature space characterizing the LV function. We show the consistency of the model for the regional motion on healthy and hypokinetic pathological cases

Abstract: In this work, we present a fully automated method for tissue deformation estimation in tagged magnetic resonance images (TMRI). Gabor filter banks, tuned independently for each left ventricle level, provide optimally filtered complex images which phase remains constant along the cardiac cycle. This fact can be thought as the brightness constancy condition required by classical optical flow (OF) methods. Pairs of these filtered sequences, together with a variational formulation are used in a second step to obtain dense continuous deformation maps that we call Harmonic Phase Flow. This method has been used to determine reference values of ventricular torsion (VT) in a set of 8 healthy volunteers. The results encourage the use of VT as a useful parameter for ventricular function assessment in clinical routine.

Abstract: The adventitia layer appears as a weak edge in IVUS images with a non-uniform grey level, which difficulties its detection. In order to enhance edges, we apply an anisotropic filter that homogenizes the grey level along the image significant structures (ridges, valleys and edges). A standard edge detector applied to the filtered image yields a set of candidate points prone to be unconnected. The final model is obtained by interpolating the former line segments along the tangent direction to the level curves of the filtered image with an anisotropic contour closing technique based on functional extension principles

Abstract: Longitudinal motion artifacts in IntraVascular UltraSound (IVUS) sequences hinders a properly 3D reconstruction and vessel measurements. Most of current techniques base on the ECG signal to obtain a gated pullback without the longitudinal artifact by using a specific hardware or the ECG signal itself. The potential of IVUS images processing for phase retrieval still remains little explored. In this paper, we present a fast forward image-based algorithm to approach ECG sampling. Inspired on the fact that maximum and minimum lumen areas are related to end-systole and end-diastole, our cardiac phase retrieval is based on the analysis of tissue density of mass along the sequence. The comparison between automatic and manual phase retrieval (0.07 ± 0.07 mm. of error) encourages a deep validation contrasting with ECG signals.