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: Medial representations are powerful tools for describing and parameterizing the volumetric shape of anatomical structures. Existing methods show excellent results when applied to 2D objects, but their quality drops across dimensions. This paper contributes to the computation of medial manifolds in two aspects. First, we provide a standard scheme for the computation of medial manifolds that avoid degenerated medial axis segments; second, we introduce an energy based method which performs independently of the dimension. We evaluate quantitatively the performance of our method with respect to existing approaches, by applying them to synthetic shapes of known medial geometry. Finally, we show results on shape representation of multiple abdominal organs, exploring the use of medial manifolds for the representation of multi-organ relations.

Abstract: Medial representations are powerful tools for describing and parameterizing the volumetric shape of anatomical structures. Existing methods show excellent results when applied to 2D
objects, but their quality drops across dimensions. This paper contributes to the computation of medial manifolds in two aspects. First, we provide a standard scheme for the computation of medial
manifolds that avoid degenerated medial axis segments; second, we introduce an energy based method which performs independently of the dimension. We evaluate quantitatively the performance of our
method with respect to existing approaches, by applying them to synthetic shapes of known medial geometry. Finally, we show results on shape representation of multiple abdominal organs,
exploring the use of medial manifolds for the representation of multi-organ relations.

Abstract: Medial representations are a widely used technique in abdominal organ shape representation and parametrization. Those methods require good medial manifolds as a starting point. Any medial
surface used to parametrize a volume should be simple enough to allow an easy manipulation and complete enough to allow an accurate reconstruction of the volume. Obtaining good quality medial
surfaces is still a problem with current iterative thinning methods. This forces the usage of generic, pre-calculated medial templates that are adapted to the final shape at the cost of a drop in volume reconstruction.
This paper describes an operator for generation of medial structures that generates clean and complete manifolds well suited for their further use in medial representations of abdominal organ volumes. While being simpler than thinning surfaces, experiments show its high performance in volume reconstruction and preservation of medial surface main branching topology.

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.