Abstract: There is general consensus that myocardial fiber architecture should be modelled in order to fully understand the electromechanical properties of the Left Ventricle (LV). Diffusion Tensor magnetic resonance Imaging (DTI) is the reference image modality for rapid measurement of fiber orientations by means of the tensor principal eigenvectors. In this work, we present a mathematical framework for across subject comparison of the local geometry of the LV anatomy including the fiber architecture from the statistical analysis of DTI studies. We use concepts of differential geometry for defining a parametric domain suitable for statistical analysis of a low number of samples. We use Riemannian metrics to define a consistent computation of DTI principal eigenvector modes of variation. Our framework has been applied to build an atlas of the LV fiber architecture from 7 DTI normal canine hearts.

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: Recent advances in endoscopic devices have increased their use for minimal invasive diagnostic and intervention procedures. Among all endoscopic modalities, bronchoscopy is one of the most frequent with around 261 millions of procedures per year. Although the use of bronchoscopy is spread among clinical facilities it presents some drawbacks, being the visual inspection for the assessment of anatomical measurements the most prevalent of them. In
particular, inaccuracies in the estimation of the degree of stenosis (the percentage of obstructed airway) decreases its diagnostic yield and might lead to erroneous treatments. An objective computation of tracheal stenosis in bronchoscopy videos would constitute a breakthrough for this non-invasive technique and a reduction in treatment cost.
This thesis settles the first steps towards on-line reliable extraction of anatomical information from videobronchoscopy for computation of objective measures. In particular, we focus on the computation of the degree of stenosis, which is obtained by comparing the area delimited by a healthy tracheal ring and the stenosed lumen. Reliable extraction of airway structures in interventional videobronchoscopy is a challenging task. This is mainly due to the large variety of acquisition conditions (positions and illumination), devices (different digitalizations) and in videos acquired at the operating room the unpredicted presence of surgical devices (such as probe ends). This thesis contributes to on-line stenosis assessment in several ways. We
propose a parametric strategy for the extraction of lumen and tracheal rings regions based on the characterization of their geometry and appearance that guide a deformable model. The geometric and appearance characterization is based on a physical model describing the way bronchoscopy images are obtained and includes local and global descriptions. In order to ensure a systematic applicability we present a statistical framework to select the optimal
parameters of our method. Experiments perform on the first public annotated database, show that the performance of our method is comparable to the one provided by clinicians and its computation time allows for a on-line implementation in the operating room.