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: A good reliable approach to cardiac triggering is of utmost importance in obtaining accurate quantitative results of atherosclerotic plaque burden from the analysis of IntraVascular UltraSound. Although, in the last years, there has been an increase in research of methods for retrospective gating, there is no general consensus in a validation protocol. Many methods are based on quality assessment of longitudinal cuts appearance and those reporting quantitative numbers do not follow a standard protocol. Such heterogeneity in validation protocols makes faithful comparison across methods a difficult task. We propose a validation protocol based on the variability of the retrieved cardiac phase and explore the capability of several quality measures for quantifying such variability. An ideal detector, suitable for its application in clinical practice, should produce stable phases. That is, it should always sample the same cardiac cycle fraction. In this context, one should measure the variability (variance) of a candidate sampling with respect a ground truth (reference) sampling, since the variance would indicate how spread we are aiming a target. In order to quantify the deviation between the sampling and the ground truth, we have considered two quality scores reported in the literature: signed distance to the closest reference sample and distance to the right of each reference sample. We have also considered the residuals of the regression line of reference against candidate sampling. The performance of the measures has been explored on a set of synthetic samplings covering different cardiac cycle fractions and variabilities. From our simulations, we conclude that the metrics related to distances are sensitive to the shift considered while the residuals are robust against fraction and variabilities as far as one can establish a pair-wise correspondence between candidate and reference. We will further investigate the impact of false positive and negative detections in experimental data.

Abstract: Medial representations are powerful tools for describing and parameterizing the volumetric shape of anatomical structures. Accurate computation of one pixel wide medial surfaces is mandatory. Those surfaces must represent faithfully the geometry of the volume. Although morphological methods produce excellent results in 2D, their complexity and quality drops across dimensions, due to a more complex description of pixel neighborhoods. This paper introduces a continuous operator for accurate and efficient computation of medial structures of arbitrary dimension. Our experiments show its higher performance for medical imaging applications in terms of simplicity of medial structures and capability for reconstructing the anatomical volume

Abstract: Fisher Linear Discriminant Analysis (FLDA) is one of the most popular techniques used in classification applying dimensional reduction. The numerical scheme involves the inversion of the within-class scatter matrix, which makes FLDA potentially ill-conditioned when it becomes singular. In this paper we present a novel explicit formulation of FLDA in terms of the eccentricity ratio and eigenvector orientations of the within-class scatter matrix. An analysis of this function will characterize those situations where FLDA response is not reliable because of numerical instability. This can solve common situations of poor classification performance in computer vision.

Abstract: We present in this paper a novel lumen centre detection for gastrointestinal and respiratory endoscopic images. The proposed method is based on the appearance and geometry of the lumen, which we defined as the darkest image region which centre is a hub of image gradients. Experimental results validated on the first public annotated gastro-respiratory database prove the reliability of the method for a wide range of images (with precision over 95 %).