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: The Diagnosis of Left Ventricle (LV) pathologies is related to regional wall motion analysis. Health indicator scores such as the rotation and the torsion are useful for the diagnose of the Left Ventricle (LV) function. However, this requires proper identification of LV segments. On one hand, manual segmentation is robust, but it is slow and requires medical expertise. On the other hand, the tag pattern in Tagged Magnetic Resonance (TMR) sequences is a problem for the automatic segmentation of the LV boundaries. Consequently, we propose a method based in the classical formulation of parametric Snakes, combined with Active Shape models. Our semantic definition of the LV is tagged tissue that experiences motion in the systolic cycle. This defines two energy potentials for the Snake convergence. Additionally, the mean shape corrects excessive deviation from the anatomical shape. We have validated our approach in 15 healthy volunteers and two short axis cuts. In this way, we have compared the automatic segmentations to manual shapes outlined by medical experts. Also, we have explored the accuracy of clinical scores computed using automatic contours. The results show minor divergence in the approximation and the manual segmentations as well as robust computation of clinical scores in all cases. From this we conclude that the proposed method is a promising support tool for clinical analysis.

Abstract: Among all filtering techniques, those based exclu- sively on image level sets (geometric flows) have proven to be the less sensitive to the nature of noise and the most contrast preserving. A common feature to existent curvature flows is that they penalize high curvature, regardless of the curve regularity. This constitutes a major drawback since curvature extreme values are standard descriptors of the contour geometry. We argue that an operator designed with shape recovery purposes should include a term penalizing irregularity in the curvature rather than its magnitude. To this purpose, we present a novel geometric flow that includes a function that measures the degree of local irregularity present in the curve. A main advantage is that it achieves non-trivial steady states representing a smooth model of level curves in a noisy image. Performance of our approach is compared to classical filtering techniques in terms of quality in the restored image/shape and asymptotic behavior. We empirically prove that our approach is the technique that achieves the best compromise between image quality and evolution stabilization.

Abstract: Tagged Magnetic Resonance Imaging (MRI) is a non-invasive technique used to examine cardiac deformation in vivo. An Angle Image is a representation of a Tagged MRI which recovers the relative position of the tissue respect to the distorted tags. Thus cardiac deformation can be estimated. This paper describes a new approach to generate Angle Images using a bank of Gabor filters in short axis cardiac Tagged MRI. Our method improves the Angle Images obtained by global techniques, like HARP, with a local frequency analysis. We propose to use the phase response of a combination of a Gabor filters bank, and use it to find a more precise deformation of the left ventricle. We demonstrate the accuracy of our method over HARP by several experimental results.