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: Crystal unbending, the process that aims to recover a perfect crystal from experimental data, is one of the more important steps in electron crystallography image processing. The unbending process involves three steps: estimation of the unit cell displacements from their ideal positions, extension of the deformation field to the whole image and transformation of the image in order to recover an ideal crystal. In this work, we present a systematic analysis of the second step oriented to address two issues. First, whether the unit cells remain undistorted and only the distance between them should be changed (rigid case) or should be modified with the same deformation suffered by the whole crystal (elastic case). Second, the performance of different extension algorithms (interpolation versus approximation) is explored. Our experiments show that there is no difference between elastic and rigid cases or among the extension algorithms. This implies that the deformation fields are constant over large areas. Furthermore, our results indicate that the main source of error is the transformation of the crystal image.

Abstract: A usual tool in cardiac disease diagnosis is vessel plaque assessment by analysis of IVUS sequences. Manual detection of lumen-intima, intima-media and media-adventitia vessel borders is the main activity of physicians in the process of plaque quantification. Large variety in vessel border descriptors, as well as, shades, artifacts and blurred response due to ultrasound physical properties troubles automated media-adventitia segmentation. This experimental work presents a solution to such a complex problem. The process blends advanced anisotropic filtering operators and statistic classification techniques, achieving an efficient vessel border modelling strategy. First of all, we introduce the theoretic base of the method. After that, we show the steps of the algorithm, validating the method with statistics that show that the media-adventitia border detection achieves an accuracy in the range of inter-observer variability regardless of plaque nature, vessel geometry and incomplete vessel borders. Finally, we present a little Matlab application to the automatic media-adventitia border.

Abstract: Accurate computation of optical flow is a key-point in many image processing fields. Detection of anomalous and unpredicted agents (such as pedestrians, bikers or cars) in urban scenes or pathology discrimination in medical imaging sequences, to mention just a two. The above kinds sequences present two main difficulties for standard optical flow techniques. On one hand, variability in acquisition conditions (illuminance, medical imaging modality, ...) force an alterantive representation for images fulfilling the britghtness constancy constrain. On the hand, current variational schemes produce oversmoothed fields unable to properly model discontinuous behaviours such as collisions or functionless pathological areas. This master project explores the abilities and limitations of local and global optical flow approaches. The master student will put especial emphasis in the theoretical grounds behind in order to design a variational framework combining the theoretical advantages of the considered techniques. In particular an optical flow based on Gabor phase tracking (developed in the group for medical imaging) will be generalized to urban scenes.

Abstract: Premise of the study: Because of their limited length, xylem conduits need to connect to each other to maintain water transport from roots to leaves. Conduit spatial distribution in a cross section plays an important role in aiding this connectivity. While indices of conduit spatial distribution already exist, they are not well defined statistically. * Methods: We used point pattern analysis to derive new spatial indices. One hundred and five cross-sectional images from different species were transformed into binary images. The resulting point patterns, based on the locations of the conduit centers-of-area, were analyzed to determine whether they departed from randomness. Conduit distribution was then modeled using a spatially explicit stochastic model. * Key results: The presence of conduit randomness, uniformity, or aggregation depended on the spatial scale of the analysis. The large majority of the images showed patterns significantly different from randomness at least at one spatial scale. A strong phylogenetic signal was detected in the spatial variables. * Conclusions: Conduit spatial arrangement has been largely conserved during evolution, especially at small spatial scales. Species in which conduits were aggregated in clusters had a lower conduit density compared to those with uniform distribution. Statistically sound spatial indices must be employed as an aid in the characterization of distributional patterns across species and in models of xylem water transport. Point pattern analysis is a very useful tool in identifying spatial patterns.

Abstract: Impairment of left ventricular (LV) contractility due to cardiovascular diseases is reflected in LV motion patterns. The mechanics of any muscle strongly depends on the spatial orientation of its muscular fibers since the motion that the muscle undergoes mainly takes place along the fiber. The helical ventricular myocardial band (HVMB) concept describes the myocardial muscle as a unique muscular band that twists in space in a non homogeneous fashion. The 3D anisotropy of the ventricular band fibers suggests a regional analysis of the heart motion. Computation of normality models of such motion can help in the detection and localization of any cardiac disorder. In this paper we introduce, for the first time, a normalized parametric domain that allows comparison of the left ventricle motion across patients. We address, both, extraction of the LV motion from Tagged Magnetic Resonance images, as well as, defining a mapping of the LV to a common normalized domain. Extraction of normality motion patterns from 17 healthy volunteers shows the clinical potential of our LV parametrization.