Abstract: In this paper we propose a new Computer Vision technique to reconstruct the vascular wall in space using a deformable model-based technique and compounding methods, based in biplane angiography and intravascular ultrasound data jicsion. It is also proposed a generalpurpose three-dimensional guided interpolation method. The three dimensional centerline of the vessel is reconstructed from geometrically corrected biplane angiographies using automatic segmentation methods and snakes. The IVUS image planes are located in the threedimensional space and correctly oriented. A led interpolation method based in B-SurJaces and snakes isused to fill the gaps among image planes

Abstract: Cardiovascular Diseases, specially those affecting the Left Ventricle (LV), are the leading cause of death in developed countries with approximately a 30% of all global deaths. In order to address this public health concern, physicians focus on diagnosis and therapy planning. On one hand, early and accurate detection of Regional Wall Motion Abnormalities (RWMA) significantly contributes to a quick diagnosis and prevents the patient to reach more severe stages. On the other hand, a thouroughly knowledge of the normal gross anatomy of the LV, as well as, the distribution of its muscular fibers is crucial for designing specific interventions and therapies (such as pacemaker implanction). Statistical models obtained from the analysis of different imaging modalities allow the computation of the normal ranges of variation within a given population. Normality models are a valuable tool for the definition of objective criterions quantifying the degree of (anomalous) deviation of the LV function and anatomy for a given subject. The creation of statistical models involve addressing three main issues: extraction of data from images, definition of a common domain for comparison of data across patients and designing appropriate statistical analysis schemes. In this PhD thesis we present generic image processing tools for the creation of statistical models of the LV anatomy and function. On one hand, we use differential geometry concepts to define a computational framework (the Normalized Parametric Domain, NPD) suitable for the comparison and fusion of several clinical scores obtained over the LV. On the other hand, we present a variational approach (the Harmonic Phase Flow, HPF) for the estimation of myocardial motion that provides dense and continuous vector fields without overestimating motion at injured areas. These tools are used for the creation of statistical models. Regarding anatomy, we obtain an atlas jointly modelling, both, LV gross anatomy and fiber architecture. Regarding function, we compute normality patterns of scores characterizing the (global and local) LV function and explore, for the first time, the configuration of local scores better suited for RWMA detection.

Abstract: Medical imaging is very useful in the assessment and treatment of many diseases. To deal with the great amount of data provided by imaging scanners and extract quantitative information that physicians can interpret, many analysis algorithms have been developed. Any process of analysis always consists of a first step of segmenting some particular structure. In medical imaging, structures are not always well defined and suffer from noise artifacts thus, ordinary segmentation methods are not well suited. The ones that seem to give better results are those based on deformable models. Nevertheless, despite their capability of mixing image features together with smoothness constraints that may compensate for image irregularities, these are naturally local methods, i. e., each node of the active contour evolve taking into account information about its neighbors and some other weak constraints about flexibility and smoothness, but not about the global shape that they should find. Due to the fact that structures to be segmented are the same for all cases but with some inter and intra-patient variation, the incorporation of a priori knowledge about shape in the segmentation method will provide robustness to it. Active Shape Models is an algorithm based on the creation of a shape model called Point Distribution Model. It performs a segmentation using only shapes similar than those previously learned from a training set that capture most of the variation presented by the structure. This algorithm works by updating shape nodes along a normal segment which often can be too restrictive. For this reason we propose a generalization of this algorithm that we call Generalized Active Shape Models and fully integrates the a priori knowledge given by the Point Distribution Model with deformable models or any other appropriate segmentation method. Two different applications to cardiac imaging of this generalized method are developed and promising results are shown.

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: Early diagnosis and accurate treatment of Left Ventricle (LV) dysfunction significantly increases the patient survival. Impairment of LV contractility due to cardiovascular diseases is reflected in its motion patterns. Recent advances in medical imaging, such as Magnetic Resonance (MR), have encouraged research on 3D simulation and modelling of the LV dynamics. Most of the existing 3D models consider just the gross anatomy of the LV and restore a truncated ellipse which deforms along the cardiac cycle. The contraction 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 fibers. It follows that such simplified models do not allow evaluation of the heart electro-mechanical function and coupling, which has recently risen as the key point for understanding the LV functionality . In order to thoroughly understand the LV mechanics it is necessary to consider the complete anatomy of the LV given by the orientation of the myocardial fibres in 3D space as described by Torrent Guasp. We propose developing a 3D patient-sensitive model of the LV integrating, for the first time, the ven- tricular band anatomy (fibers orientation), the LV gross anatomy and its functionality. Such model will represent the LV function as a natural consequence of its own ventricular band anatomy. This might be decisive in restoring a proper LV contraction in patients undergoing pace marker treatment. The LV function is defined as soon as the propagation of the contractile electromechanical pulse has been modelled. In our experiments we have used the wave equation for the propagation of the electric pulse. The electromechanical wave moves on the myocardial surface and should have a conductivity tensor oriented along the muscular fibers. Thus, whatever mathematical model for electric pulse propa- gation [4] we consider, the complete anatomy of the LV should be extracted. The LV gross anatomy is obtained by processing multi slice MR images recorded for each patient. Information about the myocardial fibers distribution can only be extracted by Diffusion Tensor Imag- ing (DTI), which can not provide in vivo information for each patient. As a first approach, we have computed an average model of fibers from several DTI studies of canine hearts. This rough anatomy is the input for our electro-mechanical propagation model simulating LV dynamics. The average fiber orientation is updated until the simulated LV motion agrees with the experimental evidence provided by the LV motion observed in tagged MR (TMR) sequences. Experimental LV motion is recovered by applying image processing, differential geometry and interpolation techniques to 2D TMR slices [5]. The pipeline in figure 1 outlines the interaction between simulations and experimental data leading to our patient-tailored model.