Azencott, Robert2019-11-08August 2012019-08August 201https://hdl.handle.net/10657/5326In order to study the valvular dynamic relying on a sequence of non-invasive echocardiographic 3D images of the mitral valve, one main goal is the reconstruction of shape deformations. In this dissertation, we use a spline technique to generate a static model of the mitral valve, which contains around 2000 points per snapshot. We find the optimal diffeomorphic matching of these mitral valves using an operator splitting method. To make the problem computationally accessible, we consider reproducing kernel Hilbert spaces using Gaussian kernels and weighted sums of Dirac measures. The objective function includes the kinetic energy of the velocity and a shape matching term. In order to efficiently optimize it, we apply an operator splitting method. Then based on the optimal diffeomorphism, the strain value of every point around the surface is calculated through a local surface strain tensor. A machine learning approach based on support vector machines is used to automatically classify patients into several subgroups.application/pdfengThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).Operator splitting methodGaussian kernelsShape Matching2019-11-08Thesisborn digital