Deformation Tracking and Diffeomorphic Matching in Medical Imaging

This thesis focuses on deformation tracking and diffeomorphic matching in 2D or 3D medical imaging. We have developed and implemented novel algorithmic approaches to track both the myocardial motion in 2D IntraCardiac Echocardiography images and the Mitral Valve deformation in 3D ultrasound images. We studied the myocardial deformation through the registration of IntraCardiac Echocardiography images, by utilizing the statistical properties of the speckle noise. Within a framework of parametric elastic registration, the deformation was estimated by optimizing the energy function computed by applying the maximum likelihood approach to the speckle noise model. And, the optimization procedure is accelerated by applying the multiresolution method and local masking, which also improve the robustness of our algorithm. Numerical results are verified perfectly by the medical data from Texas Medical Center. We then consider optimal matching of submanifolds such as curves and surfaces by a variational approach based on Hilbert spaces of diffeomorphic transformations. In an abstract setting, the optimal matching is formulated as a minimization problem, in which the objective functional consists of two parts measuring the elastic energy of the dynamically deformed surfaces and the quality of the matching. The performance of our diffeomorphic tracking in medical 3D-image movies is illustrated by numerical results for the dynamic modeling of the human mitral valve annulus by computer analysis of 3D-echocardiographic image sequences.