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In this dissertation, the author investigates five image segmentation and registration techniques based on the variational formulation for medical imaging applications. First, a novel segmentation approach is proposed to jointly delineate the boundaries of epi- and endocardium of the left ventricle on Magnetic Resonance Imaging (MRI) under a variational framework using level sets. Second, techniques are developed to examine multimodal data integration with an electroanatomic mapping data and MRI images for computer-aided catheter ablation of atrial fibrillation accurately. Third, a multimodality image registration algorithm for the alignment of myocardial perfusion SPECT (MPS) and coronary computed tomography angiography scans is presented utilizing geometric features from a reliable segmentation of MPS volumes. Fourth, a nonlinear ultrasound image registration method is proposed using the intensity and the local phase information under a variational framework. Finally, a fully automatic and accurate nonlinear volume registration for longitudinal Coronary CT angiography scan pairs is developed. The proposed algorithms combine global displacement and local deformation using nonlinear volume co-registration with a volume-preserving constraint. Extensive computer simulations have been conducted and clinical validations have been performed to demonstrate the improved accuracy of the proposed techniques.
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