This book focuses on designing segmentation and motion tracking methods of the coronary arteries in order to build pre-operative patient-specific motion models. Various vessel centreline and lumen segmentation algorithms are presented, including intensity based approaches, geometric model matching method and morphology-based method. A probabilistic atlas of the coronary arteries is formed from a group of subjects to facilitate the vascular segmentation and registration procedures. Non-rigid registration framework based on a free-form deformation model and multi-level multi-channel large deformation diffeomorphic metric mapping are proposed to track the coronary motion. The methods are applied to 4D CTA images acquired from various groups of patients and quantitatively evaluated. The thesis work presented in this book can be applied to the wide image processing and data analysis domains in general.