Aortic valve disease is an important cardio-vascular disorder, which affects 2.5% of the global population and often requires elaborate clinical management. Experts agree that visual and quantitative evaluation of the valve, crucial throughout the clinical workflow, is currently limited to 2D imaging which can potentially yield inaccurate measurements. In this paper, we propose a novel approach for morphological and functional quantification of the aortic valve based on a 4D model estimated from computed tomography data. A physiological model of the aortic valve, capable to express large shape variations, is generated using parametric splines together with anatomically-driven topological and geometrical constraints. Recent advances in discriminative learning and incremental searching methods allow rapid estimation of the model parameters from 4D Cardiac CT specifically for each patient. The proposed approach enables precise valve evaluation with model-based dynamic measurements and adv...