As decisions in cardiology increasingly rely on noninvasive methods, fast and precise image processing tools have become a crucial component of the analysis workflow. To the best of our knowledge, we propose the first automatic system for patient-specific modeling and quantification of the left heart valves, which operates on cardiac computed tomography (CT) and transesophageal echocardiogram (TEE) data. Robust algorithms, based on recent advances in discriminative learning, are used to estimate patient-specific parameters from sequences of volumes covering an entire cardiac cycle. A novel physiological model of the aortic and mitral valves is introduced, which captures complex morphologic, dynamic, and pathologic variations. This holistic representation is hierarchically defined on three abstraction levels: global location and rigid motion model, nonrigid landmark motion model, and comprehensive aortic-mitral model. First we compute the rough location and cardiac motion applying marginal space learning. The rapid and complex motion of the valves, represented by anatomical landmarks, is estimated using a novel trajectory spectrum learning algorithm. The obtained landmark model guides the fitting of the full physiological valve model, which is locally refined through learned boundary detectors. Measurements efficiently computed from the aortic-mitral representation support an effective morphological and functional clinical evaluation. Extensive experiments on a heterogeneous data set, cumulated to 1516 TEE volumes from 65 4-D TEE sequences and 690 cardiac CT volumes from 69 4-D CT sequences, demonstrated a speed of 4.8 seconds per volume and average accuracy of 1.45 mm with respect to expert defined ground-truth. Additional clinical validations prove the quantification precision to be in the range of inter-user variability. To the best of our knowledge this is the first time a patient-specific model of the aortic and mitral valves is automatically estimated from volumetric sequences.