The accurate and clinically useful estimation of the shape, motion, and deformation of the left ventricle of a heart (LV) is an important yet open research problem. Recently, computer vision techniques for reconstructing the 3-D shape and motion of the LV have been developed. The main drawback of these techniques, however, is that their models are formulated in terms of either too many local parameters that require non-trivial processing to be useful for close to real time diagnosis, or too few parameters to offer an adequate approximation to the LV motion. To address the problem, we present a new class of volumetric primitives for a compact and accurate LV shape representation in which model parameters are functions. Lagrangian dynamics are employed to convert geometric models into dynamic models that can deform according to the forces manifested in the data points. It is thus possible to make a precise estimation of the deformation of the LV shape endocardial, epicardial and anywhere in between with a small number of intuitive parameter functions. We believe that the proposed technique has a wide range of potential applications. In this thesis, we demonstrate the possibility by applying it to the 3-D LV shape and motion characterization from magnetic tagging data (MRI-SPAMM). We show that the results of our experiments with normal and abnormal heart data enable us to quantitatively verify the physicians' qualitative conception of the left ventricular wall motion.