A measure of deformation energy suitable for fitting deformable models to image data is described. An object's displacement is constrained to be globally smooth by penalizing the variation of the deformation gradient tensor. This homogeneous deformation measure is invariant to arbitrary rigid body motion of object and viewpoint, given the correspondence between model and data. It remains quadratic in the displacement parameters, leading to linear-least-squares fits. The method was used to reconstruct the nonhomogeneous 3-D motion of the heart wall from tomographic magnetic resonance images. A finite-element model of the left ventricle was deformed to fit material points tracked in biplanar views. Only the in-plane components were available from each separate image, the through-plane components being reconstructed in the fit. >
['Alistair A. Young', 'Leon Axel']
Non-rigid heart wall motion using MR tagging