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We present a new method for tracking the motion of the heart in tagged MR images using a nonrigid image registration technique based on a 4D B-spline transformation model and the maximization of mutual information. We track the motion of the heart in a sequence of tagged MR images by registering the images taken during systole to a set of reference images taken at end-diastole. Registration is achieved by maximizing the mutual information between the sequence of images taken during systole with the reference images taken at end-diastole. The resulting deformation field is spatially and temporally smooth, and as such allows quantities such as strains and velocities to be calculated at any point in both space and time. We also present results from the motion tracking in a group of normal volunteers.