Three-dimensional MR motion estimation on a single image plane based on tagged MRI and HARP processing. Tagged magnetic resonance imaging technique encodes and automatically tracks displacement of spatially modulated object in three dimensions, encoding both in plane and through-plane motion in a single image plane without affecting acquisition speed. Post-processing unravels encoding in order to directly track 3-D displacement of points within the image plane throughout image sequence. The invention is particularly suited to use on a heart for tracking and determining myocardial displacement. In one embodiment, an MR pulse sequence extends a slice following complementary spatial modulation of magnetization (CSPAMM) pulse sequence with two small z-encoding gradients immediately before the readouts in successive CSPAMM acquisitions, thereby adding a through-plane encoding from which through-plane motion can be computed from acquired images. HARP processing is used to determine in-plane motion, after which through-plane position can be determined using phase encodings. Use of balanced encodings and horizontal and vertical tags permits cancellation of systematic phase artifacts present in CSPAMM acquisitions.