MRI is unique in its ability to non-invasively and selectively alter tissue magnetization, and create grid patterns on a soft, deforming body such as the heart muscle. We track motion of myocardial tag lines with energy. minimizing B-spline snakes. Oriented tag templates are first constructed by simulating the MR imaging process. The templates are subsequently correlated with the image data, giving rise to an energy landscape, which is optimized over with dynamic programming. Tracking the valleys of the energy landscape with snakes allows for measurement of MR tag deformations due to tissue motion. Tissue deformation parameters corresponding to strain, vorticity, and compression/expansion of myocardial regions are also derived. The latter two quantities are computed from a modified thin-plate spline reconstruction of a dense motion field.