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Accurate delineation of the volumetric motion of the left ventricle (LV) of the heart from tagged magnetic resonance imaging (MRI) is an important area of research. The authors have built a system that takes extracted tag line features from short axis (SA) and long axis (LA) image sequences as input and fits a four-dimensional (4-D) time-varying B-spline model to the data by simultaneously fitting the model knot solids to MRI frames via matching three sequences of solid knot planes to the LV tag planes for 4-D tracking. Important advantages of the model are that reconstruction of tag surfaces, three-dimensional (3-D) material point localization, as well as displacement reconstruction are all achieved in a single step. The generated 3-D displacement fields are validated with a cardiac motion simulator, and 3-D motion fields capturing in vivo deformations in a porcine model with posterolateral myocardial infarction are illustrated.