Tracking of magnetic resonance (MR) tags in myocardial tissue promises to be an effective tool in the assessment of myocardial motion. The amount of data acquired is very large and the measurements are numerous and must be precise, requiring automated tracking methods. We describe a hierarchy of image processing steps that estimate both the endocardial and epicardial boundaries of the left ventricle, and also estimate the spines of radial tags that emanate outward from the left ventricular cavity. The first stage determines the position of the myocardial boundaries for each of 128 rays emanating from the origin. To counter the deleterious effects of noise and the presence of the tags when determining the boundary positions, we use nonlinear filtering concepts from mathematical morphology together with a priori knowledge related to boundary smoothness to improve the estimates. The second stage estimates the tag spines by matching a template in a direction orthogonal to the expected tag direction. We show results on tagged images and discuss further research directions.