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Tagged magnetic resonance imaging (tagged MRI or tMRI) provides a means of directly and noninvasively displaying the internal motion of the myocardium. Reconstruction of the motion field is needed to quantify important clinical information, e.g., the myocardial strain, and detect regional heart functional loss. In this paper, we present a three-step method for this task. First, we use a Gabor filter bank to detect and locate tag intersections in the image frames, based on local phase analysis. Next, we use an improved version of the robust point matching (RPM) method to sparsely track the motion of the myocardium, by establishing a transformation function and a one-to-one correspondence between grid tag intersections in different image frames. In particular, the RPM helps to minimize the impact on the motion tracking result of (1) through-plane motion and (2) relatively large deformation and/or relatively small tag spacing. In the final step, a meshless deformable model is initialized using the transformation function computed by RPM. The model refines the motion tracking and generates a dense displacement map, by deforming under the influence of image information, and is constrained by the displacement magnitude to retain its geometric structure. The 2D displacement maps in short and long axis image planes can be combined to drive a 3D deformable model, using the moving least square method, constrained by the minimization of the residual error at tag intersections. The method has been tested on a numerical phantom, as well as on in vivo heart data from normal volunteers and heart disease patients. The experimental results show that the new method has a good performance on both synthetic and real data. Furthermore, the method has been used in an initial clinical study to assess the differences in myocardial strain distributions between heart disease (left ventricular hypertrophy) patients and the normal control group. The final results show that the proposed- method is capable of separating patients from healthy individuals. In addition, the method detects and makes possible quantification of local abnormalities in the myocardium strain distribution, which is critical for quantitative analysis of patients' clinical conditions. This motion tracking approach can improve the throughput and reliability of quantitative strain analysis of heart disease patients, and has the potential for further clinical applications.