We have addressed the problem of tracking the nonrigid motion of the heart using a sequence of velocity fields and a sequence of contours. The information from both the contours and the dense velocity fields is integrated into a deforming mesh that is placed over the myocardium at one time frame and then tracked over the entire cardiac cycle. The deformation is guided by a smoothing filter that provides a compromise between (i) believing the dense field velocity and the contour data when it is crisp and coherent in a local spatial and temporal sense and (ii) employing a temporally smooth cyclic model of cardiac motion when contour and velocity data are not trustworthy. The method has been carefully evaluated with simulated data and phantom data. Experiments with in vivo data have also been conducted.