Phase velocity magnetic resonance imaging (MRI) has shown considerable potential for tracking distinct regions of the myocardium throughout the cardiac cycle. Phase contrast MR imaging produces multiple images, each phase encoded for velocity in a different direction, in which individual pixels depict the local motion of the tissue. In this work we present in detail three algorithms for tracking motion based on these images. Both simulated and phantom data are used to examine some of the problems encountered in practice in tracking points based on velocity maps. Solutions to these problems are offered when possible. The impact of noise and low order phase errors in the data on each of the three tracking approaches is examined. In addition, problems due to tissue expansion and contraction, to 2D versus 3D tracking, and to round off errors from motion which is small relative to pixel size or slice thickness, are considered. An example using data obtained in vivo is included to demonstrate the efficacy of the best of the three tracking algorithms in measuring left ventricular circumferential shortening preinfarct and postinfarct in a canine model.