A closed-form integration method is derived and analyzed for computing motion trajectories from velocity field data, particularly as measured by phase contrast (PC) cine MR imaging. By modeling periodic motion as composed of Fourier harmonics and integrating the material velocity of the tracked point in the frequency domain, this method gives an unbiased trajectory estimate in the presence of white measurement noise and eddy current effects. When applied to cine PC data, the method can incorporate compensation for the frequency response of the cine interpolation, offering a further improvement on the tracking accuracy. In simulation and phantom studies, the estimated trajectories were in excellent agreement with the true trajectories. Encouraging results have also been obtained on data from volunteers.