Image motion estimation using the spatiotemporal approach has largely relied on the constant velocity assumption, and thus becomes inappropriate when the velocity of the imaged scene or the camera changes during the data acquisition time. Using a polynomial or a trigonometric polynomial model for the time variation of the image motion, spatiotemporal algorithms are developed in this paper to handle time-varying (but space-invariant) motion. Under these models, it is shown that time-varying image motion estimation is equivalent to parameter estimation of one-dimensional (1-D) polynomial phase or phase-modulated signals, which allows one to exploit well-established results in radar signal processing. When compared with alternative approaches, the resulting motion estimation algorithms produce more accurate estimates. Simulation results are provided to demonstrate the proposed schemes.