Optical Flow Estimation for a Periodic Image Sequence

We propose a temporal modeling approach for determining image motion from a sequence of images wherein the inherent motion is periodic over time. To exploit the periodic nature of the motion, we use a Fourier harmonic representation to model the temporal evolution of the motion field for the entire sequence. We then determine the motion field simultaneously for the different image frames by estimating the parameters of this representation model, where the model order in the Fourier representation serves as a regularization parameter on the temporal coherence of the motion field. This approach can take advantage of the statistics of all the available data in the image sequence. In our experiments, we tested the proposed approach on several motion types at different noise levels, including translational motion, convergent/divergent motion, and cardiac motion. Our results demonstrate that this approach could lead to more robust estimation of the motion field in the presence of strong imaging noise compared to a frame-by-frame estimation approach.