On optimal brightness functions for optical flow

In the typical optical flow problem, the brightness function is an inherent part of the underlying physical process. In the case of magnetic resonance imaging of the heart, however, it is possible to modulate the brightness function using tagging techniques. Experimental evidence suggests that when a sinusoidal brightness function is used, there is an optimum frequency. The reasons for an optimal frequency in one dimension are investigated by formulating the optical flow problem as an optimal linear smoothing problem. A method based on minimizing the theoretical smoothed error variance is proposed for finding the optimal frequency a priori. Simulations are presented for a Wiener process velocity that show the existence of an optimal frequency and the ability of the proposed method to determine this frequency a priori