Optimal brightness patterns for 2-D optical flow

The authors describe a method for finding the optimal brightness function by formulating optical flow as an optimal linear smoothing problem and deriving an a priori performance measure based on the estimation error covariance and the effect of the temporal derivative approximation error. It is shown that the performance of optical flow is mainly a function of the curvature of the brightness function. At low curvatures, there is little variation in the spatial gradient across the image and the underlying motion is obscured by the aperture problem. At high curvatures, the numerical computation of the temporal derivative increases the measurement noise variance, and the resulting optimal estimate is oversmoothed. The optimal brightness function represents the optimal tradeoff between these two effects.<>