The maximum likelihood estimator is not “optimal” on 3-D motion estimation from noisy optical flow

We prove that the maximum likelihood estimator (MLE) for estimating 3-D motion from noisy optical flow is not “optimal”. The MLE minimizes the mean square error of the observed optical flow. We show that the MLE´s covariance matrix does not reach the Cramer-Rao lower bound, and that there is an unbiased estimator whose covariance matrix is smaller than that of the MLE when a Gaussian noise distribution is assumed for a sufficiently large number of observed points. We propose a new estimator whose covariance matrix is smaller than that of the MLE under certain conditions