The robust statistics has recently been adopted by the computer vision community. Various robust approaches in the computer vision research have been proposed in the last decade for analyzing the image motion from the image sequence. Because of the Frequent violation of the Gaussian assumption of the noise and the motion discontinuities due to multiple motions, the motion estimates based on the straightforward approaches such as the least squares estimator and the regularization often produces unsatisfactory result. Robust estimation is a promising approach to deal with these problems because it recovers the intrinsic characteristics of the original data with the reduced sensitivity to the contamination. Several previous works exist and report some isolated results, but there has been no comprehensive analysis. In this paper robust approaches to the optical flow estimation based on the maximum likelihood estimators are proposed. To evaluate the performance of the M-estimators for estimating the optical flow, comparative studies are conducted for every possible combinations of the parameters of three types of M-estimators, two types of residuals, two methods of scale estimate, and two types of starting values. Comparative studies on synthetic data show the superiority of the M-estimator of redescending psi-function using the starting value of least absolute residuals estimator using Huber scale iteration, in comparison with the other M-estimators and least squares estimator. Experimental results from the real image experiments also confirm that the proposed combinations of the M-estimators handle the contaminated data effectively and product the better estimates than the least squares estimator or the least absolute residuals estimator.