The "direct methods" achieve global image registration without explicit knowledge of feature correspondences. We employ the motion gradient constraint as the relation between the motion parameters and the measured image gradients. While this relation appears as a linear system of equations, for any motion model (other than a translation) we show that the underlying noise process is data-dependent, i.e., heteroscedastic, a fact which must be taken into account in the parameter estimation process. The improvement obtained using the adequate procedure is confirmed for the 2D rigid motion model through comparison with the traditional total least square approach.