Abstract : In this paper, we present a stochastic interpretation of the motion estimation problem. The usual optical flow constraint equation (assuming that the points keep their brightness along time), embed for instance within a Lucas-Kanade estimator, can indeed be seen as the minimization of a stochastic process under some strong constraints. These constraints can be relaxed by imposing a weaker temporal assumption on the luminance function and also in introducing anisotropic intensity based uncertainty assumptions. The amplitude of these uncertainties are jointly computed with the unknown velocity at each point of the image grid. We propose different versions depending on the various hypothesis assumed for the luminance function. The substitution of our new observation terms on a simple Lucas-Kanade estimator improves significantly the quality of the results. It also enables to extract an uncertainty connected to quality of the motion field.