In this paper, the problem of motion estimation is formulated mathematically and two classical methods are reviewed. Focus is then placed on a slightly different method which offers the advantage of stable convergence while providing a good approximation of the solution. Traditionally, the solution has been stabilized by regularization, as proposed by Tikhonov, i.e., by assuming a priori the smoothness of the solution. This hypothesis cannot be made globally over a field of motion vectors. Hence we propose a regularization process involving MOTION DISCONTINUITIES based on a Markov (MRF) model of motion. A new regularization function involving discontinuities is defined. Since the criterion is no longer quadratic, a deterministic relaxation method can be applied to estimate the global minimum. This relaxation scheme is based on the minimization of a sequence of quadratic functionals which tend toward the criterion. The algorithms presented were tested on two sequences: SPHERE, a synthetic sequence, and INTERVIEW, a real sequence.