A convex approximation of regularization models for motion estimation with Markov random fields

In most situations, the mere gray value variations do not provide sufficient information in order to estimate the displacement vectors field between two successive frames in a sequence. The regularization constraints are necessary to solve this problem. Regularization models usually employed, taking into account the discontinuities of the displacement vectors field, involve non-convex functions. Determinist algorithms do not give the optimal solution for such models. We propose a method that takes into account the discontinuities while allowing a convex approximation of a non-convex regularization model. This method is based on a Markov random field model in which we integrate a local motion amplitude obtained by Fourier analysis. The model that we thus obtained enables adaptive smoothness of the displacement field. The motion estimation is clearly improved, especially at the edges. Some results of this method on real and synthetic images are given