Multiresolution motion estimation with discontinuity preservation using MRF and determination of the regularization hyperparameter

This paper deals with the estimation of a dense displacement vector field between two successive images in a sequence using the markovian modelization. The optical flow is processed in two different hierarchical frameworks with the regularized constraint model we proposed. This model is derived from the potential function introduced by Geman and MacClure, in which we integrate the local motion amplitude obtained by Fourier analysis. It enables adaptive smoothness and then preserves motions discontinuities. First we apply a coarse-to-fine strategy in a standard multiresolution pyramid. We use the ICM algorithm only on the finest resolution scale of the pyramid, and the simulated annealing on the other scales. Secondly, we work with the multiscale scheme which allows only one resolution for the observations and a pyramidal structure for the primitives (the estimated optical flow). The results obtained on synthetic and real images sequences show that the estimation is efficiency increased. In our second contribution in this paper, we define a criterion for the determination of the regularization hyperparameter which controls the weight of the regularization term in the energy function. It is based on the entropy of the estimated motion vectors. An experimental study of this entropy allows to find the value of the hyperparameter which best fits a given sequence.