In this paper, estimation of motion vector fields containing boundaries from noisy data is investigated, where the boundaries mean edges or spatial discontinuities. Then, regularization methods which can retain boundaries are required. We adopt evolution equations with non-linear diffusion terms derived from a logarithmic stabilizing functional. Estimates are obtained in the process of time evolution of the equations. Here, discritization method become critical issue. We propose a novel discritization method for these terms, which is a sort of minmax scheme. Results of simulations are displayed, where better estimates and more distinct boundaries of them are obtained with propesed method than with naive method
