In this work, we present an implementation of discontinuity-preserving strategies in TV-L1 optical flow methods. These are based on exponential functions that mitigate the regularization at image edges, which usually provide precise flow boundaries. Nevertheless, if the smoothing is not well controlled, it may produce instabilities in the computed motion fields. We present an algorithm that allows three regularization strategies: the first one uses an exponential function together with a TV process; the second one combines this strategy with a small constant that ensures a minimum isotropic smoothing; the third one is a fully automatic approach that adapts the diffusion depending on the histogram of the image gradients. The last two alternatives are aimed at reducing the effect of instabilities. In the experiments, we observe that the pure exponential function is highly unstable while the other strategies preserve accurate motion contours for a large range of parameters.

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