We propose an efficient solution for preserving the motion boundaries in variational optical flow methods. This is a key problem of recent TV-L 1 methods, which typically create rounded effects at flow edges. A simple strategy to overcome this problem consists in inhibiting the smoothing at high image gradients. However, depending on the strength of the mitigating function, this solution may derive in an ill-posed formulation. Therefore, this type of approaches is prone to produce instabilities in the estimation of the flow fields. In this work, we modify this strategy to avoid this inconvenience. Then, we show that it provides very good results with the advantage that it yields an unconditionally stable scheme. In the experimental results, we present a detailed study and comparison between the different alternatives.

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