Preserving accurate motion contours with reliable parameter selection

The use of decreasing functions, for mitigating the regularization at image contours, is typical in many recent optical flow methods. However, finding the correct parameter for getting the best of this strategy is challenging. Most of the methods use default parameters that are conservative, providing results that are not better than traditional approaches. Configurations that clearly enhance discontinuities may produce instabilities in the computed optical flows. This is due to the fact that the regularization process may get cancelled, yielding an ill-posed problem. In this work, we analyze the problem of instabilities and propose a method for efficiently determining the value of the parameter. We show that this approach allows us to obtain well preserved discontinuities at the same time that it avoids the ill-posed problem. The experiments with synthetic sequences demonstrate that the results are accurate and the selected parameter is close to the optimal value.