A Vectorial Self-dual Morphological Filter Based on Total Variation Minimization

We present a vectorial self dual morphological filter. Contrary tomanymethods, our approach does not require the use of an ordering on vectors. It relies on theminimization of the total variationwithL norm as data fidelity on each channel. We further constraint this minimization in order not to create new values. It is shown that this minimization yields a self-dual and contrast invariant filter. Although the aboveminimization is not a convex problem, we propose an algorithm which computes a global minimizer. This algorithm relies on minimum cost cut-based optimizations.