We present a vectorial self dual morphological filter. Contrary to many methods, our approach does not require the use of an ordering on vectors. It relies on the minimization of the total variation with
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 above minimization is not a convex problem, we propose an algorithm which computes a global minimizer. This algorithm relies on minimum cost cut-based optimizations.