A note on two classical enhancement filters and their associated PDE's

We establish in 2D, the P.D.E. associated with a classical image enhancement filter, the Kramer operator and compare it with another classical shock filter, the Osher-Rudin filter. We show that each one corresponds to a non-flat mathematical morphology operator conditioned by a the sign of an edge detector. In the case of the Kramer operator, the equation is conditioned by the Canny edge detector while in the case of the original Rudin-Osher filter, the equation is conditioned by the sign of the Laplacian.