A Note on Two Classical Enhancement Filters and Their Associated PDE's

Authors:
Frédéric Guichard;Jean-Michel Morel
Affiliations:
Poseidon-Technologies, 3 rue Nationale, 92100 Boulogne-Billancourt, France. fguichard@poseidon.fr;CMLA, ENS Cachan, Avenue Président Wilson, 91235 Cachan Cedex, France. morel@cmla.ens-cachan.fr
Venue:
International Journal of Computer Vision
Year:
2003

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Abstract

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.