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.
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Guichard, F., Morel, J. A Note on Two Classical Enhancement Filters and Their Associated PDE's. International Journal of Computer Vision 52, 153–160 (2003). https://doi.org/10.1023/A:1022904124348
- shock filters
- enhancement filters
- deblurring filters