Inhomogeneous morphological PDEs for robust and adaptive image shock filters

Classical morphological filters suffer from well performing in a noisy environment, and intrinsic image structures are not taken into account. The authors propose here an alternative to overcome such weaknesses, by properly using robust shock filters and inhomogeneity. Thus, they obtain multiscale morphological operators by using image edge functions as local weights in inhomogeneous Hamiltonians in classical multiscale dilations/erosions formulated with partial differential equations (PDEs). They provide the equivalent sup–inf-based formulations, and derive sharpening/enhancement methods. In addition, they establish the PDE associated with the asymptotical iterations of the proposed robust and adaptive filters. The good behaviours of the proposed sup–inf and PDE-based methods are illustrated on synthetic, greyscale, and colour images; results are analysed both qualitatively and quantitatively.