Anomalous diffusion, dilation, and erosion in image processing

In this talk, anomalous sub- and super-diffusion arising inimage processing is considered and is modeled by a diffusionequation with fractional time derivative. It mightserve as a building block for the construction of variousfilters. The resulting partial differential equation is discretisedin space with centered differences and in time withthe explicit or implicit Euler method, respectively. A numericalinvestigation is performed to illustrate new andinteresting results. Additionally, the time derivative of thepartial differential equation describing dilation and erosionis replaced by a fractional time derivative and then solvednumerically. Interesting new questions arise from the presentednumerical results