Partial difference equations on graphs for Mathematical Morphology operators over images and manifolds

The main tools of Mathematical Morphology are a broad class of nonlinear image operators. They can be defined in terms of algebraic set operators or as Partial Differential Equations (PDEs). We propose a framework of partial difference equations on arbitrary graphs for introducing and analyzing morphological operators in local and non local configurations. The proposed framework unifies the classical local PDEs-based morphology for image processing, generalizes them for non local configurations and extends them to the processing of any discrete data living on graphs.