Nonlocal PDEs-Based Morphology on Weighted Graphs for Image and Data Processing

Mathematical morphology (MM) offers a wide range of operators to address various image processing problems. These operators can be defined in terms of algebraic (discrete) sets or as partial differential equations (PDEs). In this paper, we introduce a nonlocal PDEs-based morphological framework defined on weighted graphs. We present and analyze a set of operators that leads to a family of discretized morphological PDEs on weighted graphs. Our formulation introduces nonlocal patch-based configurations for image processing and extends PDEs-based approach to the processing of arbitrary data such as nonuniform high dimensional data. Finally, we show the potentialities of our methodology in order to process, segment and classify images and arbitrary data.