Nonlocal PDE morphology: a generalized shock operator on graph

Abstract

This paper presents an adaptation and extension of the shock filters on weighted graphs using the formalism of partial difference equations. This adaptation leads to new morphological operators that alternate between nonlocal dilation and nonlocal erosion filter type on graphs. Furthermore, this adaptation extends the shock filter applications to any data that can be represented by graphs. This approach is illustrated through image, data defined on region maps, and 3D point cloud processing.