Morphological PDEs on graphs for filtering and inpainting of point clouds

In this paper, we propose an adaptation of morphological Partial Differential Equations (PDEs) on graphs using the framework of Partial difference Equations (PdEs). This enables to define adaptive morphological operators on graphs. We then show how these operators can be used for interpolation and filtering of raw point clouds. To enable a patch-based processing of point clouds, we also show how a weighted graph based on patches can be associated with a point cloud. Finally, we present applications in cultural heritage¹.