Morphological PDEs on Graphs for Image Processing on Surfaces and Point Clouds

Abstract

Partial Differential Equations (PDEs)-based morphology offers a wide range of continuous operators to address various image processing problems. Most of these operators are formulated as Hamilton-Jacobi equations or curve evolution level set and morphological flows. In our previous works, we have proposed a simple method to solve PDEs on point clouds using the framework of PdEs (Partial difference Equations) on graphs. In this paper, we propose to apply a large class of morphological-based operators on graphs for processing raw 3D point clouds and extend their applications for the processing of colored point clouds of geo-informatics 3D data. Through illustrations, we show that this simple framework can be used in the resolution of many applications for geo-informatics purposes.