Hierarchical morphological graph signal multi‐layer decomposition for editing applications

Abstract

We address the problem of editing signals such as 2D color images or 3D colored meshes that are represented under the general framework of graph signals. As state-of-the-art editing approaches decompose an image into several layers in order to manipulate them, we propose a hierarchical multi-layer decomposition of graph signals that relies on morphological filtering. Since morphological filtering operators require a complete lattice, a dedicated approach for the morphological processing of vectorial data on graphs is used. By iterating the application of morphological filterings of decreasing sizes, the graph signal is decomposed into several detail layers, each capturing a given detail level. Editing applications such as abstraction, sharpness enhancement and tone mapping are shown to illustrate the benefits of the proposed approach.