Graph signal decomposition for multi-scale detail manipulation

In this paper we introduce a new unified framework for multi-scale detail manipulation of graph signals. The key to this unification is to model any kind of data as signals defined on appropriate weighted graphs. Graph signals are represented as the sum of successive layers, each capturing a given scale of detail. Detail layers are obtained through a series of regularization procedures based on total variation penalization over graphs. Layers are then processed separately before being recombined, thus achieving detail manipulation. The benefit of the approach is shown on images, 3D meshes and 3D colored point clouds.