Abstract

The decomposition of images into their meaningful compo- nents is one of the ma jor tasks in computer vision. Tadmor, Nezzar and Vese [1] have proposed a general approach for multiscale hierarchical de- composition of images. On the basis of this work, we propose a multiscale hierarchical decomposition of functions on graphs. The decomposition is based on a discrete variational framework that makes it possible to pro- cess arbitrary discrete data sets with the natural introduction of nonlocal interactions. This leads to an approach that can be used for the decom- position of images, meshes, or arbitrary data sets by taking advantage of the graph structure. To have a fully automatic decomposition, the issue of parameter selection is fully addressed. We illustrate our approach with numerous decomposition results on images, meshes, and point clouds and show the benefits.