Manifold-based mathematical morphology for graph signal editing of colored images and meshes

This paper presents a framework for morphological processing of graph signals and investigates its usage for colored images and meshes editing tasks. The proposed method enables, with the help of the construction of a manifold-based ordering of color vectors, to define a new representation of graph signals in the form of an ordering of vectors and an index. The ordering relies on three steps: dictionary learning, manifold learning, and out of sample extension. This enables to formulate morphological operators for graphs signals and we demonstrate the performance of the proposed method on various colored image and mesh editing applications (simplification, abstraction, enhancement).