Learning graph neighborhood topological order for image and manifold morphological processing

The extension of lattice based operators to multivariate images is a challenging theme in mathematical morphology. We propose to consider manifold learning as the basis for the construction of a complete lattice by learning graph neighborhood topological order. With these propositions, we dispose of a general formulation of morphological operators on graphs that enables us to process by morphological means any kind of data modeled by a graph.