Graph-based morphological processing of multivariate microscopy images and data bases

The extension of lattice based operators to manifolds is still a challenging theme in mathematical morphology. In this paper, we propose to explicitly construct complete lattices and replace each element of a manifold by its rank suitable for classical morphological processing. Manifold learning is considered as the basis for the construction of a complete lattice. The whole processing of multivariate functions is expressed on graphs to have a formalism that can be applied on images, region adjacency graphs, and image databases. Several examples in microscopy do illustrate the benefits of the proposed approach.