Rank transformation and manifold learning for multivariate mathematical morphology

The extension of lattice based operators to multivariate images is still a challenging theme in mathematical morphology. In this paper, we propose to explicitly construct complete lattices and replace each element of a multivariate image by its rank, creating a rank image suitable for classical morphological processing. Manifold learning is considered as the basis for the construction of a complete lattice after reducing a multivariate image to its main data by Vector Quantization. A quantitative comparison between usual ordering criteria is performed and experimental results illustrate the abilities of our proposal.