Patch-based mathematical morphology for image processing, segmentation and classification

Abstract

In this paper, a new formulation of patch-based adaptive mathematical morphology is addressed. In contrast to classical approaches, the shape of structuring elements is not modified but adaptivity is directly integrated into the definition of a patch-based complete lattice. The manifold of patches is learned with a nonlinear bijective mapping, interpreted in the form of a learned rank transformation together with an ordering of vectors. This ordering of patches relies on three steps: dictionary learning, manifold learning and out of sample extension. The performance of the approach is illustrated with innovative examples of patch-based image processing, segmentation and texture classification.