Patch-Based Mathematical Morphology for Image Processing, Segmentation and Classification

Abstract

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.

Patch-Based Identification of Lexical Semantic Relations

“…First, studies about the mental lexicon [13,23] theorize that words are highly interconnected within a mental semantic network, such that conceptual information is encoded in one's mind rather than single words alone. Second, studies in image segmentation show that dividing up an image into a patch work of regions, each of which being homogeneous, leads to successful results [18,20]. Analogously, we propose to define a word patch as a source word augmented by its semantically close related neighbors, and expect that performance gains can be achieved by grounding the decision process on finding representation regularities between word patches.…”