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Homotopy Semilattices

Keshet, Renato

HPL-2004-1

Keyword(s): mathematical morphology; complete inf-semilattices; erosion; opening; topographic distance; reconstruction; fillhole

Abstract: A new, quasi-self-dual approach for morphological image processing is introduced. This approach is based on a complete semilattice framework. The related morphological erosion, for instance, shrinks connected components in an image, regardless to whether they are bright or dark. In the binary case, the morphological operators are based on a complete inf-semilattice that is related to the homotopy tree. Two grayscale generalizations are investigated. The first is based on the topographic-distance concept, whereas the second one utilizes the reconstruction-based fillhole operation.

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