Abstract
Mathematical morphology was originally conceived as a set theoretic approach for the processing of binary images. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory. This paper discusses and compares several well-known and new approaches towards gray-scale and fuzzy mathematical morphology. We show in particular that a certain approach to fuzzy mathematical morphology ultimately depends on the choice of a fuzzy inclusion measure and on a notion of duality. This fact gives rise to a clearly defined scheme for classifying fuzzy mathematical morphologies. The umbra and the level set approach, an extension of the threshold approach to gray-scale mathematical morphology, can also be embedded in this scheme since they can be identified with certain fuzzy approaches.
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Sussner, P., Valle, M.E. Classification of Fuzzy Mathematical Morphologies Based on Concepts of Inclusion Measure and Duality. J Math Imaging Vis 32, 139–159 (2008). https://doi.org/10.1007/s10851-008-0094-1
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DOI: https://doi.org/10.1007/s10851-008-0094-1