Paper
1 February 1992 Intrinsically fuzzy approach to mathematical morphology
Divyendu Sinha, Edward R. Dougherty
Author Affiliations +
Abstract
Whereas gray-scale morphology has been formally interpreted in the context of fuzzy sets, heretofore there has not been developed a truly fuzzy mathematical morphology. Specifically, mathematical morphology is based on the notion of fitting, and rather than simply characterize standard morphological fitting in fuzzy terms, a true fuzzy morphology must characterize fuzzy fittings. Moreover, it should preserve the nuances of both mathematical morphology and fuzzy sets. In the present paper, we introduce a framework that satisfies these criteria. In contrast to the unusual binary or gray-scale morphology, herein erosion measures the degree to which one image is beneath (which is a subset type relation) another image, and it does so by employing an index for set inclusion. The result is a quite different `fitting' paradigm. Based on this new fitting approach, we define erosion, dilation, opening, and closing. The true fuzziness of the theory can be seen in a number of ways, one being that the dilation does not commute with union. (The commutativity lies at the heart of nonfuzzy lattice-based mathematical morphology.) However, we do arrive at a counterpart of Matheron's Representation Theorem for increasing translation-invariant mappings.
© (1992) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Divyendu Sinha and Edward R. Dougherty "Intrinsically fuzzy approach to mathematical morphology", Proc. SPIE 1607, Intelligent Robots and Computer Vision X: Algorithms and Techniques, (1 February 1992); https://doi.org/10.1117/12.57084
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Cited by 10 scholarly publications.
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KEYWORDS
Fuzzy logic

Binary data

Mathematical morphology

Computer vision technology

Machine vision

Robot vision

Robots

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