Abstract
In this paper a fuzzy mathematical morphology based on fuzzy logical operators is proposed and the Generalized Idempotence (GI) property for fuzzy opening and fuzzy closing operators is studied. It is proved that GI holds in fuzzy mathematical morphology when the selected fuzzy logical operators are left-continuous uninorms (including left-continuous t-norms) and their corresponding residual implications, generalizing known results on continuous t-norms. Two classes of left-continuous uninorms are emphasized as the only ones for which duality between fuzzy opening and fuzzy closing holds. Implementation results for these two kinds of left-continuous uninorms are included. They are compared with the classical umbra approach and the fuzzy approach using t-norms, proving that they are specially adequate for edge detection.
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González-Hidalgo, M., Torres, A.M., Ruiz-Aguilera, D., Sastre, J.T. (2009). Edge-Images Using a Uninorm-Based Fuzzy Mathematical Morphology: Opening and Closing. In: Tavares, J.M.R.S., Jorge, R.M.N. (eds) Advances in Computational Vision and Medical Image Processing. Computational Methods in Applied Sciences, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9086-8_8
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