Abstract
We establish in this paper the link between the two main approaches for fuzzy mathematical morphology, based on duality with respect to complementation and on the adjunction property, respectively. We also prove that the corresponding definitions of fuzzy dilation and erosion are the most general ones if a set of classical properties is required.
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References
Dubois, D., Prade, H.: Inverse Operations for Fuzzy Numbers. In: Sanchez, E., Gupta, M. (eds.) Fuzzy Information, Knowledge Representation and Decision Analysis, IFAC Symposium, Marseille, France, pp. 391–396 (1983)
Bloch, I., Maître, H.: Fuzzy Mathematical Morphologies: A Comparative Study. Pattern Recognition 28, 1341–1387 (1995)
Sinha, D., Dougherty, E.R.: Fuzzification of Set Inclusion: Theory and Applications. Fuzzy Sets and Systems 55, 15–42 (1993)
Baets, B.D.: Idempotent Closing and Opening Operations in Fuzzy Mathematical Morphology. In: ISUMA-NAFIPS 1995, College Park, MD, pp. 228–233 (1995)
Bandemer, H., Näther, W.: Fuzzy Data Analysis. In: Theory and Decision Library, Serie B: Mathematical and Statistical Methods. Kluwer Academic Publisher, Dordrecht (1992)
Popov, A.T.: Morphological Operations on Fuzzy Sets. IEE Image Processing and its Applications,, 837–840 (1995)
Nachtegael, M., Kerre, E.E.: Classical and Fuzzy Approaches towards Mathematical Morphology. In: Kerre, E.E., Nachtegael, M. (eds.) Fuzzy Techniques in Image Processing. Studies in Fuzziness and Soft Computing, pp. 3–57. Springer, Heidelberg (2000)
Deng, T.Q., Heijmans, H.: Grey-Scale Morphology Based on Fuzzy Logic. Journal of Mathematical Imaging and Vision 16, 155–171 (2002)
Maragos, P.: Lattice Image Processing: A Unification of Morphological and Fuzzy Algebraic Systems. Journal of Mathematical Imaging and Vision 22, 333–353 (2005)
Rosenfeld, A.: The Fuzzy Geometry of Image Subsets. Pattern Recognition Letters 2, 311–317 (1984)
Bloch, I.: Fuzzy Mathematical Morphology and Derived Spatial Relationships. In: Kerre, E., Nachtegael, N. (eds.) Fuzzy Techniques in Image Processing, pp. 101–134. Springer, Heidelberg (2000)
Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New-York (1980)
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Bloch, I. (2006). Duality vs Adjunction and General Form for Fuzzy Mathematical Morphology. In: Bloch, I., Petrosino, A., Tettamanzi, A.G.B. (eds) Fuzzy Logic and Applications. WILF 2005. Lecture Notes in Computer Science(), vol 3849. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11676935_44
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DOI: https://doi.org/10.1007/11676935_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32529-1
Online ISBN: 978-3-540-32530-7
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