JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (1): 36-48.doi: 10.6040/j.issn.1671-9352.0.2025.088

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Fuzzy mathematical morphology edge detection method derived from general overlap functions

  

  1. 1. School of Science, Xian Shiyou University, Xian 710065, Shaanxi, China;
    2. School of Computer Science, Xian Shiyou University, Xian 710065, Shaanxi, China
  • Published:2026-01-15

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Abstract: Two types of fuzzy mathematical morphology operators are constructed based on the general overlap function, and the corresponding fuzzy mathematical morphological edge detection methods are proposed, which are successfully applied to image edge extraction. Based on the general overlap functions and their corresponding residuated implications, two types of fuzzy mathematical morphological operators, including fuzzy erosion and fuzzy dilation, are constructed, respectively, and their related algebraic properties are studied. A new fuzzy mathematical morphological edge detection method is proposed by combining the fuzzy clustering method with the fuzzy erosion and fuzzy dilation. This edge detection method is wider than that of the edge detection method of the triangular norms and the classical conjuction, and the experimental results show that the noise introduction rate can be effectively reduced under the premise of extracting the edge of the complete image as much as possible.

Key words: general overlap function, residuated implication, fuzzy mathematical morphology, image edge detection and extraction

CLC Number: 

  • TP391
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