基于一般重叠函数的模糊数学形态学边缘检测方法

doi:10.6040/j.issn.1671-9352.0.2025.088

摘要/Abstract

摘要： 基于一般重叠函数与其诱导的剩余蕴涵分别构造了模糊膨胀和模糊腐蚀两类模糊数学形态学算子,并研究模糊膨胀、模糊腐蚀算子的代数性质,将模糊聚类方法与模糊膨胀、模糊腐蚀算子结合,提出一种新的模糊数学形态学边缘检测方法,利用该算法对多个灰度图像边缘检测。相较于三角模和经典合取算子的边缘检测方法,文中提出的边缘检测方法适用范围更广,实验结果表明,在尽可能提取到完整图像边缘的前提下,本文边缘检测方法能够有效减少噪声引入率。

关键词: 一般重叠函数, 剩余蕴涵, 模糊数学形态学, 图像边缘检测和提取

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

中图分类号:

TP391

王军涛,黄强. 基于一般重叠函数的模糊数学形态学边缘检测方法[J]. 《山东大学学报(理学版)》, 2026, 61(1): 36-48.

参考文献

[1] BUSTINCE H, FERNANDEZ J, MESIAR R, et al. Overlap functions[J]. Nonlinear Analysis: Theory, Methods & Applications, 2010, 72(3/4):1488-1499.
[2] JURIO A, BUSTINCE H, PAGOLA M, et al. Some properties of overlap and grouping functions and their application to image thresholding[J]. Fuzzy Sets and Systems, 2013, 229:69-90.
[3] HÁJEK P. Metamathematics of fuzzy logic[M]. Dordrecht: Springer Science & Business Media, 2013:27-56.
[4] DROSSOS C A. Generalized t-norm structures[J]. Fuzzy Sets and Systems, 1999, 104(1):53-59.
[5] DE MIGUEL L, GÓMEZ D, RODRÍGUEZ J T, et al. General overlap functions[J]. Fuzzy Sets and Systems, 2019, 372:81-96.
[6] BACZYNSKI M, BELIAKOV G, SOLA HB, et al. Advances in fuzzy implication functions[M]. Berlinb: Springer, 2013:1-30.
[7] YAGER R R. On some new classes of implication operators and their role in approximate reasoning[J]. Information Sciences, 2004, 167(1):193-216.
[8] RUAN D, KERRE E E. Fuzzy implication operators and generalized fuzzy method of cases[J]. Fuzzy Sets and Systems, 1993, 54(1): 23-37.
[9] SERRA J. Image analysis and mathematical morphology[M]. London: Academic Press, 1982:591-597.
[10] MATHERON G. Random sets and integral geometry[M]. New York: Wiley, 1975:277-278.
[11] BLOCH I, HEIJMANS H, RONSE C. Mathematical morphology[M]. Dordrecht: Springer, 2007:857-944.
[12] 石炜,刘松,杨锦春,等. 列车滚子轴承表面缺陷图像的边缘提取[J]. 机械设计与制造,2024,405(11):179-183. SHI Wei, LIU Song, YANG Jinchun, et al. Edge extraction of surface defect image of train roller bearing[J]. Machinery Design & Manufacture, 2024, 405(11):179-183.
[13] SINHA D, DOUGHERTY E R. Fuzzy mathematical morphology[J]. Journal of Visual Communication and Image Representation, 1992, 3:286-302.
[14] DE BAETS B, KERRE E E, GUPTA M. The fundamentals of fuzzy mathematical morphology part 1: basic concepts[J]. International Journal of General Systems, 1995, 23:155-171.
[15] IZAKIAN H, ABRAHAM A. Fuzzy C-means and fuzzy swarm for fuzzy clustering problem[J]. Expert Systems with Applications, 2011, 38(3):1835-1838.
[16] NACHTEGAEL M, KERRE E E. Classical and fuzzy approaches towards mathematical morphology[M] //KERRE E E, NACHTEGAEL M. Fuzzy Techniques in Image Processing. Berlin: Springer, 2000:3-57.
[17] GONZÁLEZ-HIDALGO M, MASSANET S. A fuzzy mathematical morphology based on discrete t-norms: fundamentals and applications to image processing[J]. Soft Computing, 2014, 18:2297-2311.
[18] ZHANG Xiaohong, LI Mengyuan, LIU Hui. Overlap functions-based fuzzy mathematical morphological operators and their applications in image edge extraction[J]. Fractal and Fractional, 2023, 465(7):1-23.
[19] ZHANG Xiaohong, LI Mengyuan, SHAO Songtao, et al.(I,O)-fuzzy rough sets based on overlap functions with their applications to feature selection and image edge extraction[J]. IEEE Transactions on Fuzzy Systems, 2024, 32(4):1796-1809.
[20] LI Mengyuan, ZHANG Xiaohong, SHANG Jiaoyan, et al. General quasi overlap functions and fuzzy neighborhood systems-based fuzzy rough sets with their applications[J]. IEEE Transactions on Knowledge and Date Engineering, 2024, 36(12):8349-8361.

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