基于一般重叠函数的模糊数学形态学边缘检测方法

Fuzzy mathematical morphology edge detection method derived from general overlap functions

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。

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 conjunction, 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.

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

Key words

general overlap function / residuated implication / fuzzy mathematical morphology / image edge detection and extraction

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基金资助

国家自然科学基金资助项目(12471442)

陕西省自然科学基础研究计划资助项目(2025JC-YBQN-092)

陕西省自然科学基础研究计划资助项目(2025JC-YBMS-034)

陕西省教育厅青年高校创新团队科研项目(23JP132)

西安石油大学研究生创新项目(YCX2413141)