摘要
作为一种传统的非线性图像处理算法,数学形态学在很多领域有着广泛应用。由于非局部形态学同时具备了自适应和非局部自相似的优点,其在近年引起研究者的关注。然而,现有算法往往具有对噪声较为敏感的缺陷。同时,由于其结构体包含了整个搜索窗的所有像素,这导致成员的可靠性较差,进而影响了算法性能。针对上述不足,提出了一种新的非局部数学形态学(RNLMM)。通过相互近邻策略,使结构体成员的可靠性得到提升。并且,将经典形态学(局部)与非局部形态学相结合,设计出一个算子的串行实现方式,有效提高了其对噪声的鲁棒性。理论表明,这些算子依然能够保留经典形态学算子所具备的一些重要数学性质。最后的去噪实验初步验证了RNLMM算法的优良性能。
As a traditional nonlinear tool for image processing,mathematical morphology(MM)is yet applied widely.Among the relevant researches,nonlocal extensions have been studied due to their advantages of adaptivity and nonlocal self-similarity.However,the existing extensions are generally fragile to noises.Meanwhile,because their structuring element(SE)contains all the pixels of the whole search window,the reliability of the SE member is discounted inevitably.In this paper,a novel nonlocal mathematical morphology(RNLMM)is proposed.The reliability of structure elements is improved by k-reciprocal nearest neighbors(KRNN).To improve the robustness to noise effectively,the traditional(local)method and nonlocal one are serially combined in the operator implementation.Theoretical proofs indicate that the operators from RNLMM successfully keep the important mathematical properties.The good performance of RNLMM is preliminarily verified via denoising experiments.
作者
吕美琪
孙忠贵
Lü Meiqi;SUN Zhonggui(School of Mathematical Sciences,Liaocheng University,Liaocheng 252059,China)
出处
《聊城大学学报（自然科学版）》
2022年第6期19-26,共8页
Journal of Liaocheng University:Natural Science Edition
基金
国家自然科学基金项目(11801249)
山东省自然科学基金项目(ZR2020MF040)
聊城大学开放课题(319312101-01)资助。
关键词
数学形态学
非局部方法
相互近邻
数学性质
鲁棒性
mathematical morphology
nonlocal method
k-reciprocal nearest neighbors
mathematical property
robustness
