电子学报 ›› 2018, Vol. 46 ›› Issue (8): 1969-1975.DOI: 10.3969/j.issn.0372-2112.2018.08.023

• 学术论文 • 上一篇    下一篇

一个具有附益性及保序性算子的形态学非局部拓展

孙忠贵1,2, 高新波2, 张冬梅1, 李洁2, 王颖2   

  1. 1. 聊城大学数学科学学院, 山东聊城 252000;
    2. 西安电子科技大学电子工程学院, 陕西西安 710071
  • 收稿日期:2017-05-24 修回日期:2017-10-26 出版日期:2018-08-25
    • 通讯作者:
    • 高新波
    • 作者简介:
    • 孙忠贵 男,1971年出生,山东聊城人,博士,现为聊城大学数学科学学院副教授、硕士生导师,主要研究方向为图像处理与机器学习.E-mail:altlp@nuaa.edu.cn.
    • 基金资助:
    • 国家自然科学基金 (No.61432014,No.61671339,No.U1605252); 山东省自然科学基金 (No.ZR2014FM032); 聊城大学博士科研基金 (No.318051711)

A Nonlocal Extension of Morphology with Adjunction and Order-Preservation Operators

SUN Zhong-gui1,2, GAO Xin-bo2, ZHANG Dong-mei1, LI Jie2, WANG Ying2   

  1. 1. School of Mathematics Science, Liaocheng University, Liaocheng, Shandong 252000, China;
    2. School of Electronic Engineering, Xidian University, Xi'an, Shaanxi 710071, China
  • Received:2017-05-24 Revised:2017-10-26 Online:2018-08-25 Published:2018-08-25

摘要: 近年,形态学非局部拓展工作在图像处理领域受到众多关注.而附益性算子是经典形态学的最基本形式,也是形态学分析方法最重要的变换工具.为此,一些研究者就形态学非局部拓展中如何保持算子的附益性开展工作.本文从理论及实例两个方面说明,相关拓展工作为保持算子的附益性而丢失了保序性的不足;进一步,通过设计非局部权值的获取过程,并结合现有工作,本文提出了一个新的形态学非局部拓展,并定理证明了所得算子同时具备附益性及保序性两个重要性质;人工合成图像及自然图像上的仿真实验也表明了本文所提算法的有效性.

关键词: 形态学, 非局部, 附益性, 保序性, 腐蚀, 膨胀

Abstract: Due to the success in image denoising,the nonlocal strategies have recently been introduced to extend morphology from local to nonlocal.And the operators with adjunction property (adjunction operators for short) are the basic operator form in traditional morphology,which are fundamental in morphological analyzing.However,the adjunction property of operators has usually been missed in the extended works.To overcome the problem,some extensions for nonlocal morphology with adjunctions operators have been provided.Unfortunately,as declared in this paper,another important property,i.e.,order-preservation,has been lost in these extensions.To make up the defect of losing order-preservation,by adapting the nonlocal weights acquisition,a novel nonlocal morphology is proposed in this study.Meanwhile,it has been proved that adjunction and order-preservation properties are both kept in the proposed extension.Finally,the experimental results on synthetic and natural images validate its feasibility and effectiveness.

Key words: morphology, nonlocal, adjunction, order-preservation, erosion, dilation

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