Morphological Operators Based on Matrix Partial Ordering Relation

WANG Na; WANG Jun-ping; ZHU Jun-hui

doi:10.12263/DZXB.20220007

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Morphological Operators Based on Matrix Partial Ordering Relation

PAPERS | 更新时间：2025-07-02

- Morphological Operators Based on Matrix Partial Ordering Relation
- ACTA ELECTRONICA SINICA Vol. 51, Issue 1, Pages: 213-221(2023)
- 作者机构：
  
  西安电子科技大学通信工程学院，陕西西安 710071
- 作者简介：
- 基金信息：
- DOI：10.12263/DZXB.20220007
  CLC： TP391.4;
- Received：29 December 2021，
  
  Revised：2022-05-04，
  
  Published：25 January 2023
- 稿件说明：
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王娜,王俊平,朱俊辉.基于矩阵偏序关系的形态学算子[J].电子学报,2023,51(01):213-221.

WANG Na,WANG Jun-ping,ZHU Jun-hui.Morphological Operators Based on Matrix Partial Ordering Relation[J].ACTA ELECTRONICA SINICA,2023,51(01):213-221.
王娜,王俊平,朱俊辉.基于矩阵偏序关系的形态学算子[J].电子学报,2023,51(01):213-221. DOI： 10.12263/DZXB.20220007.

WANG Na,WANG Jun-ping,ZHU Jun-hui.Morphological Operators Based on Matrix Partial Ordering Relation[J].ACTA ELECTRONICA SINICA,2023,51(01):213-221. DOI： 10.12263/DZXB.20220007.

摘要

已有形态偏序由于忽略了图像像素的局部相关性导致运算结果产生噪声叠加、拓扑失真等问题，本文在矩阵Frobenius范数的基础上定义了一种新的偏序关系，从理论上证明了该序满足的自反性、传递性和反对称性.在此基础上，本文提出了基于新序的形态学膨胀、腐蚀算子和相关的梯度运算算子.为验证新序和算子的有效性，与已有的算法进行对比实验，结果表明，新序和相应的算子在保证颜色分量相关性的同时，利用矩阵运算保证了像素的局部相关性，在抑制噪声和边缘保持方面均优于现有的算法.同时，通过结果对比和理论分析发现，新的形态算子对结构元素尺寸的包容性强，克服了形态算子在应用时难以选择合适结构元素大小的问题.这种新序是多通道图像处理的基础，可以扩宽形态学理论的应用范围.

Abstract

The existing morphological partial orderings neglect the local correlation of image pixels

which leads to problems such as noise superposition and topological distortion in the calculation results. This paper defines a new partial ordering relation based on the matrix Frobenius norm

which theoretically proves the reflexivity

transitivity and antisymmetry of the ordering. On this basis

this paper proposes the morphological dilation

erosion operators and the related gradient operators based on the new ordering. In order to verify the effectiveness of the new ordering and operators

those new operators are compared with the existing algorithms. The experimental results show that the new ordering and the corresponding operators ensure the correlation of the color components while using matrix operation to ensure the local correlation of the pixels. It outperforms the existing algotirhms in terms of noise suppression and edge preservation. At the same time

through comparison of the results and theoretical analysis

it is found that the new morphological operators have a strong tolerance for the size of structural element

which overcomes the difficulty of selecting suitable size when the morphological operators are applied. This new ordering is the basis of multi-channel image processing and it can broaden the application range of morphological.

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references

GUO Y Y . Adaptive weighted morphological filters [C]// Proceedings of the 2020 12th International Conference on Machine Learning and Computing . Shenzhen : ACM , 2020 : 439 - 442 .

王弘毅 , 赵欢 . 基于数学形态学预处理的Canny算子边缘检测算法 [J]. 菏泽学院学报 , 2019 , 41 ( 2 ): 25 - 29 .

WANG H Y , ZHAO H . Canny operator edge detection algorithm based on mathematical morphology pretreatment [J]. Journal of Heze University , 2019 , 41 ( 2 ): 25 - 29 . (in Chinese)

WANG C , DENG C X , YUE X H , et al . Detection algorithm based on wavelet threshold denoising and mathematical morphology [J]. International Journal of Performability Engineering , 2020 , 16 ( 3 ): 470 - 481 .

REN H E , XU X Y , ZHU M , et al . A new kind of image edge detection based on the theory of the adaptive lifting wavelet and morphology [J]. Journal of Information Technology Research , 2018 , 11 ( 3 ): 90 - 104 .

SAZAK Ç , NELSON C J , OBARA B . The multiscale bowler-hat transform for blood vessel enhancement in retinal images [J]. Pattern Recognition , 2019 , 88 : 739 - 750 .

GE Y , JIANG X M . Mathematical morphology and deep learning-based approach for bearing fault recognition [J]. International Journal of Performability Engineering , 2018 , 14 ( 5 ): 995 - 1003 .

BOATO G , DANG-NGUYEN D T , DE NATALE F G B . Morphological filter detector for image forensics applications [J]. IEEE Access , 2020 , 8 ( 1 ): 13549 - 13560 .

WITTE V D , SCHULTE S , NACHTEGEAL M , et al . Vector morphological operators for colour images [C]// International Conference Image Analysis and Recognition(ICIAR 2005) . Toronto : Springer , 2005 : 667 - 675 .

APTOULA E , LEFÈVRE S . On lexicographical ordering in multivariate mathematical morphology [J]. Pattern Recognition Letters , 2008 , 29 ( 2 ): 109 - 118 .

APTOULA E , LEFÈVRE S . α-trimmed lexicographical extrema for pseudo-morphological image analysis [J]. Journal of Visual Communication and Image Representation , 2008 , 19 ( 3 ): 165 - 174 .

COMER M L , DELP E J . Morphological operations for color image processing [J]. Journal of Electronic Imaging , 1999 , 8 ( 3 ): 279 - 289 .

RIVEST J F . Morphological operators on complex signals [J]. Signal Processing , 2004 , 84 ( 1 ): 133 - 139 .

ANGULO J . Morphological colour operators in totally ordered lattices based on distances: application to image filtering, enhancement and analysis [J]. Computer Vision and Image Understanding , 2007 , 107 ( 1-2 ): 56 - 73 .

GONZALEZ P , CABEZAS V , MORA M , et al . Morphological color images processing using distance-based and lexicographic order operators [C]// 2010 XXIX International Conference of the Chilean Computer Science Society . Antofagasta : IEEE , 2010 : 258 - 264 .

李亚宁 , 王俊平 , 高艳红 . 图空间上彩色矢量形态学算子 [J]. 电子学报 , 2015 , 43 ( 3 ): 424 - 430 .

LI Y N , WANG J P , GAO Y H . Color vector morphological operators on graph space [J]. Acta Electronica Sinica , 2015 , 43 ( 3 ): 424 - 430 . (in Chinese)

BURGETH B , KLEEFELD A . An approach to color-morphology based on Einstein addition and Loewner order [J]. Pattern Recognition Letters , 2014 , 47 : 29 - 39 .

WELK M , KLEEFELD A , BREUß M . Quantile filtering of colour images via symmetric matrices [J]. Mathematical Morphology-Theory and Applications , 2016 , 1 : 136 - 174 .

BOUCHET A , ALONSO P , PASTORE J I , et al . Fuzzy mathematical morphology for color images defined by fuzzy preference relations [J]. Pattern Recognition , 2016 , 60 : 720 - 733 .

路文 , 李帅 , 徐红强 , 等 . 一种利用像素局部相关性的图像质量评价方法 [J]. 西安电子科技大学学报 , 2017 , 44 ( 1 ): 94 - 99 .

LU W , LI S , XU H Q , et al . Local pixel correlation for image quality assessment [J]. Journal of Xidian University , 2017 , 44 ( 1 ): 94 - 99 . (in Chinese)

TRÉMEAU A , COLANTONI P . Regions adjacency graph applied to color image segmentation [J]. IEEE Transactions on Image Processing , 2000 , 9 ( 4 ): 735 - 744 .

YAO Y , DONG G H , XIAO X , et al . Frobenius-norm-based measures of quantum coherence and asymmetry [J]. Scientific Reports , 2016 , 6 : 1 - 12 .

JOHNSON S C , WICKS M , ŽEFRAN M , et al . The structured distance to the nearest system without property P [J]. IEEE Transactions on Automatic Control , 2018 , 63 ( 9 ): 2960 - 2975 .

YOU S H , AHN C K , ZHAO S Y , et al . Frobenius norm-based unbiased finite impulse response fusion filtering for wireless sensor networks [J]. IEEE Transactions on Industrial Electronics , 2022 , 69 ( 2 ): 1867 - 1876 .

NACHTEGAEL M , SUSSNER P , MÉLANGE T , et al . On the role of complete lattices in mathematical morphology: From tool to uncertainty model [J]. Information Sciences , 2011 , 181 ( 10 ): 1971 - 1988 .

WANG J P , LIANG G M , WU Y , et al . New colour morphological operators on hypergraph [J]. IET Image Processing , 2018 , 12 ( 5 ): 690 - 695 .

ZHAO L L , WANG J P , LI Y B . Colour morphological operators based on formal concept analysis [J]. Signal Image and Video Processing , 2020 , 14 : 151 - 158 .

ONISHI H , SASA Y , NAGAI K , et al . A pattern defect inspection method by parallel grayscale image comparison without precise image alignment [C]// IEEE 2002 28th Annual Conference of the Industrial Electronics Society . Seville : IEEE , 2002 : 2208 - 2213 .

NAWA K , SURYANI E , PRASETYO H . Dengue virus infected leukocyte classification on microscopic images with image histogram based support vector machine [C]// 2019 5th International Conference on Science and Technology(ICST) . Yogyakarta : IEEE , 2019 : 1 - 5 .

惠振阳 , 胡友健 . 基于LiDAR数字高程模型构建的数学形态学滤波方法综述 [J]. 激光与光电子学进展 , 2016 , 53 ( 8 ): 7 - 13 .

HUI Z Y , HU Y J . Review on morphological filtering algorithms based on LiDAR digital elevation model construction [J]. Laser & Optoelectronics Progress , 2016 , 53 ( 8 ): 7 - 13 . (in Chinese)

周琳娜 , 王东明 , 郭云彪 , 等 . 基于数字图像边缘特性的形态学滤波取证技术 [J]. 电子学报 , 2008 , 36 ( 6 ): 1047 - 1051 .

ZHOU L N , WANG D M , GUO Y B , et al . Exposing digital forgeries by detecting image blurred mathematical morphology edge [J]. Acta Electronica Sinica , 2008 , 36 ( 6 ): 1047 - 1051 . (in Chinese)

KILIAN J , HAALA N , ENGLICH M . Capture and evaluation of airborne laser scanner data [J]. International Archives of Photogrammetry and Remote Sensing , 1996 , 31 ( B3 ): 383 - 388 .

ZHANG K Q , CHEN S C , WHITMAN D , et al . A progressive morphological filter for removing nonground measurements from airborne LIDAR data [J]. IEEE Transactions on Geoscience and Remote Sensing , 2003 , 41 ( 4 ): 872 - 882 .

ZHANG L , ZHANG L , MOU X Q , et al . FSIM: A feature similarity index for image quality assessment [J]. IEEE Transactions on Image Processing , 2011 , 20 ( 8 ): 2378 - 2386 .

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