A ROBUST COLOR EDGE DETECTION ALGORITHM BASED ON THE QUATERNION HARDY FILTER

doi:10.1007/s10473-022-0325-3

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (3): 1238-1260.doi: 10.1007/s10473-022-0325-3

• 论文 • 上一篇

A ROBUST COLOR EDGE DETECTION ALGORITHM BASED ON THE QUATERNION HARDY FILTER

毕文姗¹, 程冬², 刘万凯³, 高洁欣¹

1. Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China;
2. Research Center for Mathematics and Mathematics Education, Beijing Normal University at Zhuhai, Zhuhai, 519087, China;
3. School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, 250014, China

收稿日期:2021-01-29 修回日期:2021-07-04 发布日期:2022-06-24
通讯作者: Kit Ian KOU,E-mail:kikou@um.edu.mo E-mail:kikou@um.edu.mo
基金资助:
This work was supported in part by the Science and Technology Development Fund, Macau SAR FDCT/085/2018/A2 and the Guangdong Basic and Applied Basic Research Foundation (2019A1515111185).

A ROBUST COLOR EDGE DETECTION ALGORITHM BASED ON THE QUATERNION HARDY FILTER

Wenshan BI¹, Dong CHENG², Wankai LIU³, Kit Ian KOU¹

1. Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China;
2. Research Center for Mathematics and Mathematics Education, Beijing Normal University at Zhuhai, Zhuhai, 519087, China;
3. School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, 250014, China

Received:2021-01-29 Revised:2021-07-04 Published:2022-06-24
Contact: Kit Ian KOU,E-mail:kikou@um.edu.mo E-mail:kikou@um.edu.mo
Supported by:
This work was supported in part by the Science and Technology Development Fund, Macau SAR FDCT/085/2018/A2 and the Guangdong Basic and Applied Basic Research Foundation (2019A1515111185).

摘要/Abstract

摘要： This paper presents a robust filter called the quaternion Hardy filter (QHF) for color image edge detection. The QHF can be capable of color edge feature enhancement and noise resistance. QHF can be used flexibly by selecting suitable parameters to handle different levels of noise. In particular, the quaternion analytic signal, which is an effective tool in color image processing, can also be produced by quaternion Hardy filtering with specific parameters. Based on the QHF and the improved Di Zenzo gradient operator, a novel color edge detection algorithm is proposed; importantly, it can be efficiently implemented by using the fast discrete quaternion Fourier transform technique. From the experimental results, we conclude that the minimum PSNR improvement rate is 2.3% and the minimum SSIM improvement rate is 30.2% on the CSEE database. The experiments demonstrate that the proposed algorithm outperforms several widely used algorithms.

关键词: Boundary values, color image edge detection, quaternion analytic signal, discrete quaternion Fourier transform

Abstract: This paper presents a robust filter called the quaternion Hardy filter (QHF) for color image edge detection. The QHF can be capable of color edge feature enhancement and noise resistance. QHF can be used flexibly by selecting suitable parameters to handle different levels of noise. In particular, the quaternion analytic signal, which is an effective tool in color image processing, can also be produced by quaternion Hardy filtering with specific parameters. Based on the QHF and the improved Di Zenzo gradient operator, a novel color edge detection algorithm is proposed; importantly, it can be efficiently implemented by using the fast discrete quaternion Fourier transform technique. From the experimental results, we conclude that the minimum PSNR improvement rate is 2.3% and the minimum SSIM improvement rate is 30.2% on the CSEE database. The experiments demonstrate that the proposed algorithm outperforms several widely used algorithms.

Key words: Boundary values, color image edge detection, quaternion analytic signal, discrete quaternion Fourier transform

中图分类号:

11R52

毕文姗, 程冬, 刘万凯, 高洁欣. A ROBUST COLOR EDGE DETECTION ALGORITHM BASED ON THE QUATERNION HARDY FILTER[J]. 数学物理学报(英文版), 2022, 42(3): 1238-1260.

Wenshan BI, Dong CHENG, Wankai LIU, Kit Ian KOU. A ROBUST COLOR EDGE DETECTION ALGORITHM BASED ON THE QUATERNION HARDY FILTER[J]. Acta mathematica scientia,Series B, 2022, 42(3): 1238-1260.

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A ROBUST COLOR EDGE DETECTION ALGORITHM BASED ON THE QUATERNION HARDY FILTER

A ROBUST COLOR EDGE DETECTION ALGORITHM BASED ON THE QUATERNION HARDY FILTER

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