建立新型边缘泄露补偿机制的四阶方程图像平滑方法

doi:10.3969/j.issn.0372-2112.2016.04.009

电子学报 ›› 2016, Vol. 44 ›› Issue (4): 813-820.DOI: 10.3969/j.issn.0372-2112.2016.04.009

建立新型边缘泄露补偿机制的四阶方程图像平滑方法

易三莉, 陈勇, 贺建峰

昆明理工大学信息工程与自动化学院, 云南昆明 650500

收稿日期:2014-10-21 修回日期:2015-01-20 出版日期:2016-04-25
- 通讯作者:
- 贺建峰
- 作者简介:
- 易三莉 女,1977年12月出生,湖南岳阳人.2011年毕业于中南大学生物医学工程系,取得博士学位,2012年进入昆明理工大学生物医学工程系从事医学图像处理方面的研究. E-mail:152514845@qq.com;陈勇 男,1986年11月出生,四川泸县人.硕士研究生.主要研究方向为计算机图像处理与模式识别. E-mail:2269134036@qq.com
- 基金资助:
- 国家自然科学基金 (No.11265007); 教育部回国人员科研启动基金 (No.2010-1561); 云南省人培基金 (No.KKSY201203030)

A Novel Compensation Mechanism of Edge Leakage for Fourth Order Equation Smoothing Image

YI San-li, CHEN Yong, HE Jian-feng

Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming, Yunnan 650500, China

Received:2014-10-21 Revised:2015-01-20 Online:2016-04-25 Published:2016-04-25
- Supported by:
- National Natural Science Foundation of China (No.11265007); Scientific Research Starting Foundation for Returned Overseas Chinese Scholars, Ministry of Education , China (No.2010-1561); Talent Training Fund of Yunnan Province (No.KKSY201203030)

摘要/Abstract

摘要：

针对传统的四阶偏微分方程(四阶方程)降噪算法容易造成图像边缘泄露的问题,本文提出了一种基于边缘检测理论的泄露修补算法.该算法首先用非线性的双边滤波器对噪声图像进行预处理,得到边缘结构较好的预处理图像,然后基于梯度算子具有检测图像边缘特征的特点,提出将结果图像和预处理图像二者梯度差值的二范数平方作为边缘保持约束项,并将其加入到四阶方程算法的能量泛函中.另外,基于图像局部方差构造了自适应的拉格朗日乘子,从而实现对边缘保持约束项的自适应调整,以提高其边缘保持性能.实验测试结果表明,本文算法不仅继承了传统四阶算法具有的优点,而且增强了对边缘结构的保持能力.

关键词: 四阶偏微分方程, 边缘泄露, 边缘检测, 边缘保持约束

Abstract:

As the traditional fourth order partial differential equation(fourth order equation)algorithm causes edge leakage of image,a leakage compensation method is proposed based on edge detection theory.Firstly the noise image is preprocessed by a nonlinear bilateral filter to obtain the better edge preservation image.Based on the feature of the gradient operator on the detection of image edge and the squared two-norm of gradient difference which is between the result image and the preprocessed image,a constraint item is built.Then the constraint item is added to the corresponding energy functional of fourth order equation.Finally,to adaptively adjust the edge preservation constraint item and improve the performance of edge preservation,an adaptive Lagrange multiplier which is based on image local variance is constructed.The experimental results show that the proposed algorithm not only inherits the advantage of traditional fourth order equation,but also enhances its ability of edge preservation.

Key words: fourth order partial differential equation, edge leakage, edge detection, edge preservation constraint

中图分类号:

TP391.41

易三莉, 陈勇, 贺建峰. 建立新型边缘泄露补偿机制的四阶方程图像平滑方法[J]. 电子学报, 2016, 44(4): 813-820.

YI San-li, CHEN Yong, HE Jian-feng . A Novel Compensation Mechanism of Edge Leakage for Fourth Order Equation Smoothing Image[J]. Acta Electronica Sinica, 2016, 44(4): 813-820.

参考文献

[1] 李春芳,杨鑫,张旭明,丁明跃.基于MAP的超声图像分解去噪算法研究[J].电子学报,2014,42(7):1291-1298. Li Chun-fang,Yang Xin,Zhang Xun-ming,Ding Ming-yue.MAP based ultrasound image decomposition and denoising method[J].Acta Electronica Sinica,2014,42(7):1291-1298.(in Chinese)
[2] 徐小军,王友仁.基于离散分数阶正交小波变换图像降噪新方法[J].电子学报,2014,42(2):280-287. Xu Xiao-jun,Wang You-ren.Novel image denoising method based on discrete fractional orthogonal wavelet transform[J].Acta Electronica Sinica,2014,42(2):280-287.(in Chinese)
[3] 徐焕宇,孙权森,李大禹,宣丽.基于投影的稀疏表示与非局部正则化图像复原方法[J].电子学报,2014,42(7):1299-1304. Xu Huan-yu,Sun Quan-sen,Li Da-yu,Xuan Li.Projection-based image restoration via sparse representation and nonlocal regularization[J].Acta Electronica Sinica,2014,42(7):1299-1304.(in Chinese)
[4] Witkin A P.Scale space filtering[A].Proceedings of International Joint Conference on Artificial Intelligence[C].New York,USA:Artificial Intelligence,1983.1019-1021.
[5] Perona P,Mailik J.Scale space and edge detection using anisotropic diffusion[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1990,12(7):629-639.
[6] Catte F,Lions P L,Morel J M,Coll T.Image selective smoothing and edge detection by nonlinear diffusion[J].SIAM Journal on Numerical Analysis,1992,29(1):182-193.
[7] Black M J,Sapiro G,Marimont D H,Heeger D.Robust anisotropic diffusion[J].IEEE Transactions on Image Processing,1998,7(3):421-432.
[8] 余庆军,谢胜利.基于人类视觉系统的各向异性扩散图像平滑方法[J].电子学报,2004,32(1):17-20. Yu Qing-jun,Xie Sheng-li.An anisotropic diffusion image smoothing method based on human visual system[J].Acta Electronica Sinica,2004,32(1):17-20.(in Chinese)
[9] Gilboa G,Sochen N,Zeevi Y Y.Image enhancement and denoising by complex diffusion process[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2004,26(8):689-703.
[10] 朱立新,王平安,夏德深.引入耦合梯度保真项的非线性扩散图像去噪方法[J].计算机研究与发展,2007,44(8):1390-1398. Zhu Li-xin,Pheng Ann Heng,Xia De-shen.Nonlinear diffusion based image denoising coupling gradient fidelity term[J].Journal of Computer Research and Development,2007,44(8):1390-1398.(in Chinese)
[11] 王志明,张丽.局部结构自适应的图像扩散[J].自动化学报,2009,35(3):244-250. Wang Zhi-ming,Zhang Li.Local-structure-adapted image diffusion[J].Acta Automatica Sinica,2009,35(3):244-250.(in Chinese)
[12] Yang M,Liang J K,Zhang J H,et al.Non-local means theory based Perona-Malik model for image denoising[J].Neurocomputing,2013,120(SI):262-267.
[13] You Y,Kaveh M.Fourth-order partial differential equations for noise removal[J].IEEE Transactions on Image Processing,2000,9(10):1723-1730.
[14] Li F,Shen C M,Fan J S,Shen C L.Image restoration combining a total variational filter and a fourth-order filter[J].Journal Visual Communication & Image Representation,2007,18(4):322-330.
[15] Zhang J H,Li L C,Yang J.An enhanced fourth-order PDE model based on laplacian and gradient operator[A].Proceedings of International Conference on Computer and Information Technology[C].Nanjing,China:IEEE,2012.144-146.
[16] Gonzalez R C,Woods R E.数字图像处理[M].阮秋琦,阮宇智,译.北京:电子工业出版社,2010.
[17] Danny Barash.A fundamental relationship between bilateral filtering,adaptive smoothing,and the nonlinear diffusion equation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,24(6):844-847.
[18] Chao S M,Tsai D M.An improved anisotropic diffusion model for detail and edge preserving smoothing[J].Pattern Recognition Letters,2010,31(13):2012-2023.
[19] Jing T,Li C.Image noise estimation using a variation adaptive evolutionary approach[J].IEEE Signal Processing Letters,2012,19(7):395-398.
[20] Wang Z,Bovik A C,Sheikh H R,Simoncelli E P.Image quality assessment:from error visibility to structural similarity[J].IEEE Transactions on Image Processing,2004,13(4):600-612.
[21] Lysaker M,Lundervold A,Xue-Cheng T.Noise removal using fourth order partial differential equation with applications to medical magnetic resonance images in space and time[J].IEEE Transactions on Image Processing,2003,12(12):1579-1590.
[22] 贾迪野,黄凤岗,苏菡.一种新的基于高阶非线性扩散的图像平滑方法[J].计算机学报,2005,28(5):882-891. Jia Di-ye,Huang Feng-gang,Su Han.A new noise removal method based on fourth order nonlinear diffusion[J].Chinese Journal of Computer,2005,28(5):882-891.(in Chinese)

建立新型边缘泄露补偿机制的四阶方程图像平滑方法

A Novel Compensation Mechanism of Edge Leakage for Fourth Order Equation Smoothing Image

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