基于梯度与曲率相结合的图像平滑模型的研究

周先春; 汪美玲; 石兰芳; 周林锋; 吴琴

doi:10.7498/aps.64.044201

摘要

在图像处理过程中, 为了在图像去噪时更好地保留图像边缘细节信息, 首先结合扩散系数和曲率的性质建立了一个曲率平滑模型. 考虑到图像受到噪声污染时曲率会发生显著变化, 将图像的水平集曲率作为一个检测因子代入到上述模型中, 提出了一个梯度与曲率相结合的新模型. 分析与仿真结果表明, 该模型与Perona-Malik模型相比较保留了更多的图像信息, 有效地增强了图像尖锐的边缘, 同时很好地保持了图像的直线和曲线边缘、角点、斜坡和小尺度特征, 是一个理想的模型.

关键词:

Abstract

In image processing, in order to keep the detailed information about image edge, we propose a curvature smoothing model based on the nature of diffusion coefficient and curvature. Considering the fact that the curvature will change significantly when the image is affected by noise pollution, in this article we will continue to take the level set curvature as a detection factor and substitute it into the model, then we present a new model which combines gradient and curvature. Analysis and simulation indicate that the new model can keep more image information than the Perona-Malik model, and it can strengthen the sharp edge of the image efficiently, and well keep the straight lines of image, and edges, corners, slopes and small-scale features of curve at the same time, so this model is an ideal model.

Keywords:

作者及机构信息

1.
南京信息工程大学电子与信息工程学院, 南京 210044;

2.
南京信息工程大学, 江苏省大气环境与装备技术协同创新中心, 南京 210044;

3.
南京信息工程大学, 江苏省气象探测与信息处理重点实验室, 南京 210044;

4.
南京信息工程大学数学与统计学院, 南京 210044

基金项目: 国家自然科学基金(批准号: 11202106, 61302188)、高等学校博士学科点专项科研基金(批准号: 20123228120005)、江苏省“信息与通信工程”优势学科建设项目、江苏省自然科学基金(批准号: BK20131005)、江苏省青蓝工程和江苏省高校自然科学研究项目(批准号: 13KJB170016)资助的课题.

Authors and contacts

1.
College of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China;

2.
Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology, Nanjing University of Information Science and Technology, Nanjing 210044, China;

3.
Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science and Technology, Nanjing 210044, China;

4.
College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11202106, 61302188), the Specialized Research Fund for the Doctoral Program of Institution of Higher Education of China (Grant No. 20123228120005), the Jiangsu Information and Communication Engineering Preponderant Discipline Platform, China, the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20131005), the Jiangsu Qing Lan Project, China, and the Natural Sciences Foundation from the Universities of Jiangsu Province, China (Grant No. 13KJB170016).

参考文献

[1]	Gonzalez R C, Woods R E (translated by Ruan Q Q, Ruan Y Z) 2010 Digital Image Processing (3rd Ed.) (Beijing: Publishing House of Electronics Industry) pp197-213 (in Chinese) [冈萨雷斯R C, 伍兹R E 著(阮秋琦, 阮宇智译) 2010 数字图像处理(第三版) (北京: 电子工业出版社)第197–213页]
[2]	Zhou X C, Lin W T, Lin Y H, Mo J Q 2012 Acta Phys. Sin. 61 240202 (in Chinese) [周先春, 林万涛, 林一骅, 莫嘉琪 2012 61 240202]
[3]	Zhou X C, Lin W T, Lin Y H, Mo J Q, Yao J S 2011 Acta Phys. Sin. 60 110207 (in Chinese) [周先春, 林万涛, 林一骅, 莫嘉琪, 姚静荪 2011 60 110207]
[4]	Lu J F, Guan Z 2004 Numerical Solution of Partial Differential Equations (2nd Ed.) (Beijing: Tsinghua University Press) (in Chinese) [陆金甫, 关治 2004 偏微分方程数值解法(第二版) (北京: 清华大学出版社)]
[5]	Li Z B, Liu Z Z, Shi W Z 2014 IEEE Geosci. Remote Sens. 11 743
[6]	Bumsub H, Dongbo M, Kwanghoon S 2013 IEEE Trans. Image Process. 22 1096
[7]	Do H C, Guillermo S 2000 IEEE Trans. Med. Imaging 19 763
[8]	Anastasia S, Petros M 2008 IEEE Trans. Image Process. 17 364
[9]	Wang Z, Huang X, Li Y X, Song X N 2013 Chin. Phys. B 22 010504
[10]	Wang Z, Huang X, Li Y X, Song X N 2012 Chin. Phys. B 21 050506
[11]	Zhu L X, Wang P A, Xia D S 2006 J. Computer-Aid. Des. Comput. Graph. 18 1519 (in Chinese) [朱立新, 王平安, 夏德深 2006 计算机辅助设计与图形学学报 18 1519]
[12]	Xie M H, Yu Z M 2006 Acta Electron. Sin. 34 59 (in Chinese) [谢美华, 于正明 2006 电子学报 34 59]
[13]	Perona P, Malik J 1990 IEEE Trans. Pattern Anal. Mach. Intell. 12 629
[14]	Catte F, Lions P L, Morel J M 1992 SIMA J. Numer. Anal. 29 182
[15]	Gilboa G, Sochen N, Zeevi Y Y 2002 IEEE Trans. Image Process. 11 689
[16]	Cheng L Y, Tang C, Yan S 2011 Opt. Commun. 284 5549
[17]	Li J C, Ma Z H, Peng Y X, Huang B 2013 Acta Phys. Sin. 62 099501 (in Chinese) [李金才, 马自辉, 彭宇行, 黄斌 2013 62 099501]
[18]	Wang D K, Hou Y Q, Peng J Y 2008 Partial Differential Equation Method of Image Processing (Beijing: Science Press) pp13-17 (in Chinese) [王大凯, 侯愉青, 彭进业 2008 图像处理的偏微分方程方法(北京: 科学出版社)第13–17页]
[19]	Weickert J, Bary H R, Max A V 1998 IEEE Trans. Image Process. 7 398
[20]	Canny J 1986 IEEE Trans. Pattern Anal. Mach. Intell. 8 679

施引文献

[1]	Gonzalez R C, Woods R E (translated by Ruan Q Q, Ruan Y Z) 2010 Digital Image Processing (3rd Ed.) (Beijing: Publishing House of Electronics Industry) pp197-213 (in Chinese) [冈萨雷斯R C, 伍兹R E 著(阮秋琦, 阮宇智译) 2010 数字图像处理(第三版) (北京: 电子工业出版社)第197–213页]
[2]	Zhou X C, Lin W T, Lin Y H, Mo J Q 2012 Acta Phys. Sin. 61 240202 (in Chinese) [周先春, 林万涛, 林一骅, 莫嘉琪 2012 61 240202]
[3]	Zhou X C, Lin W T, Lin Y H, Mo J Q, Yao J S 2011 Acta Phys. Sin. 60 110207 (in Chinese) [周先春, 林万涛, 林一骅, 莫嘉琪, 姚静荪 2011 60 110207]
[4]	Lu J F, Guan Z 2004 Numerical Solution of Partial Differential Equations (2nd Ed.) (Beijing: Tsinghua University Press) (in Chinese) [陆金甫, 关治 2004 偏微分方程数值解法(第二版) (北京: 清华大学出版社)]
[5]	Li Z B, Liu Z Z, Shi W Z 2014 IEEE Geosci. Remote Sens. 11 743
[6]	Bumsub H, Dongbo M, Kwanghoon S 2013 IEEE Trans. Image Process. 22 1096
[7]	Do H C, Guillermo S 2000 IEEE Trans. Med. Imaging 19 763
[8]	Anastasia S, Petros M 2008 IEEE Trans. Image Process. 17 364
[9]	Wang Z, Huang X, Li Y X, Song X N 2013 Chin. Phys. B 22 010504
[10]	Wang Z, Huang X, Li Y X, Song X N 2012 Chin. Phys. B 21 050506
[11]	Zhu L X, Wang P A, Xia D S 2006 J. Computer-Aid. Des. Comput. Graph. 18 1519 (in Chinese) [朱立新, 王平安, 夏德深 2006 计算机辅助设计与图形学学报 18 1519]
[12]	Xie M H, Yu Z M 2006 Acta Electron. Sin. 34 59 (in Chinese) [谢美华, 于正明 2006 电子学报 34 59]
[13]	Perona P, Malik J 1990 IEEE Trans. Pattern Anal. Mach. Intell. 12 629
[14]	Catte F, Lions P L, Morel J M 1992 SIMA J. Numer. Anal. 29 182
[15]	Gilboa G, Sochen N, Zeevi Y Y 2002 IEEE Trans. Image Process. 11 689
[16]	Cheng L Y, Tang C, Yan S 2011 Opt. Commun. 284 5549
[17]	Li J C, Ma Z H, Peng Y X, Huang B 2013 Acta Phys. Sin. 62 099501 (in Chinese) [李金才, 马自辉, 彭宇行, 黄斌 2013 62 099501]
[18]	Wang D K, Hou Y Q, Peng J Y 2008 Partial Differential Equation Method of Image Processing (Beijing: Science Press) pp13-17 (in Chinese) [王大凯, 侯愉青, 彭进业 2008 图像处理的偏微分方程方法(北京: 科学出版社)第13–17页]
[19]	Weickert J, Bary H R, Max A V 1998 IEEE Trans. Image Process. 7 398
[20]	Canny J 1986 IEEE Trans. Pattern Anal. Mach. Intell. 8 679

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