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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.
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Keywords:
- combination of gradient and curvature /
- curvature /
- image smoothing /
- image denosing
[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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[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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