基于偏微分方程的图像修补方法研究
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摘要
数字图像修补技术在污损图像修补、目标移除、图像压缩等图像处理领域扮演着很重要的角色。本文主要研究基于偏微分方程的图像修补方法。
在污损区初始化方面,本文考虑到污损区域周围信息与缺失信息的相关性,提出“相关随机初始化”方案。相较于其它初始化方案,该方案能够有效改善修补效果并提高修补效率。
在修补模型方面,本文在整体变分模型的基础上,分析了图像的梯度和水平集曲率对传导系数的影响,提出G-C修补模型,使得修补效果更加自然。与此同时,综合考虑沿等照度线切向与法向的扩散,将G-C模型和BSCB模型进行组合,提出统一修补模型。实验结果证明,相比于G-C模型,统一模型的修补效率有很大提高。
Digital image inpainting plays an important role in image processing, including inpainting destroyed images, disocclusion, image compression and so on. The paper focuses on research of image inpainting models based on PDE.
About the initialization of destroyed area, we take the relativity of the destroyed area and the natural area into consideration, and then the "related random initialization" is proposed. The experimental results show that compare with previous schemes, the method can make the inpainting outputs more natural and improve the inpainting efficiency as well.
About the inpainting models, we mainly observe the two important characters of images, the gradient and the curvature of the isophotes, and introduce the G-C model based on total variation. The model can restore the information of the destroyed area naturally and connect the broken level sets smoothly. Meanwhile, we combine the diffusion along the tangent and normal direction, and then present a combined model based on G-C model and BSCB model. The results show that the novel model performs better than G-C model in inpainting efficiency.
在污损区初始化方面,本文考虑到污损区域周围信息与缺失信息的相关性,提出“相关随机初始化”方案。相较于其它初始化方案,该方案能够有效改善修补效果并提高修补效率。
在修补模型方面,本文在整体变分模型的基础上,分析了图像的梯度和水平集曲率对传导系数的影响,提出G-C修补模型,使得修补效果更加自然。与此同时,综合考虑沿等照度线切向与法向的扩散,将G-C模型和BSCB模型进行组合,提出统一修补模型。实验结果证明,相比于G-C模型,统一模型的修补效率有很大提高。
Digital image inpainting plays an important role in image processing, including inpainting destroyed images, disocclusion, image compression and so on. The paper focuses on research of image inpainting models based on PDE.
About the initialization of destroyed area, we take the relativity of the destroyed area and the natural area into consideration, and then the "related random initialization" is proposed. The experimental results show that compare with previous schemes, the method can make the inpainting outputs more natural and improve the inpainting efficiency as well.
About the inpainting models, we mainly observe the two important characters of images, the gradient and the curvature of the isophotes, and introduce the G-C model based on total variation. The model can restore the information of the destroyed area naturally and connect the broken level sets smoothly. Meanwhile, we combine the diffusion along the tangent and normal direction, and then present a combined model based on G-C model and BSCB model. The results show that the novel model performs better than G-C model in inpainting efficiency.
引文
1.Bertalmio M,Sapiro G,CasellesV,etal,Image inpainting[A],In:Proceedings of International Conference on Computer Graphics and Interactive Techniques[C],New Orleans,Louisiana,USA,2000:417-424.
2.王树根,郑精灵,基于纹理匹配的影像缺损信息填充方法[J],测绘通报,2004(12):21-23.
3.Ran X,Farvardin N,A perceptually motivated three-component image model-Part Ⅰ:description of the model[J],IEEE Transactions on Image Processing,Apr.1995,vol.4:401-415.
4.Karu K,Jain A K,and Bolle R.M,Is there any texture in the image?[J],Pattern Recognit.,1996,vol.29,no.9:1437-1446.
5.Chan T F,Shen J H,Non-texture inpainting by curvature-driven diffusions(CDD)[J],Journal of Visual Communication and Image Representation,2001,12(4):436-449.
6.Geman S,German D,Stochastic relaxation,Gibbs distribution and the Bayesian restoration images,IEEE Transactions on Pattern Analysis and Machine Intelligence,November,1984,PAMI-6(6).
7.Rudin L,Osher S,Fatemi E,Nonlinear total variation based noise removal algorithms,Physica D,1992,60:259-268.
8.Chan T F,Shen J H,Mathematical models for local non-.texture inpainting[J],SIAM Journal of Applied Mathematics,2001,62(3):1019-1043.
9.Chan T F,Kang S H,Shen J H,Euler's elastica and curvature based inpainting[J],SIAM Journal of Applied Mathematics,2002,63(2):564-592.
10.Tsai A,Yezzi J A,Willsky A S,Curve evolution implementation of the Mumford-Shah functional for image segmentation,denoising,interpolation and magnification[J],IEEE Transactions on Image Processing,2001,10(8):1169-1186.
11.Esedoglu S,Shen J H,Digital inpainting based on the Mumford-Shah-Euler image model[J],European Journal on Applied Mathematics,2002,13(4):353-370.
12.张红英等,数字图像修补技术综述[J],中国图象图形学报,2007,2(1):1-10.
13.Drori I,Daniel C O,Hezy Y,Fragment based image completion[J],ACM Transactions on Graphics, 2003, 22 (3): 303-312.
14. Zhang Y J, Xiao J G, ShahM, Region Completion in A Single Image [EB/OL], www. cs.ucf. edu /vision /papers/ zhang_xiao_shah_EG2004.pdf, 2005204221.
15. Criminisi A, Perez P, Toyama K, Region filling and object removal by exemplar-based image inpainting [J], IEEE Transactions on Image Processing,2004,13 (9): 1200-1212.
16. Tang F, Ying Y T, Wang J, etal, A novel texture synthesis based algorithm for object removal in photographs [A], In: Proceedings of Ninth Asian Computing Science Conference [C], Chiang Mai, Thailand, 2004: 248-258.
17. Criminisi A, Perez P, Toyama K, Object removal by exemplar-based inpainting [A], In:Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition [C], Monona Terrace Convention Center Madison, Wisconsin, USA,2003,2:18-20.
18. Bertalmio M, Vese L, Sapiro G, etal, Simultaneous texture and structure image inpainting [J], IEEE Transactions on Image Processing, 2003,12 (8): 882-889.
19. Harald G, A combined PDE and texture synthesis approach to inpainting [A], In:Proceedings of 8th European Conference on Computer Vision [C], Prague, Czech Republic, 2004, 2: 214-224.
20. Rane S D, Sapiro G, Bertalmio M, Structure and texture filling-in of missing image blocks in wireless transmission and compression applications [J], IEEE Transactions on Image Processing, 2003,12 (3): 296-303.
21. Yamauchi H, Haber J, Seidel H P, Image restoration using multiresolution texture synthesis [A], In: Proceedings of Computer Graphics International Conference (CGI'2003) [C], Tokyo, Japan,2003:1530-1552.
22. 王大凯等,《图像处理中的偏微分方程方法》,校内讲义,2005,3.
23. Weickert J, Anisotropic Diffusion in Image Processing, ECMI series, Teubner-Verlog,Stuttgart, Germany, 1998.
24. Perona P and Malik J, Scale-space and edge detection using anisotropic diffusion, IEEE PAMI, 1990,12: 629-639.
25. Catte F, Lions P L, Morel J M and Coll T, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer.Anal.,1992, Vol. 29:182-193.
26. You Yu-Li etal, Behavioral Analysis of Anisotropic Diffusion in Image Processing, IEEE IP,1996,5,11:1539-1553.
27.祝轩等,曲率驱动与边缘停止相结合的非线性扩散及其在图像去噪中的应用,光子学报,2008,37(3):609-612.
28.何小海,图像通信,西安,西安电子科技大学出版社,2005,5:15.
29.容观澳,计算机图象处理,北京,清华大学出版社,2000.
30.张旭东,卢国栋,冯健,图像编码基础和小波压缩技术-原理、算法和标准,北京,清华大学出版社,2004.
31.Osher S,Sethian J,Fronts propagating with curvature dependent speed:algorithms based on Hamilton-Jacobi formulations,Journal of Computational Physics,1988,79:12-49.
32.Marquina A and Osher S,Explicit algorithms for a new time dependent model based on level set motion for nonlinear debluring and noise removal,UCLA CAM Report 99-5,January 1999.
33.郑精灵,王树根,整体变分法在图像修补中的应用研究[J],计算机辅助设计与图形学学报,2003,15(10).
34.邵肖伟,刘政凯,宋璧,一种基于TV模型的自适应图像修补方法[J],电路与系统学报,2004(02).
35.张红英,彭启琮,吴亚东,数字破损图像的非线性各向异性扩散修补算法[J],计算机辅助设计与图形学学报,2006,18(10):79-84.
36.Sapiro G,Caselles V,Histogram modification via differential equations,J,Diff,Equat,1997,135:238-268.
37.Caselles V,etal,Shape-Preserving local contrast enhancement,IEEE IP,1999,8:220-230.
38.顾建平,韩华等,基于水平线插值的图像修补算法[J],计算机工程,2006,32(7):7-9.
39.Masnou S,Disocclusion:A Variational Approach Using Level Lines[J],IEEE Transactions on Image Processing,2002,11(2):68-76.
40.Chan T F and Shen J H,Morphologically Invariant PDE Inpaintings,UCLA CAM Report 2001-15,2001.
2.王树根,郑精灵,基于纹理匹配的影像缺损信息填充方法[J],测绘通报,2004(12):21-23.
3.Ran X,Farvardin N,A perceptually motivated three-component image model-Part Ⅰ:description of the model[J],IEEE Transactions on Image Processing,Apr.1995,vol.4:401-415.
4.Karu K,Jain A K,and Bolle R.M,Is there any texture in the image?[J],Pattern Recognit.,1996,vol.29,no.9:1437-1446.
5.Chan T F,Shen J H,Non-texture inpainting by curvature-driven diffusions(CDD)[J],Journal of Visual Communication and Image Representation,2001,12(4):436-449.
6.Geman S,German D,Stochastic relaxation,Gibbs distribution and the Bayesian restoration images,IEEE Transactions on Pattern Analysis and Machine Intelligence,November,1984,PAMI-6(6).
7.Rudin L,Osher S,Fatemi E,Nonlinear total variation based noise removal algorithms,Physica D,1992,60:259-268.
8.Chan T F,Shen J H,Mathematical models for local non-.texture inpainting[J],SIAM Journal of Applied Mathematics,2001,62(3):1019-1043.
9.Chan T F,Kang S H,Shen J H,Euler's elastica and curvature based inpainting[J],SIAM Journal of Applied Mathematics,2002,63(2):564-592.
10.Tsai A,Yezzi J A,Willsky A S,Curve evolution implementation of the Mumford-Shah functional for image segmentation,denoising,interpolation and magnification[J],IEEE Transactions on Image Processing,2001,10(8):1169-1186.
11.Esedoglu S,Shen J H,Digital inpainting based on the Mumford-Shah-Euler image model[J],European Journal on Applied Mathematics,2002,13(4):353-370.
12.张红英等,数字图像修补技术综述[J],中国图象图形学报,2007,2(1):1-10.
13.Drori I,Daniel C O,Hezy Y,Fragment based image completion[J],ACM Transactions on Graphics, 2003, 22 (3): 303-312.
14. Zhang Y J, Xiao J G, ShahM, Region Completion in A Single Image [EB/OL], www. cs.ucf. edu /vision /papers/ zhang_xiao_shah_EG2004.pdf, 2005204221.
15. Criminisi A, Perez P, Toyama K, Region filling and object removal by exemplar-based image inpainting [J], IEEE Transactions on Image Processing,2004,13 (9): 1200-1212.
16. Tang F, Ying Y T, Wang J, etal, A novel texture synthesis based algorithm for object removal in photographs [A], In: Proceedings of Ninth Asian Computing Science Conference [C], Chiang Mai, Thailand, 2004: 248-258.
17. Criminisi A, Perez P, Toyama K, Object removal by exemplar-based inpainting [A], In:Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition [C], Monona Terrace Convention Center Madison, Wisconsin, USA,2003,2:18-20.
18. Bertalmio M, Vese L, Sapiro G, etal, Simultaneous texture and structure image inpainting [J], IEEE Transactions on Image Processing, 2003,12 (8): 882-889.
19. Harald G, A combined PDE and texture synthesis approach to inpainting [A], In:Proceedings of 8th European Conference on Computer Vision [C], Prague, Czech Republic, 2004, 2: 214-224.
20. Rane S D, Sapiro G, Bertalmio M, Structure and texture filling-in of missing image blocks in wireless transmission and compression applications [J], IEEE Transactions on Image Processing, 2003,12 (3): 296-303.
21. Yamauchi H, Haber J, Seidel H P, Image restoration using multiresolution texture synthesis [A], In: Proceedings of Computer Graphics International Conference (CGI'2003) [C], Tokyo, Japan,2003:1530-1552.
22. 王大凯等,《图像处理中的偏微分方程方法》,校内讲义,2005,3.
23. Weickert J, Anisotropic Diffusion in Image Processing, ECMI series, Teubner-Verlog,Stuttgart, Germany, 1998.
24. Perona P and Malik J, Scale-space and edge detection using anisotropic diffusion, IEEE PAMI, 1990,12: 629-639.
25. Catte F, Lions P L, Morel J M and Coll T, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer.Anal.,1992, Vol. 29:182-193.
26. You Yu-Li etal, Behavioral Analysis of Anisotropic Diffusion in Image Processing, IEEE IP,1996,5,11:1539-1553.
27.祝轩等,曲率驱动与边缘停止相结合的非线性扩散及其在图像去噪中的应用,光子学报,2008,37(3):609-612.
28.何小海,图像通信,西安,西安电子科技大学出版社,2005,5:15.
29.容观澳,计算机图象处理,北京,清华大学出版社,2000.
30.张旭东,卢国栋,冯健,图像编码基础和小波压缩技术-原理、算法和标准,北京,清华大学出版社,2004.
31.Osher S,Sethian J,Fronts propagating with curvature dependent speed:algorithms based on Hamilton-Jacobi formulations,Journal of Computational Physics,1988,79:12-49.
32.Marquina A and Osher S,Explicit algorithms for a new time dependent model based on level set motion for nonlinear debluring and noise removal,UCLA CAM Report 99-5,January 1999.
33.郑精灵,王树根,整体变分法在图像修补中的应用研究[J],计算机辅助设计与图形学学报,2003,15(10).
34.邵肖伟,刘政凯,宋璧,一种基于TV模型的自适应图像修补方法[J],电路与系统学报,2004(02).
35.张红英,彭启琮,吴亚东,数字破损图像的非线性各向异性扩散修补算法[J],计算机辅助设计与图形学学报,2006,18(10):79-84.
36.Sapiro G,Caselles V,Histogram modification via differential equations,J,Diff,Equat,1997,135:238-268.
37.Caselles V,etal,Shape-Preserving local contrast enhancement,IEEE IP,1999,8:220-230.
38.顾建平,韩华等,基于水平线插值的图像修补算法[J],计算机工程,2006,32(7):7-9.
39.Masnou S,Disocclusion:A Variational Approach Using Level Lines[J],IEEE Transactions on Image Processing,2002,11(2):68-76.
40.Chan T F and Shen J H,Morphologically Invariant PDE Inpaintings,UCLA CAM Report 2001-15,2001.