偏微分方程在图像处理中应用的研究
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摘要
图像是人类获取、传递信息的重要媒介,因此图像广泛应用在人们生活中,并且成为一种科学研究和社会生产的重要工具。偏微分方程是一类重要的数学分析模型,不同方程得处理特性由具体的扩散项和扩散方向决定。本文研究偏微分方程作为一类重要的数学工具在数字图像处理中的应用。偏微分方程具有各向异性扩散性能,并且整个扩散过程在局部信息的作用下进行;方程直接使用图像中的几何特征控制扩散项及扩散方向,因此偏微分方程处理图像可在平滑同质区域的同时保持区域边界等几何特征。
本文以偏微分方程图像处理模型作为研究对象,运用泛函分析、马尔可夫随机场、小波变换、模式识别等多种理论和方法,研究偏微分方程的有效性及其与其它现代图像处理方法的关系。重点对偏微分方程与基于全局信息图像处理方法的互补性和相关性进行了深入的研究和探讨。本文分别研究偏微分方程及复合模型在图像去噪、图像放大、图像修复以及复杂条件下人脸识别预处理系统中的应用,对偏微分方程各向异性扩散性能、平滑图像及局部特征保持性能进行多层次、多角度的分析和研究。
整个研究中的创新性工作主要体现在以下几个方面:
1.复合偏微分方程去噪模型。本文根据泛函分析和马尔可夫随机场理论,证明了经典偏微分方程去噪模型与小波阈值收缩模型、高斯-马尔可夫模型的结构一致性,提出了两类偏微分方程与现代图像处理方法结合的复合去噪模型。复合模型在实现去噪的同时保持图像中的边缘、纹理特征,同时减弱了传统偏微分方程模型引起的块状效应,并减弱处理后得到图像中的Gibbs效应;
2.提出双层约束的图像放大模型。传统插值操作得到的图像中存在严重的锯齿效应、振铃效应,本文提出在原始未插值图像中真实几何信息约束下处理放大图像,在减弱噪声的同时保持了边缘特征,减弱了振铃、锯齿效应。本文对放大操作的改进包括两部分:
提出一种双前向扩散的偏微分方程模型,模型可以在保持边缘特征的同时减弱图像中的锯齿、振铃效应。模型中的扩散项和扩散方向是原始未插值图像中真实几何信息作用的结果;
提出一种双层约束的同时基于局部信息和全局信息的图像放大模型。模型使用双向扩散的偏微分方程处理几何特征,在减弱边缘位置的锯齿、振铃效应的同时增强区域边界特征;图像中的纹理和噪声则由基于全局信息的非局部均值算法处理。该模型可直接应用于自然场景图像、纹理图像和噪声图像的放大操作中;
3.提出一种适用于缺失较小信息区域及不包含纹理信息图像的偏微分方程修复模型。已知区域的梯度信息通过优化整体变分能量泛函扩散入目标区域,像素灰度信息根据更新的正交几何方向向目标区域内扩散,扩散过程具有形态学不变性,模型在保持原图像几何特征的同时可平滑地修复图像;
4.提出一种基于模块匹配的修复模型,可修复缺失较大信息区域及包含复杂纹理特征的自然场景图像。模型以模块为基本单元基于全局信息处理图像,使用切向等照度线扩散的偏微分方程约束模块的修复顺序。偏微分方程具有形态学不变性,且在边缘特征宽度的约束下扩散,因此沿几何特征的模块具有较高的修复优先级,从而模型可以较好地保持图像中的几何特征。本文在CIELAB空间下实现模块相似度匹配,并使用偏微分方程减弱填充模块之间存在的接缝效应。本文最后还对基于模块模型进行扩展,可以实现更多的复杂修复目的;
5.提出一种复杂条件下人脸识别系统的预处理模型。模型使用偏微分方程和朗伯表面模型提取图像中具有光照不变性的小尺度特征,同时使用偏微分方程模型和局部直方图均衡化方法生成增强的大尺度特征,然后在特征级融合两类图像特征得到最终的样本图像。模型预处理后的图像不仅对复杂光照条件下的人脸识别具有鲁棒性,同时应用于表情、遮挡等复杂条件下的人脸识别也可提高传统方法的识别率。
本文分别从数学角度和图像处理角度分析了偏微分方程不同扩散项和扩散方向的特性,证明了偏微分方程模型与其他现代图像处理方法的区别与联系,并证明了偏微分方程在图像处理中应用的有效性。本文将具有不同扩散性能的偏微分方程模型分别应用于底层、中层和高级图像处理的预处理操作等不同领域,并将其与不同的现代图像处理方法相结合,提出了满足不同应用要求的有效的图像处理模型。
Image is an important method to obtaining and conveying information.It is widely used in human life,and is critical for scientific research and social production.Partial Differential Equation(PDE) is an important mathematical analysis method,and its property is determined by the diffusion directions and diffusion items in the equation.In this paper,the usage of PDE in image processing is deeply analyzed and compared.The PDE anisotropiccally diffuses in image domain and the diffusion procedure is constrained by the local geometric information.The diffusion items and directions could be computed by the geometric properties in image directly.So PDE smoothes image while preserving the edge information.
In this thesis,we focus on the research on the PDE models used in image processing.We give the profound research on functional theory,Markov random filed theory,Wavelet transform analysis,pattern recognition etc..We analyze the validity of PDE models and prove the relationship between PDE and other modern image processing methods.Our objective is to explore the interdependency and complementarity between PDE and the image processing methods based on the global information.We explore the effective PDE models and the composite models used in image denoising,image magnification,image inpainting,and the pre-processing step for face recognition under complex conditions.The anisotropic diffusion property, smoothing and locality preserving property of PDE are analyzed and proved from various aspects and feature levels.
The main creative work in this thesis is summarized as follows:
1.The composite image denoising models.In this paper,the relationship between PDE and the Wavelet shrinkage denoising method,and the relationship between PDE and the Gaussian-Markov model are proved based on the Functional theory and the Markov random field theory,respectively.Then two composite denoising models are proposed.The composite models could denoise while preserving the edge and textured information in image.Also it decreases the blocky effects caused by PDE. There is no Gibbs phenomenon in the denoised results;
2.The two-layer constrained image magnification models.There are severe zigzag effects and ringing effects in the interpolated image processed by the conventional magnification models.In the two-layer constrained models,the processing procedures are executed under the constraint of the geometric information in the original image.So the processed image is smoothed and preserves the geometric property;there is less zigzag and ringing effect.The two-layer constrained model has two forms:
A PDE model which forward diffuses along two orthogonal directions.It preserves the linear structure and removes the zigzag and ringing effects.The diffusion items and directions in this PDE model are the constrained result of the geometric properties in the original image;
A magnification model which is based on both local and global image information.This model uses a bi-directional diffused PDE to preserve the geometric property.Then the zigzag and ringing effects are weakened while preserving the linear structure.The textured and noisy information in the image is processed by the non-local means algorithm.This model could be directly used to magnify the natural image,texture image and noisy image;
3.A PDE inpainting model which is used to restore the image with a small target region and containing no textured information.The gradient information is diffused into the target region by minimizing the total variation energy function.The pixel's gray value is diffused along two orthogonal directions based on the updated geometric vectors.The diffusion PDEs are all morphological invariant.The novel model could smoothly restore the image while preserving the geometric property;
4.An exemplar-based model which is used to restore the natural image with the large target region and containing the textured information.The exemplar is the basic processing unit and its processing order is determined by a cross isophote diffused PDE.This PDE is morphological invariant,and it is diffused under the constraint of the edge width.The exemplar along the linear structure has a higher processing priority.So the model could preserve the geometric property of image better.The similarity comparison of exemplar is implemented in the CIELAB space and PDE is used to remove the seams between exemplars.The model is further extended for more complex restoring tasks;
5.A pre-processing model for face recognition under complex conditions.The model uses PDE and the Lambertian surface model to extract the illumination invariant small-scaled image features.Also it uses PDE and the region-based histogram equalization method to extract the enhanced large-scaled image features.Last,two scaled image features are fused at the feature-level.The face sample processed by this model is robust to the lighting conditions.This model achieves good performances in the face databases with the large variations of expression,occlusion, etc.
In this paper,the diffusion items and diffusion directions of PDE are analyzed based on the mathematical theory and image processing theory,respectively.The difference and connection between PDE and other modern image processing methods are proved.Different PDEs are used in low-level,middle-level and pre-processing for high-level image processing fields.They are combined with other modern image processing methods and achieve good performances in different image processing tasks.
本文以偏微分方程图像处理模型作为研究对象,运用泛函分析、马尔可夫随机场、小波变换、模式识别等多种理论和方法,研究偏微分方程的有效性及其与其它现代图像处理方法的关系。重点对偏微分方程与基于全局信息图像处理方法的互补性和相关性进行了深入的研究和探讨。本文分别研究偏微分方程及复合模型在图像去噪、图像放大、图像修复以及复杂条件下人脸识别预处理系统中的应用,对偏微分方程各向异性扩散性能、平滑图像及局部特征保持性能进行多层次、多角度的分析和研究。
整个研究中的创新性工作主要体现在以下几个方面:
1.复合偏微分方程去噪模型。本文根据泛函分析和马尔可夫随机场理论,证明了经典偏微分方程去噪模型与小波阈值收缩模型、高斯-马尔可夫模型的结构一致性,提出了两类偏微分方程与现代图像处理方法结合的复合去噪模型。复合模型在实现去噪的同时保持图像中的边缘、纹理特征,同时减弱了传统偏微分方程模型引起的块状效应,并减弱处理后得到图像中的Gibbs效应;
2.提出双层约束的图像放大模型。传统插值操作得到的图像中存在严重的锯齿效应、振铃效应,本文提出在原始未插值图像中真实几何信息约束下处理放大图像,在减弱噪声的同时保持了边缘特征,减弱了振铃、锯齿效应。本文对放大操作的改进包括两部分:
提出一种双前向扩散的偏微分方程模型,模型可以在保持边缘特征的同时减弱图像中的锯齿、振铃效应。模型中的扩散项和扩散方向是原始未插值图像中真实几何信息作用的结果;
提出一种双层约束的同时基于局部信息和全局信息的图像放大模型。模型使用双向扩散的偏微分方程处理几何特征,在减弱边缘位置的锯齿、振铃效应的同时增强区域边界特征;图像中的纹理和噪声则由基于全局信息的非局部均值算法处理。该模型可直接应用于自然场景图像、纹理图像和噪声图像的放大操作中;
3.提出一种适用于缺失较小信息区域及不包含纹理信息图像的偏微分方程修复模型。已知区域的梯度信息通过优化整体变分能量泛函扩散入目标区域,像素灰度信息根据更新的正交几何方向向目标区域内扩散,扩散过程具有形态学不变性,模型在保持原图像几何特征的同时可平滑地修复图像;
4.提出一种基于模块匹配的修复模型,可修复缺失较大信息区域及包含复杂纹理特征的自然场景图像。模型以模块为基本单元基于全局信息处理图像,使用切向等照度线扩散的偏微分方程约束模块的修复顺序。偏微分方程具有形态学不变性,且在边缘特征宽度的约束下扩散,因此沿几何特征的模块具有较高的修复优先级,从而模型可以较好地保持图像中的几何特征。本文在CIELAB空间下实现模块相似度匹配,并使用偏微分方程减弱填充模块之间存在的接缝效应。本文最后还对基于模块模型进行扩展,可以实现更多的复杂修复目的;
5.提出一种复杂条件下人脸识别系统的预处理模型。模型使用偏微分方程和朗伯表面模型提取图像中具有光照不变性的小尺度特征,同时使用偏微分方程模型和局部直方图均衡化方法生成增强的大尺度特征,然后在特征级融合两类图像特征得到最终的样本图像。模型预处理后的图像不仅对复杂光照条件下的人脸识别具有鲁棒性,同时应用于表情、遮挡等复杂条件下的人脸识别也可提高传统方法的识别率。
本文分别从数学角度和图像处理角度分析了偏微分方程不同扩散项和扩散方向的特性,证明了偏微分方程模型与其他现代图像处理方法的区别与联系,并证明了偏微分方程在图像处理中应用的有效性。本文将具有不同扩散性能的偏微分方程模型分别应用于底层、中层和高级图像处理的预处理操作等不同领域,并将其与不同的现代图像处理方法相结合,提出了满足不同应用要求的有效的图像处理模型。
Image is an important method to obtaining and conveying information.It is widely used in human life,and is critical for scientific research and social production.Partial Differential Equation(PDE) is an important mathematical analysis method,and its property is determined by the diffusion directions and diffusion items in the equation.In this paper,the usage of PDE in image processing is deeply analyzed and compared.The PDE anisotropiccally diffuses in image domain and the diffusion procedure is constrained by the local geometric information.The diffusion items and directions could be computed by the geometric properties in image directly.So PDE smoothes image while preserving the edge information.
In this thesis,we focus on the research on the PDE models used in image processing.We give the profound research on functional theory,Markov random filed theory,Wavelet transform analysis,pattern recognition etc..We analyze the validity of PDE models and prove the relationship between PDE and other modern image processing methods.Our objective is to explore the interdependency and complementarity between PDE and the image processing methods based on the global information.We explore the effective PDE models and the composite models used in image denoising,image magnification,image inpainting,and the pre-processing step for face recognition under complex conditions.The anisotropic diffusion property, smoothing and locality preserving property of PDE are analyzed and proved from various aspects and feature levels.
The main creative work in this thesis is summarized as follows:
1.The composite image denoising models.In this paper,the relationship between PDE and the Wavelet shrinkage denoising method,and the relationship between PDE and the Gaussian-Markov model are proved based on the Functional theory and the Markov random field theory,respectively.Then two composite denoising models are proposed.The composite models could denoise while preserving the edge and textured information in image.Also it decreases the blocky effects caused by PDE. There is no Gibbs phenomenon in the denoised results;
2.The two-layer constrained image magnification models.There are severe zigzag effects and ringing effects in the interpolated image processed by the conventional magnification models.In the two-layer constrained models,the processing procedures are executed under the constraint of the geometric information in the original image.So the processed image is smoothed and preserves the geometric property;there is less zigzag and ringing effect.The two-layer constrained model has two forms:
A PDE model which forward diffuses along two orthogonal directions.It preserves the linear structure and removes the zigzag and ringing effects.The diffusion items and directions in this PDE model are the constrained result of the geometric properties in the original image;
A magnification model which is based on both local and global image information.This model uses a bi-directional diffused PDE to preserve the geometric property.Then the zigzag and ringing effects are weakened while preserving the linear structure.The textured and noisy information in the image is processed by the non-local means algorithm.This model could be directly used to magnify the natural image,texture image and noisy image;
3.A PDE inpainting model which is used to restore the image with a small target region and containing no textured information.The gradient information is diffused into the target region by minimizing the total variation energy function.The pixel's gray value is diffused along two orthogonal directions based on the updated geometric vectors.The diffusion PDEs are all morphological invariant.The novel model could smoothly restore the image while preserving the geometric property;
4.An exemplar-based model which is used to restore the natural image with the large target region and containing the textured information.The exemplar is the basic processing unit and its processing order is determined by a cross isophote diffused PDE.This PDE is morphological invariant,and it is diffused under the constraint of the edge width.The exemplar along the linear structure has a higher processing priority.So the model could preserve the geometric property of image better.The similarity comparison of exemplar is implemented in the CIELAB space and PDE is used to remove the seams between exemplars.The model is further extended for more complex restoring tasks;
5.A pre-processing model for face recognition under complex conditions.The model uses PDE and the Lambertian surface model to extract the illumination invariant small-scaled image features.Also it uses PDE and the region-based histogram equalization method to extract the enhanced large-scaled image features.Last,two scaled image features are fused at the feature-level.The face sample processed by this model is robust to the lighting conditions.This model achieves good performances in the face databases with the large variations of expression,occlusion, etc.
In this paper,the diffusion items and diffusion directions of PDE are analyzed based on the mathematical theory and image processing theory,respectively.The difference and connection between PDE and other modern image processing methods are proved.Different PDEs are used in low-level,middle-level and pre-processing for high-level image processing fields.They are combined with other modern image processing methods and achieve good performances in different image processing tasks.
引文
[1]Daubechies,Orthonormal Bases of Compactly Supported Wavelets,Comm.Pure Appl Math.,vol.41,pp.906-966,1988
[2]S Mallat,S.Zhong,Characterization of signals from multiscale edges,IEEE Trans.Pattern Anal.Mach.Intell.,vol.l4,no.7,pp.710-732,1992
[3]S Mallat,W.L.Hwang,Singularity detection and processing with wavelets,IEEE Trans.Info.Theory,vol.38,pp.617-643,1992
[4]Cohen,I.Daubechies,J.C.Feauveau,Biorthogonal Bases of Compactly Supported Wavelets,Commun.Pure Appl.Math.,vol.XLV,pp.485-560,1992
[5]A.S.Lewis,G.Knowles,Image Compression Using the 2-D Wavelet Transform,IEEE Trans.Image Process.,vol.1,no.2,pp.244-250,1992
[6]D.L.Donoho,De-Noising by soft thresholding,IEEE Trans.Info.Theory,vol.43,pp.933-936,1993
[7]D.L.Donoho,L.M.Johnstone,Ideal spatial adaptation via wavelet shrinkage,Biometrica,vol.81,pp.425-455,1994
[8]D.L.Donoho,Denoising by soft-thresholding,IEEE Trans.Inf.Theory,vol.41,no.3,pp.613-627,1995
[9]Bezvesilniy,V.Vinogradov,D.Vavriv,K.Schunemann,Wavelet-based image processing,edge detection and noise reduction,Proc.Int.Conf.Applied Electronagnetics and Communications (ICECom),Dubrovnik,Croatia,pp.123-126,2003
[10]A.D.Dempster,N.M.Laird,D.B.Rudin,Maximum likelihood from incomplete data via the EM algorithm,J.Roy.Strat.Soc,vol.B39,pp.1-37,1977
[11]R.L.Lagendijk,J.Biemond,D.E.Boekee,Identification and restoration of noise blurred images using the expectation-max-minimization algorithm,IEEE Trans.Acoustics,Speech & Signal Proc,vol.38,no.7,pp.1180-1191
[12]K.T.Lay,K.Katsaggelos,Image identification and restoration based on the expectation-maximization algorighm,Opt.Eng.,vol.29,pp.436-445,1990
[13]A.M.Tekalp,H.Kaufman,On statistical identification of a class of linear space-invariant image blurs using non-minimum-phase ARMA models,IEEE Trans.Acoust.Speech & Signal Proc,ol.36,pp.1360-1363,1988
[14]T.F.Chan,J.Shen,Mathematical models for local nontexture inpaintings,SIAM J.Appl.Math.,vol.62,no.3,pp.1019-1043,2001
[15]G.Gilboa,N.Sochen,Y.Y.Zeevi,Forward-and-backward diffusion processes for adaptive image enhancement and denoising,IEEE.Trans.Image Process.,vol.11,no.7,pp.689-703,2002
[16]L.Alvarez,F.Guichard,PL.Lions,J.M.Morel,Axioms and fundamental equations of image processing,Archive for Rational Mechanics and Analysis,vol.123,no.3,pp.199-257,1993
[17]G.Aubert,P.Kornprobst,Mathematical problems in image processing:partial differential equations and the calculus of variations,Appl.Math.Sci.,New York:Springer-Verlag,2001
[18]C.Ballester,M.Bertalmio,VCaselles,GSapiro,J.Verdera,Filling-in by joint-interpolation of vector fields and gray levels,IEEE Trans Image Process.,vol 10,no 8,pp.1200-1211,2001
[19]M.Kass,A.Witkin,D.Terzopoulos,Snakes:active contour models,Int.J.Comp.Vis.,vol.1,no.4,pp.321-331,1987
[20]P.Perona,J.Malik,Scale-space and edge detection using anisotropic diffusion,IEEE Trans.Pattern Anal.Machine Intell.,vol.12,no.7,pp.720-727,1990
[21]L.Rudin,S.Osher,E.Fatemi,Nonlinear total variation based noise removal algorithms,Phys.D:Nonlinear Phenom.,vol.60,pp.259-268,1992
[22]D.M.Strong,T.F.Chan,Relation of regularization parameter and scale in total variation based image denosing,CAM Report 96-7,1996
[23]D.M.Strong,P.Blomgren,T.F.Chan,Spatially adaptive local feature-driven total variation minimizing image restoration,SPIE Proceedings Series,vol.3167,pp.222-233,1997
[24]T.F.Chan,J.Shen,Morphologically invariant PDE inpaintings,UCLA CAM Report 2001
[25]M.Bertalmio,GSapiro,VCaselles,C.Ballester,Image inpainting,SIGGRAPH 2000,New Orleans,USA,July,2000
[26]GSapiro,Image inpainting,SIAM News,vol.35,no.4,pp.1-2,2002
[27]S D Rane,G.Sapiro,M.Bertalmio,Structure and texture filling in of missing image blocks in wireless transmission and compression applications,IEEE Trans.Image Process.,vol.12,no.3,pp.296-303,2003
[28]N.Paragios,Y.Chen,O.Faugeras,Handbook of mathematical models in computer vision,New York:Springer Verlag,2006
[29]S.J.Fu,Q.Q.Ruan,W.Wang,F.Gao,and H.D.Cheng,A feature-dependent fuzzy bidirectinal flow for adaptive image sharpening,Neurocomputing,vol.70,pp.83-895,2007
[30]G.Gilboa,N.Sochen,Y.Y.Zeevi,Forward-and-backward diffusion processes for adaptive image enhancement and denoising,IEEE.Trans.Image Process.,vol.11,no.7,pp.689-703,2002
[31]G.Gilboa,N.Sohen,Y.Y.Zeevi,Image enhancement and denoising by complex diffusion processes,IEEE Trans.Pattern Anal Mach.Intell.,vol.26,no.8,pp.1020-1036
[32]F.Catte,P.L.Lions,J.M.Morel,T Coll,Image selective smoothing and edge detection by nonlinear diffusion,SIAM J.Num.Anal.,vol.29,no.1,pp.182-193,1992
[33]L.Alvarez,P.L.Lions,J.M.Morel,Image selective smoothing and edge detection by nonlinear diffusion,SIAM J.Numer.Anal.,vol.29,no.3,pp.845-866,1992
[34]G.Gilboa,Y.Y.Zeevi,N.Sochen,Resolution enhancement by forward-and-backward nonlinear diffusion processes,Proc.Nonlinear Signal Image Process.,Baltimore,Maryland,2001
[35]J.Weickert,Anisotropic diffusion in image processing,Stuttgart:Teubner-Verlag
[36]J.Weickert,Coherence-enhancing diffusion filtering,Int.J.Comput.Vis.,vol.31,no.2,pp.111-127,1999
[37]A.I.El-Fallah,G.E.Ford,On mean curvature diffusion in nonlinear image filtering,Pattern Recogn.Letters,vol.19,pp.433-437,1998
[38]D.Mumford,J.Shah,Optimal approximations by piecewise smooth functions and associated variational problems,Commun.Pure and Appl.Math.,vol.42,no.5,pp.577-685,1989
[39]L.Alvarez,L.Mazorra,Signal and image restoration using shock filters and anisotropic diffusion,SIAM J.on Numer.Anal.,vol.31,no.2 pp.590-605,1994
[40]T.F.Chan,S.H.Kang,J.Shen,Euler's elastica and curvature based inpainting,SIAM J.Appl.Math.,vol.2,no.63,pp.564-592,2002
[41]X.C.Tai,Image inpainting using a TV-Stokes equation,Int.Conf.Appl.Harmonic Analysis:Approximation Appl.,Beijing,2006
[42]赵一凡,夏良正,李久贤,一种自适应小波域图像降噪方法,信号处理,vol 23,no 6,pp.810-813
[43]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,计算机研究与发展,vol.44,no 8,pp.1390-1398,2008
[44]贾迪野,黄凤岗,苏菡,一种新的基于高阶非线性扩敞的图像平滑方法,计算机学报,vol.28,no.5,pp.882-891,2005
[45]谢美华,王正明,基于边缘定向增强的各向异性扩散抑噪方法,电子学报,vol 34,no.1,pp.59-64,2006
[46]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算法,电子学报,vol.32,no.1,pp.17-20,2004
[47]周宏潮,朱炬波,王正明,SAR图像增强的前向-后向扩散方程方法,电子学报,vol.2,no.12,pp.2070-2073,2004
[48]高鑫,刘来福,黄海洋,基于PDE和几何曲率流驱动扩散的图像分析与处理,数学进展,vol.32,no.3,pp.285-294,2003
[49]王岩,梁甸农,郭汉伟,基于改进正则化方法的SAR图像增强技术,电子学报,vol.31,no.9,pp.1307-1309,2003
[50]Tsai,A.Yezzi,A.S.Willsky,A PDE approach to image smoothing and magnification using the Mumford-Shah functional,Proc.Conf.Record of the Thirty-Fourth Asilomar Conf.Signals,Systems Comput.,Pacific Grove,CA,USA,vol.1,pp.473-477,2000
[51]W.Shao,Z.Wei,image magnification using geometric structure reconstruction,Proc.int.Conf.Intell.Comput.,Kunming,China,vol.345,pp.925-931,2006
[52]D.Tschumperle,R.Deriche,Vector-valued image regularization with PDE's:a common framework for different applications,Proc.IEEE Int.Conf.Comput.Vis.Pattern Recogn.,vol.1,pp.651-656,2003
[53]S.J.Fu,Adaptive image interpolation using coupled bidirectional flow,Proc.IEEE Int.Conf.Image Process.(ICIP'05),Genoa,Italy,vol.2,Ⅱ-970-3,2005
[54]D.Tschumperlé,R.Deriche,Vector-Valued Image Regularization with PDE's:A Common Framework for Different Applications,IEEE Trans.Pattern Anal.Mach.Intell.,vol.27,no.4,pp.506-517,2005
[55]Z.Liu,H.Wang,S.Peng,Image magnification method using joint diffusion,J.Comput.Sci.Technol.,vol.19,no.5,pp.698-707,2004
[56]B.Morse,D.Schwartzwald,Isophote-based interpolation,Proc.IEEE Int.Conf.Image Process.,Chicago,Illinois,USA,vol.3,pp.227-231,1998
[57]B.Morse,D.Schwartzwald,Image magnification using level-set reconstruction,Proc.Comput.Vis.Pattern Recogn.Hawaii,USA,vol.Ⅰ,pp.333-341,2001
[58]朱宁,吴静,王忠谦,图像放大的偏微分方程方法,计算机辅助设计与图形学学报,vol.17,no.9,pp 1941-1945,2005
[59]J.Allebach,PW.Wong,Edge-directed interpolation,Proc.IEEE Int.Conf.Image Process.,Lausanne,Switzerland,vol.3,pp.707-710,1996
[60]M.Nitzberg,D.Mumford,T.Shiota,Filtering,segmentation,and depth,Lecture Notes in Computer Science,vol.662,Springer-Verlag,Berlin,1993
[61]S.Masnou,J.M.Morel,Level-lines based disocclusion,Proc.IEEE Int.Conf.Image Process.,Chicago,vol.3,pp.259-263,1998
[62]H.Y.Zhang,Q.C.Peng,Y.D.Wu,Wavelet inpainting based on p-Laplace operator,Acta Automatica Sinica,vol.33,no.5,pp.546-549,2007
[63]S.J.Fu,Q.Q.Ruan,A local nontexture image inpainting and denoising based on nonlinear PDEs,Proc.Int.Conf.Signal Process.,Beijing,China,vol.2,pp.1029-1032,2004
[64]M.Bertalmio,L.Vese,GSapiro,S.Osher,Simultaneous structure and texture image inpainting,IEEE Trans.Image Process.,vol.12,no.8,pp.882-889,2003
[65]M.Bertalmio,Strong-continuation,contrast-invariant inpainting with a third-order optimal PDE, IEEE Trans.Image Process.,vol.15,no.7,pp.1934-1938,2006
[66]C.Barcelos,M.Batista,AMartins,A.Nogueira,Geodesic path based digital inpainting,J.Appl.Math.Comput.,vol.18,no.2,pp.1662-1674,2007
[67]V.Caselles,R.Kimmel,GSapiro,Geodesic active contours,Int.J.Comp.Vision,vol.22,no.l,pp.61-79,1997
[68]S.Osher,R.PFedkiw,Level set methods and dynamic implicit surfaces,New York:Springer-Verlag,2002
[69]杨新,图像偏微分方程的原理与应用,上海交通大学出版社,2003
[70]R.A.Hummel.Representations based on zero-crossings in scale-space.Proc.Int.Cont.Comput.Vis.Pattern Recogn.Miami,USA,pp.204-209,1986
[71]J.Koenderink,The structure of images,Biol.Cyberm.,vol.50,pp.363-370,1984
[72]T.F.Chan,J.Shen,Non-texture inpainting by curvature-driven diffusions(CDD),J.Vis.Commun.Image Representation,vol.4,no.12,pp.436-449,2001
[73]D.Adalsteinsson,J.A.Sethian,The fast construction of extension velocities in level set methods,J.Comput.Physics,vol.148,pp.2-22,1999
[74]W.Yin,D.Goldfarb,S.Osher,Image Cartoon-Texture Decomposition and Feature Selection using The Total Variation Regularized L1 Functional,Proc.Variational,Geom.,Level Set Methods Comput.Vis.,Lecture Notes in Computer Science,Springer,pp.73-84,2005
[75]W.Yin,D.Goldfarb,S.Osher,The Total Variation Regularized L1 Model for Multiscale Decomposition,SIAM J.Multiscale Model.Simul.,vol.6,no.1,pp.190-211,2006
[76]M.Y.Zou,Deconvolution and signal recovery,Beijing:National Defence Industry Press,2001
[77]A.N.Tikhonov,Regularization of incorrectly posed problems,Soviet Math.,Doklady,vol.4,pp.1624-1627,1963
[78]T.F.Chan,S.Osher,J.Shen,The digital TV filter and nonlinear denoising,IEEE Trans.Image Process.,vol.10,no.10,pp.231-241,2001
[79]T.F.Chan,J.Shen,Variational image inpainting,Commun.Pure Appl.Math.,vol.58,no.5,pp.579-619,2005
[80]T.F.Chan,J.Shen,H.M.Zhou,Total variation wavelet inpainting,J.Math.Imaging Vis.,vol.25,no.1,pp.107-125,2006
[81]GSapiro,Geometric partial differential equations and image analysis,Cambridge University Press,New York,NY,USA,2001
[82]S.Osher,L.Rudin,Feature-oriented image enhancement using shock filters,SIAM J.Num.Anal.vol.27,no.4,pp.919-940,1990
[83]G.Gilboa,Y.YZeevi,N.Sochen,Anisotropic selective inverse diffusion for signal enhancement in the presence of noise,Proc.IEEE Int.Conf.Acoust.,Speech,Signal Process.(ICASSP),Istanbul,Turkey,vol 1,pp.221-224,2000
[84]N.Sochen,G.Gilboa,Y,Y,Zeevi,Color image enhancement by a forward-and-backward adaptive Beltrami flow,AFPAC-2000,LNCS188,New York:Springer-Verlag,pp.319-328,2000
[85]GAubert,L.Vese,A variational method in image recovery,SIAM J.Number.Anal.,vol.34,pp.1948-1979,1997
[86]A.N.Tikhonov,V.Y.Arsenin,Solutions of ill-posed problems,Winston and Sons,Washington,D.C.,1997
[87]T.F.Chan,P.Mulet,On the convergence of the lagged diffusivity fixed point method in total variation image restoration,SIAM J.Numer.Anal.,vol.36,pp.354-367,1999
[88]T.F.Chan,S.Osher,J.Shen,The digital TV filter and nonlinear denoising,IEEE Trans.Image Process.,vol.10,no.2,pp.231-241,2000
[89]T.F.Chan,J.Shen,Variational restoration of non-flat image features:models and algorithms,SIAM J.Appl.Math.,vol.61,no.4,pp.1338-1361,2000
[90]P.Mrazek,Selection of optimal stopping time for nonlinear diffusion filtering,Proc.IEEE Wkshp.Scale-Space Morphology Comput.Vis.,Vancouver,Canada,pp.290-298,2001
[91]P.Mrazek,J.Weickert,GSteidl and M.Welk,On iterations and scales of nonlinear filters,Proc.Comput.Vis.Winter Wkshp.,Valtice,Czech Republic,pp.61-66,2003
[92]Y.You,M.Kaveh,W.Xu,and A.Tannenbaum,Analysis and design of anisotropic diffusion for image processing,Proc.Int.Conf.Image Process.,vol.2,pp.497-501,1994
[93]T.Brox,M.Welk,GSteidl,J.Weickert,Equivalence results for TV diffusion and TV regularization,Scale Space Methods Comput.Vis.,Lecture Notes in Computer Science,2695,Springer,Berlin,vol.99,pp.86-100,2003
[94]L.A.Vese,S.J.Osher,Modeling textures with total variation minimization and oscillating patterns in image processing,J.Sci.Comput,vol.19,no.1,pp.553-572
[95]S.Osher,A.Sole,L.Vese,Image decomposition and restoration using total variation minimization and the h-1 norm,J.Multiscale Model.Simul.,vol.1,no.3,pp.349-370,2003
[96]L.A.Vese,S.J.Osher,Image denoising and decomposition with total variation minimization and oscillatory functions,Math.Imaging Vis.,vol.20,pp.7-18,2004
[97]T.F.Chan,H M.Zhou,Optimal constructions of wavelet coefficients using total variation regularization in image compression,CAM Report,No.00-27,Dept.of Math,UCLA,July 2000
[98]G.Steidl,J.Weickert,T.Brox,On the equivalence of soft wavelet shrinkage,total variation diffusion,total variation regularization,and SIDEs,SIAM.J.Numer.Anal.,vol.42,no.2,pp.686-713,2004
[99]Y.D.Wu,S.X.Sun,A new hybrid image de-noising algorithm based on 2D wavelet shrinkage and nonlinear diffusion,Acta Electronica Sinica,vol.34,no.1,pp 163-166,2006
[100]D.H.Jiang,X.C.Feng,G.X.Song,An anisotropic diffusion equation based on nonlinear wavelet shrinkage,Acta Electronica Sinica,vol.34,no.1,pp.170-172,2006
[101]刘来福,高鑫,基于水平集曲率的图像滤噪与增强,北京师范大学学报(自然科学版),vol.37,no.1,pp.5-9,2001
[102]耿芮芮,蔡安妮,孙景鳌,一种非线性扩散线形纹理图像增强的方法,计算机辅助设计与图形学学报,vol.14,no.2,pp 140-143,2002
[103]付树军,阮秋琦,王文洽,基于特征驱动的双向耦合扩散方程的图像去噪和边缘锐化,光学精密工程,vol.14,no.2,pp.315-319,2006
[104]S.Robert,Cognitive Psychology Fourth Edition,Thomas Wadsworth,2006
[105]T.F.Chan,S.H.Kang,Error analysis on image inpainting problems,J.Math.Imaging Vis.,vol.26,pp.85-103,2006
[106]Chanmbolle,P.L.Lions,Image recovery via total variational minimization and related problems,Numer.Math.,vol.76,pp.167-188,1997
[107]P.Charbonnier,L.B.Feraud,G Aubert,M.Barlaud,Deterministic edge-preserving regularization in computed imaging,IEEE Trans.Image Process.,vol.6,no.2,pp.298-310,1997
[108]C.Price,P.Wambacq,A.Ooosterlinck,Applications of reaction-diffusion equations to image processing,Proc.Int.Cont.Image Process.Appl.,Warwick,UK,pp.49-53,1989
[109]M.Turk,A.Pentland,Eigenfaces for recognition,J.Cogn.Neurosci.,vol.3,pp.72-86,1991
[110]D.M.Strong,PBlomgren,T.F.Chan,Spatially adaptive local feature-driven total variation minimizing image restoration,Proc.SPIE,vol.3167,1997
[111]D.M.Strong,T.F.Chan,Spatially and scale adaptive total variation based regularization and anisotropic diffusion in image processing,UCLA CAM Report 96-46,Nov 1996
[112]G.Aubert,P.Kornprobst,Mathematical problems in image processing:partial differential equations and the calculus of variations(second edition),New York:Springer-Verlag,2006
[113]M.Frazier,B.Jawerth,GWeiss,Littlewood-paley theory and the study of function spaces,CBMS Regional Conf.Series,vol.79,Providence,Amer.Math.Soc.,1991
[114]Daubechies,Orthonormal Bases of Compactly Supported Wavelets,Comm.Pure Appl.Math.,vol.41,pp.906-966,1988
[115]Daubechies,Orthonormal bases of compactly support wavelets:II variations on a theme,SIAM J.Math.Anal.,vol.24,pp.499-519,1993
[116]S.Mallat,S.Zhong,Characterization of signals from multiscale edges,IEEE Trans.Pattern Anal.Mach.Intell.,vol.14,no.7,pp.710-732,1992
[117]S.Mallat,W.L.Hwang,Singularity detection and processing with wavelets,IEEE Trans.Info.Theory,vol.38,pp.617-643,1992
[118]T.D.Bui,GChen,Translation invariant de-noising using multi-wavelets,1EEE Trans.Signal Process.,vol.46,no.12,pp.3414-3420,1998
[119]C.Taswell,Specifications and standards for reproducibility of wavelet transforms,Proc.Int.Conf.Signal Process.Appl.Techn.,Miller Freeman,pp.1923-1927,1996
[120]戴维,于盛林,孙枪,基于Contourlet变换自适应阈值的图像去噪算法,电子学报,vol.35,no.10,pp 1939-1943,2007
[121]陈莹,纪志成,韩崇昭,基于小波域加权阈值的图像去噪方法,计算机工程,vol.33,no.19,pp.183-185,2007
[122]D.L.Donoho,I,M.Johnstone,Adapting to unknown smoothness via wavelet shrinkage,J.Am.Stat.Assoc.,vol.90,no.432,pp.1200-1224,1995
[123]D.L.Donoho,I.M.Johnstone,GKerkyacharian,D.Picard,Wavelet shrinkage:Asymptopia?With discussion,J.R.Statis.Soc.,Series B,vol.57,no.2,pp.301-369,1995
[124]K.Chandrawansa,F.H.Ruymgaart,A.C.M.Wan Rooij,Controlling the Gibbs phenomenon in noisy deconvolution of irregular multivariable input signals,J.Appl.Math.Stochastic Anal.vol.13,no.1,pp.1-14,2000
[125]J.W.Gibbs,Letter to the editor,Nature 59,p.200
[126]J.WGibbs,Letter to the editor,Nature 59,p.606
[127]X.P.Shen,Gibbs phenomenon in orthogonal wavelet expansion,J.Math.Study,vol.35,no.4,1919.343-357,2002
[128]高清维,李海鹰,庄镇泉,王涛,基于平稳小波变换的心电信号噪声消除方法,电子学报,vol.31,no.2,pp.1-3,2003
[129]J.W.Woods,Two-dimensional discrete Markovian Fields,IEEE Trans.Inf.Theory,vol.18,pp.232-240,1972
[130]E.Ising,Zeitschrift Physik,vol.31,P.253
[131]H.S.Hou,H.CAndrews,Cubic splines for image interpolation and digital filtering,IEEE Trans.Acoust.,Speech & Signal Process.,vo126,no.6,pp.508-517,1978
[132]S.K.Park,RASchowengerdt,Image reconstruction by parametric cubic convolution,Comput.Vis.Graph.Image Process.,vol.23,pp258-272,1983
[133]R.Keys,Cubic convolution interpolation for digital image processing,IEEE Trans.Acoustics,Speech & Signal Proc.,voI.ASSP-29,no.6,pp.1153-1160,1981
[134]S.EReichenbach,F.Geng,Two-dimensional cubic convolution,IEEE Trans.Image Process., vol.12,no.8,pp.857-865,2003
[135]C.Boor,A practical guide to splines,Springer-Verlag,New York,1978
[136]P Haeberli,D.Voorhies,Image Processing by Linear Interpolation and Extrapolation,IRIS Universe Magazine,no.28,Silicon Graphics,1994
[137]李天倩,吴援明,杨建军等,两种新图像放大算法研究,信号处理,Vol.19,no.3,pp 234-236,2003
[138]K.Revathy,G.Raju,S.R.Prabhakran Nayar,Image zooming by wavelets,fractals,Fractals-complex geometry patterns and scaling in nature and society,vol.8,no.3,pp.247-253,2000
[139]K.Jensen,D.Anastassiou,Subpixel edge localization and the interpolation of still images,IEEE Trans.Image Process.,vol.4,pp.285-295,1995
[140]X.Li,M.T.Orchard,New edge directed interpolation,Proc.IEEE Int.Conf.Image Process.,Vancouver,BC,Canada,vol.2,pp.311-314,2000
[141]X.Li,M.T.Orchard,New edge-directed interpolation,IEEE Trans.Image Process.,vol.10,no.10,pp.1521-1527,2001
[142]B.Antoni,C.Bartomeu,J.M.Morel,On image denoising methods,CMLA Preprint,CMLA,2004
[143]B.Antoni,C.Bartomeu,J.MMorel,Denoising image sequences does not require motion estimation,Proc.IEEE Conf.Advanced Video and Signal Based Surveillance(AVSS'05),Teatro Sociale,Como,Italy,pp.70-74,2005
[144]T.Wittman,Mathematical techniques for image interpolation,Oral Exam Paper,July 2005
[145]S.J.Fu,Q.Q.Ruan,W.Q.Wang,J.N.Chen,Feature preserving nonlinear image interpolation,Proc.Int.Conf.Signal Process.,Guilin,China,2006
[146]S.Walden,The ravished image,St.Martin's Press,New York,1985
[147]M.Bertalmio,A.L.Bertozzi,GSapiro,Navier-Stokes,fluid dynamics,and image and video inpainting,Proc.IEEE int.conf.Comput.Vis.Pattern Recogn.,Hawaii,USA,vol.1,pp.355-362,2001
[148]C.A.Z.Barcelos,M.A.Batista,Image inpainting and denoising by nonlinear partial differential equations,Proc.Brazilian Symp.Comput.Graph.Image Process.(SIBGRAPI),Brazil,pp.287-293,2003
[149]M.M.Oliveira,B.Bowen,R.McKenna,YS.Chang,Fast digital image inpainting,Proc.Int.Conf.Vis.image Image Process.,Marbella,Spain,pp.261-266,2001
[150]S.Esedoglu,J.Shen,Digital image inpainting by the Mumford-Shah-Euler image model,European J.Appl.Math.,vol.13,pp.353-370,2002
[151]S.Osher,J.A.Sethian,Front propagating with curvature dependent speed:algorithms based on Hamilton-Jacobi formulations,J Comput.Phys.,vol.79,pp.12-49,1988
[152]Z.N.Dong,Inviscid fluid mechanics,Beijing:Tsinghua University Press,2003
[153]Rares,M.J.T.Reinders,J.Biemond,Image sequence restoration in the presence of pathological motion and severe artifacts,Proc.Int.Conf.Acoust.Speech Signal Process.,Orlando,vol.4,pp.3365-3368,2002
[154]Rares,M.J.T.Reinders,J.Biemond,R.L.Lagendijk,A spatiotemporal image sequence restoration algorithm,Proc Int.Conf.Image Process,Rochester,New York,USA,vol.2,pp.857-860,2002
[155]J.J.Gibson,The perception of the visual world,Houghton Mifflin,Boston,Massachusetts,1950
[156]B.Julesz,Visual pattern discrimination,IEEE Trans.Inf.Theory,vol.8,no.2,pp.84-92,1962
[157]M.Tran,A.Datta,Synthesising textures using variable neighborhood searching,Proc.Int.Conf.Digital Image Comput.Techn.Appl.,Sydney,pp.643-652,2003
[158]T.Y.Ng,C.Wen,T.S.Tan,X.Zhang,Y J.Kim,Generating an w-tile set for texture synthesis,Proc.Comput.Graph.Int.,Stony Brook,NY,USA,pp.177-184,2005
[159]D.J.Heeger,J.R.Bergen,Pyramid-based texture analysis/synthesis,Proc.ACM SIGGRAPH,Los Angeles,California,pp.229-238,1995
[160]J.Potilla,E.PSimoncelli,A parametric texture model based on joint statistics of complex wavelet coefficients,Int.J.Comput.Vis.,vol.40,no.1,pp.49-71,2000
[161]Efros,T.Leung,Texture synthesis by nonparametric sampling,Proc.Int.Conf.Comput.Vis.,Greece,pp.1033-1038,1999
[162]L.Y.Wei,M.Levoy,Fast texture synthesis using tree-structured vector quantization,Proc.SIGGRAPH2000,San Antonio,pp.479-488,2000
[163]P.Harrison,A non-hierarchical procedure for re-synthesis of complex textures,Proc.Int.Conf.Central Europe Comput.Graph.Vis.(WSCG 2001),Plzen,Czech Republic,pp.190-197,2001
[164]M.Ashikhmin,Synthesizing Natural Textures,Proc.ACM Symp.Interactive 3D Graphics,Research Triangle Park,NorthCarolina,pp.217-226,2001
[165]Efros,W.F.Freeman,Image quilting for texture synthesis and transfer,Proc.ACM Conf.Comput.Graph.(SIGGRAPH),Los Angeles,pp.341-346,2001
[166]R.Bornard,E.Lecam,L.Laborelli,Missing data correction in still images and image sequences,Proc.ACM.Multimedia,Juan-les-Pins,France,pp.355-361,2002
[167]P.Perez,M.Gangnet,A.Blake,Patch Works:example-based region tiling for image editing,Microsoft Research Report MSR-TR-2004-04,2004
[168]D.Drori,O.Cohen,H.Yeshurun,Fragment-based image completion,ACM Trans.Graph.,vol.22,no.3,pp.303-312,2003
[169]J.Sun,L.Yuan,J.Jia,H.Y.Shum,Image completion with structure propagation,ACM Trans.Graph.,vol.24,no.3,pp.861-868,2005
[170]Criminisi,P.Perez,and K.Toyama,Region filling and object removal by exemplar-based image inpainting,IEEE.Trans.Image Process.,vol.13,no.9,pp.1200-1212,2004
[171]Dewdney,A potpourri of programmed prose and prosody,Scientific America,122-TK,June 1989
[172]K.Popat,R.W.Picard,Novel cluster-based probability model for texture synthesis,classification,and compression,Proc.SPIE Vis.Comm.Image Process.,USA,pp.756-768,1993
[173]J.S.D.Bonet,Multiresolution sampling procedure of analysis and synthesis of texture images.Proc.SIGGRAPH'97,Los Angeles,CA,USA,pp.361-368,1997
[174]J.Portilla,E.PSimoncelli,Texture representation and synthesis using correlation of complex wavelet coefficient magnitudes,TR 54,CSIC,Madrid,April 1999
[175]E.PSimoncelli,J.Portilla,Texture characterization via joint statistics of wavelet coefficient magnitudes,Proc.Int.Conf.Image Process.,Chicago,vol.1,pp.62-66,1998
[176]S.C.Zhu,YWu,D.Mumford,Filters,random fields and maximum entropy(frame),Int.J.Comput.Vis.,vol.27,no.2,pp.1-20,1998
[177]J.Davis,Mosaics of scenes with moving objects,Proc.IEEE Conf.on Comput.Visi.Pattern Recogn.,Santa Barbara,CA,USA,pp.354-360,1998
[178]Criminisi,PPerez,K.Toyama,Object removal by exemplar-based inpainting,Proc.Int.Conf.Comput.Vis.Pattern Recogn.,Madison,WI,vol.2,pp.721-728,2003
[179]阮秋琦,阮宇智等译,电子工业出版社,北京,2007
[180]阮秋琦,数字图像处理学(第二版),电子工业出版社,北京,2008
[181]R.C.Gonzalez,R.EWoods,Digital image processing,Addison-Wesley,Reading,Mass,1992
[182]T.F.Chan,A.Marquina,P.Mulet,Second order differential functionals in total variation-based image restoration,CAM 97-56,1998
[183]M.Kirby,L.Sirovich,Application of the Karhunen-Loeve procedure for the characterization of human faces,IEEE Trans.Pattern Anal.Mach Intell.,vol.12,no.1,pp.103-108,1990
[184]L.Sirovich,M.Kirby,Low-dimensional procedure for the characterization of human faces,J.Opt.Soc.Amer.,vol.4 no.3,pp.519-524,1987
[185]R.A.Fisher,The statistical utilization of multiple measurements,Ann.Eugen.,vol.8,pp.376-386,1938
[186]B.Moghaddam,A.Pentland,Probabilistic visual learning for object representation,IEEE Trans.Pattern Anal.Mach Intell.,vol.19,pp.696-710,1997
[187]P J.Phillips,Support vector machines applied to face recognition,Adv.Neural Inform.Process.Syst.,vol.11,pp.803-809,1998
[188]MS.Bartlett,J.RMovellan,T.J.Sejnowski,Face recognition by independent component analysis,IEEE Trans.Neural Netw,vol.13,no.6,pp.1450-1464,2002
[189]B.Sch(o|¨)kopf,A.Smola,K.R.Müller,Nonlinear component analysis as a kernel eigenvalue problem,Neural Comput.,vol.10,pp.1299-1319,1998
[190]C.J.Liu,Gabor-based kernel PCA with fractional power polynomial models for face recognition,IEEE Trans.Pattern Anal.Mach.Intell.,vol.26,pp.572-581,2004
[191]J.Yang,X.Gao,D.Zhang,J.Yang,Kernel ICA:An alternative formulation and its application to face recognition,Pattern Recogn.,vol.38,pp.1784-1787,2005
[192]S.Mika,GRatsch,J.Weston,B.Scholkopf,K.Muller,Fisher discriminant analysis with kernels,Proc.IEEE Wkshp.Neural Netw.Signal Process.,Madison,Wisconsin,USA,vol.9,pp.41-48,1999
[193]A.L.Yuille,D.S.Cohen,Feature extraction from faces using deformable templates,Int.J.Comput.r Vis.,vol.8,no.2,pp.99-111,1992
[194]Lanitis,C.J.Taylor,T.FCootes,Automatic interpretation and coding of face images using flexible models,IEEE Trans.Pattern Anal.Mach.Intell.,vol.19,no.7,pp.743-756,1997
[195]T.F.Cootes,GJ.Edwards,C.J.Taylor,Advances in active appearance models,Proc.Int.Conf.Comput.Vis.,Kerkyra,Corfu,Greece,pp.137-142,1999
[196]L.D.Hamon,The recognition of faces,Sci.Am.,vol.229,pp.71-82,1973
[197]J.Sergent,Microgenesis of face perception,In Aspects of Face Processing.,H.D.Ellis,M.A.,Jeeves,F.Newcombe,and A.Young,Eds.A Young(Dordrecht:Martinus Nijhoff),1986
[198]W.Zhao,R.Chellappa,P.J.Phillips,A.Rosenfeld,Face recognition:a literature survey,ACM Comput.Surv.,vol.35,no.4,pp.399-458,2003
[199]王蕴红,范伟,谭铁牛,融合全局与局部特征的子空间人脸识别算法计算机学报,vol 28,no.10,pp 1657一1663,2005
[200]H.Bernd,S.Thomas,P.Massimiliano,V.Thomas,P.Tomaso,Categorization by learning and combining object parts,Proc.Advances in Neural Information Processing systems NIPS),Vancouver,Canada,pp.1239-1245,2002
[201]Y.C.Fang,T.NTan,Y.H.Wang,Fusion of global and local features for face verification,Proc.IEEE Int.Conf.Pattern Recogn.,Quebec,Canada,vol.2,pp.382-385,2002
[202]J.Huang,P.C.Yuen,J.H.Lai,C.H.Li,Face recognition using local and global features, EURASIP J.Appl.Signal Process.,vol.4,pp.530-541,2004
[203]Martinez,A.Kak,PCA versus LDA,IEEE Trans.Pattern Anal.Mach Intell.,vol.23,no.2,pp.228-233,2001
[204]Pentland,B.Moghaddam,T.Starner,View-based and modular eigenspaces for face recognition,Proc.IEEE Int.Conf.Comput.Vis.Pattern Recogn.,ilton Head,SC,USA,pp.84-91,1994
[205]Y.Adini,Y.Moses,S.Ullman,Face recognition:the problem of compensating for changes in illumination direction,IEEE Trans.Pattern Anal.Mach.Intell.,vol.19,no.7,pp.721-732,July 1997
[206]T.Sim,T.Kanade,Combining models and exemplars for face recognition:an illuminating example,Proc.Wkshp.Model.Versus Exemplars Comput.Vis.,Hawaii,USA,pp.1-10,2001
[207]P.W.Hallinan,A low-dimensional representation of human faces for arbitrary lighting conditions,Proc.Int.Cone Comp.Vis.Pattern Recogn.,Seattle,WA,USA,pp.995-999,1994
[208]R.Basri,D.Jacobs,Lambertian reflectance and linear subspaces,Proc.Int.Conf.Compu.Vis.(ICCV),Vancouver,Canada,pp.383-390,2001
[209]R.Ramamoorthi,PHanrahan,On the relationship between radiance and irradianc:Determining the illumination from images of a convex Lambertian object,J.Opt.Soc.Am.,A,vol.18,no.10,pp.2448-2459,2001
[210]Y.K.Hu,Z.F.Wang,Face recognition under different illuminations,J.Image Graph.,vol.10,no.7,pp.844-849,2005
[211]卿来云,山势光,陈熙霖,高文,基于球面谐波基图像的任意光照下的人脸识别,计算机学报,vol.29,no.5,pp.760-768,2006
[212]P.N.Belhumeur,D.J.Kriegman,What is the set of images of an object under all possible lighting conditions? Proc.IEEE Int.Conf.Comput.Vis.Pattern Recogn.,San Francisco,pp.270-277,1996
[213]A.S.Georghiades,P.N.Belhumeur,D.J.Kriegman,From few to many:Illumination cone models for face recognition under differing pose and lighting,IEEE Trans.Pattern Anal.Mach.Intell.,vol.23,pp.643-660,2001
[214]S.G.Shan,WGao,B.Cao,D.Zhao,Illumination normalization for robust face recognition against varying lighting conditions,Proc.IEEE Int.Wkshp.Anal.Model.Faces Gestures Recogn.,Nice,France,pp.157-164,2003
[215]Shashua,T.Riklin-Raviv,The quotient image:class-based re-rendering and recognition with varying illuminations,IEEE Trans.Pattern Anal.Mach.Intell.,voi.23,no.2,pp.129-139,2001
[216]W.Zhao,R.Chellappa,Illumination-insensitive face recognition using symmetric shape-from-shading,Proc.Int.Cone Comput.Vis.Pattern Recogn.,South Carolina,vol.1,pp. 286-293,2000
[217]K.Okada,C.Malsburg,Pose-invariant face recognition with parametric linear subspaces,Proc.Int.Conf.Aut.Face Gesture Recogn.,Southampton,UK,pp.71-76,2002
[218]W.Gao,S.Shan,X.Chai,X.Fu,Virtual face image generation for illumination and pose insensitive face recognition,Proc.IEEE Int.Conf.Acoust.Speech,Signal Process,Hong Kong,vol.Ⅳ,pp.776-779,2003
[219]T.Chen,W.Yin,X.S.Zhou,D.Comaniciu,T.S.Huang,Total Variation Models for Variable Lighting Face Recognition,IEEE Trans.Pattern Anal Mach.Intell.,vol 28,pp.1519-1524,2006
[220]P.J.Phlips,Y.Vardi,Efficient illumination normalization of facial images,Pattern Recogn.Lett.,vol.17,pp.921-927,1996
[221]X.Xie,K.M.Lam,An efficient illumination normalization method for face recognition,Pattern Recogn.Lett.,vol.27,pp.609-617,2006
[222]Shashua,T Riklin-Raviv,The quotient image:class-based re-rendering and recognition with varying illuminations,IEEE Trans.Pattern Anal.Mach.Intell.,vol.23,no.2,pp.129-139,2001
[223]H.Wang,S.Z.Li,Y.Wang,Generalized quotient image,Proc.IEEE Int.Conf.Comput.Vis.Pattern Recogn.,Washington,DC,USA.vol.2,pp.498-505,2004
[224]D.J.Jobson,Z.Rahman,Properties and performance of a center/surround retinex,IEEE Trans.Image Process.,vol.6,no.3,pp.451-462,1997
[225]T.Chen,WYin,X.S.Zhou,D.Comaniciu,T.S.Huang,Illumination Normalization for Face Recognition and Uneven Background Correction Using Total Variation Based Image Models,Proc.IEEE Int.Conf.Comput.Vis.Pattern Recogn.,San Diego,CA,USA,vol.2,pp.532-539,2005
[226]Witkin,Scale-space filtering,Proc.Int.Joint Conf.Artif.Intell.,Karlsruhe,Germany,pp.1019-1022,1983
[227]J.F.Aujol,G Gilboa,T.Chan,S.Osher,Structure-texture image decomposition-modeling,algorithms,and parameter selection,Int.J.of Comput.Vis.,vol.67,no.1,pp.111-136,2006
[228]Y.Meyer,Oscillating patterns in image processing and nonlinear evolution equations,The Fifteenth Dean Jacquelines B.Lewis Memorial Lectures,2001
[229]W.Yin,D.Goldfarb,S.Osher,Total variation based image cartoon-texture decomposition,Columbia University CORC Report TR-2005-01,UCLA CAM Report 05-27,2005
[230]T.Chan,S.Esedoglu,Aspects of total variation regularized L1 function approximation,SIAM J.Appl.Math.,vol.65,pp.1817-1837,2004
[231]M.M.Meendonca,J.GDenipote,A.S.Ricardo,F.M.Stela,V.Paiva,Illumination normalization methods for face recognition,sibgrapi.sid.inpe.br/col/sid.inpe.br/sibgrapi@80/2007/09.19.15.08/doc/ArtigoSIBGRAPI_2007_Ingles.Final.pdf
[232]X.Xie,K.M.Lam,Face recognition under varying illumination based on a 2D face shape model,Pattern Recogn.,vol.38,no.2,pp.221-230,2005
[233]A.A.Ross,K.Nandakumar,A K.Jain,Handbook of multibiometncs,Springer,2006
[234]K.Delac,M.Grgic,S.Grgic,Independent Comparative Study of PCA,ICA,and LDA on the FERET Data Set,Technical Report,University of Zagreb,2004
[235]K.C.Lee,J.Ho,D.Knegman,Acquiring linear subspaces for face recognition under variable lighting,IEEE Trans.Pattern Anal.Mach.Intell.,vol.27,no.5,pp.684-698,2005
[2]S Mallat,S.Zhong,Characterization of signals from multiscale edges,IEEE Trans.Pattern Anal.Mach.Intell.,vol.l4,no.7,pp.710-732,1992
[3]S Mallat,W.L.Hwang,Singularity detection and processing with wavelets,IEEE Trans.Info.Theory,vol.38,pp.617-643,1992
[4]Cohen,I.Daubechies,J.C.Feauveau,Biorthogonal Bases of Compactly Supported Wavelets,Commun.Pure Appl.Math.,vol.XLV,pp.485-560,1992
[5]A.S.Lewis,G.Knowles,Image Compression Using the 2-D Wavelet Transform,IEEE Trans.Image Process.,vol.1,no.2,pp.244-250,1992
[6]D.L.Donoho,De-Noising by soft thresholding,IEEE Trans.Info.Theory,vol.43,pp.933-936,1993
[7]D.L.Donoho,L.M.Johnstone,Ideal spatial adaptation via wavelet shrinkage,Biometrica,vol.81,pp.425-455,1994
[8]D.L.Donoho,Denoising by soft-thresholding,IEEE Trans.Inf.Theory,vol.41,no.3,pp.613-627,1995
[9]Bezvesilniy,V.Vinogradov,D.Vavriv,K.Schunemann,Wavelet-based image processing,edge detection and noise reduction,Proc.Int.Conf.Applied Electronagnetics and Communications (ICECom),Dubrovnik,Croatia,pp.123-126,2003
[10]A.D.Dempster,N.M.Laird,D.B.Rudin,Maximum likelihood from incomplete data via the EM algorithm,J.Roy.Strat.Soc,vol.B39,pp.1-37,1977
[11]R.L.Lagendijk,J.Biemond,D.E.Boekee,Identification and restoration of noise blurred images using the expectation-max-minimization algorithm,IEEE Trans.Acoustics,Speech & Signal Proc,vol.38,no.7,pp.1180-1191
[12]K.T.Lay,K.Katsaggelos,Image identification and restoration based on the expectation-maximization algorighm,Opt.Eng.,vol.29,pp.436-445,1990
[13]A.M.Tekalp,H.Kaufman,On statistical identification of a class of linear space-invariant image blurs using non-minimum-phase ARMA models,IEEE Trans.Acoust.Speech & Signal Proc,ol.36,pp.1360-1363,1988
[14]T.F.Chan,J.Shen,Mathematical models for local nontexture inpaintings,SIAM J.Appl.Math.,vol.62,no.3,pp.1019-1043,2001
[15]G.Gilboa,N.Sochen,Y.Y.Zeevi,Forward-and-backward diffusion processes for adaptive image enhancement and denoising,IEEE.Trans.Image Process.,vol.11,no.7,pp.689-703,2002
[16]L.Alvarez,F.Guichard,PL.Lions,J.M.Morel,Axioms and fundamental equations of image processing,Archive for Rational Mechanics and Analysis,vol.123,no.3,pp.199-257,1993
[17]G.Aubert,P.Kornprobst,Mathematical problems in image processing:partial differential equations and the calculus of variations,Appl.Math.Sci.,New York:Springer-Verlag,2001
[18]C.Ballester,M.Bertalmio,VCaselles,GSapiro,J.Verdera,Filling-in by joint-interpolation of vector fields and gray levels,IEEE Trans Image Process.,vol 10,no 8,pp.1200-1211,2001
[19]M.Kass,A.Witkin,D.Terzopoulos,Snakes:active contour models,Int.J.Comp.Vis.,vol.1,no.4,pp.321-331,1987
[20]P.Perona,J.Malik,Scale-space and edge detection using anisotropic diffusion,IEEE Trans.Pattern Anal.Machine Intell.,vol.12,no.7,pp.720-727,1990
[21]L.Rudin,S.Osher,E.Fatemi,Nonlinear total variation based noise removal algorithms,Phys.D:Nonlinear Phenom.,vol.60,pp.259-268,1992
[22]D.M.Strong,T.F.Chan,Relation of regularization parameter and scale in total variation based image denosing,CAM Report 96-7,1996
[23]D.M.Strong,P.Blomgren,T.F.Chan,Spatially adaptive local feature-driven total variation minimizing image restoration,SPIE Proceedings Series,vol.3167,pp.222-233,1997
[24]T.F.Chan,J.Shen,Morphologically invariant PDE inpaintings,UCLA CAM Report 2001
[25]M.Bertalmio,GSapiro,VCaselles,C.Ballester,Image inpainting,SIGGRAPH 2000,New Orleans,USA,July,2000
[26]GSapiro,Image inpainting,SIAM News,vol.35,no.4,pp.1-2,2002
[27]S D Rane,G.Sapiro,M.Bertalmio,Structure and texture filling in of missing image blocks in wireless transmission and compression applications,IEEE Trans.Image Process.,vol.12,no.3,pp.296-303,2003
[28]N.Paragios,Y.Chen,O.Faugeras,Handbook of mathematical models in computer vision,New York:Springer Verlag,2006
[29]S.J.Fu,Q.Q.Ruan,W.Wang,F.Gao,and H.D.Cheng,A feature-dependent fuzzy bidirectinal flow for adaptive image sharpening,Neurocomputing,vol.70,pp.83-895,2007
[30]G.Gilboa,N.Sochen,Y.Y.Zeevi,Forward-and-backward diffusion processes for adaptive image enhancement and denoising,IEEE.Trans.Image Process.,vol.11,no.7,pp.689-703,2002
[31]G.Gilboa,N.Sohen,Y.Y.Zeevi,Image enhancement and denoising by complex diffusion processes,IEEE Trans.Pattern Anal Mach.Intell.,vol.26,no.8,pp.1020-1036
[32]F.Catte,P.L.Lions,J.M.Morel,T Coll,Image selective smoothing and edge detection by nonlinear diffusion,SIAM J.Num.Anal.,vol.29,no.1,pp.182-193,1992
[33]L.Alvarez,P.L.Lions,J.M.Morel,Image selective smoothing and edge detection by nonlinear diffusion,SIAM J.Numer.Anal.,vol.29,no.3,pp.845-866,1992
[34]G.Gilboa,Y.Y.Zeevi,N.Sochen,Resolution enhancement by forward-and-backward nonlinear diffusion processes,Proc.Nonlinear Signal Image Process.,Baltimore,Maryland,2001
[35]J.Weickert,Anisotropic diffusion in image processing,Stuttgart:Teubner-Verlag
[36]J.Weickert,Coherence-enhancing diffusion filtering,Int.J.Comput.Vis.,vol.31,no.2,pp.111-127,1999
[37]A.I.El-Fallah,G.E.Ford,On mean curvature diffusion in nonlinear image filtering,Pattern Recogn.Letters,vol.19,pp.433-437,1998
[38]D.Mumford,J.Shah,Optimal approximations by piecewise smooth functions and associated variational problems,Commun.Pure and Appl.Math.,vol.42,no.5,pp.577-685,1989
[39]L.Alvarez,L.Mazorra,Signal and image restoration using shock filters and anisotropic diffusion,SIAM J.on Numer.Anal.,vol.31,no.2 pp.590-605,1994
[40]T.F.Chan,S.H.Kang,J.Shen,Euler's elastica and curvature based inpainting,SIAM J.Appl.Math.,vol.2,no.63,pp.564-592,2002
[41]X.C.Tai,Image inpainting using a TV-Stokes equation,Int.Conf.Appl.Harmonic Analysis:Approximation Appl.,Beijing,2006
[42]赵一凡,夏良正,李久贤,一种自适应小波域图像降噪方法,信号处理,vol 23,no 6,pp.810-813
[43]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,计算机研究与发展,vol.44,no 8,pp.1390-1398,2008
[44]贾迪野,黄凤岗,苏菡,一种新的基于高阶非线性扩敞的图像平滑方法,计算机学报,vol.28,no.5,pp.882-891,2005
[45]谢美华,王正明,基于边缘定向增强的各向异性扩散抑噪方法,电子学报,vol 34,no.1,pp.59-64,2006
[46]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算法,电子学报,vol.32,no.1,pp.17-20,2004
[47]周宏潮,朱炬波,王正明,SAR图像增强的前向-后向扩散方程方法,电子学报,vol.2,no.12,pp.2070-2073,2004
[48]高鑫,刘来福,黄海洋,基于PDE和几何曲率流驱动扩散的图像分析与处理,数学进展,vol.32,no.3,pp.285-294,2003
[49]王岩,梁甸农,郭汉伟,基于改进正则化方法的SAR图像增强技术,电子学报,vol.31,no.9,pp.1307-1309,2003
[50]Tsai,A.Yezzi,A.S.Willsky,A PDE approach to image smoothing and magnification using the Mumford-Shah functional,Proc.Conf.Record of the Thirty-Fourth Asilomar Conf.Signals,Systems Comput.,Pacific Grove,CA,USA,vol.1,pp.473-477,2000
[51]W.Shao,Z.Wei,image magnification using geometric structure reconstruction,Proc.int.Conf.Intell.Comput.,Kunming,China,vol.345,pp.925-931,2006
[52]D.Tschumperle,R.Deriche,Vector-valued image regularization with PDE's:a common framework for different applications,Proc.IEEE Int.Conf.Comput.Vis.Pattern Recogn.,vol.1,pp.651-656,2003
[53]S.J.Fu,Adaptive image interpolation using coupled bidirectional flow,Proc.IEEE Int.Conf.Image Process.(ICIP'05),Genoa,Italy,vol.2,Ⅱ-970-3,2005
[54]D.Tschumperlé,R.Deriche,Vector-Valued Image Regularization with PDE's:A Common Framework for Different Applications,IEEE Trans.Pattern Anal.Mach.Intell.,vol.27,no.4,pp.506-517,2005
[55]Z.Liu,H.Wang,S.Peng,Image magnification method using joint diffusion,J.Comput.Sci.Technol.,vol.19,no.5,pp.698-707,2004
[56]B.Morse,D.Schwartzwald,Isophote-based interpolation,Proc.IEEE Int.Conf.Image Process.,Chicago,Illinois,USA,vol.3,pp.227-231,1998
[57]B.Morse,D.Schwartzwald,Image magnification using level-set reconstruction,Proc.Comput.Vis.Pattern Recogn.Hawaii,USA,vol.Ⅰ,pp.333-341,2001
[58]朱宁,吴静,王忠谦,图像放大的偏微分方程方法,计算机辅助设计与图形学学报,vol.17,no.9,pp 1941-1945,2005
[59]J.Allebach,PW.Wong,Edge-directed interpolation,Proc.IEEE Int.Conf.Image Process.,Lausanne,Switzerland,vol.3,pp.707-710,1996
[60]M.Nitzberg,D.Mumford,T.Shiota,Filtering,segmentation,and depth,Lecture Notes in Computer Science,vol.662,Springer-Verlag,Berlin,1993
[61]S.Masnou,J.M.Morel,Level-lines based disocclusion,Proc.IEEE Int.Conf.Image Process.,Chicago,vol.3,pp.259-263,1998
[62]H.Y.Zhang,Q.C.Peng,Y.D.Wu,Wavelet inpainting based on p-Laplace operator,Acta Automatica Sinica,vol.33,no.5,pp.546-549,2007
[63]S.J.Fu,Q.Q.Ruan,A local nontexture image inpainting and denoising based on nonlinear PDEs,Proc.Int.Conf.Signal Process.,Beijing,China,vol.2,pp.1029-1032,2004
[64]M.Bertalmio,L.Vese,GSapiro,S.Osher,Simultaneous structure and texture image inpainting,IEEE Trans.Image Process.,vol.12,no.8,pp.882-889,2003
[65]M.Bertalmio,Strong-continuation,contrast-invariant inpainting with a third-order optimal PDE, IEEE Trans.Image Process.,vol.15,no.7,pp.1934-1938,2006
[66]C.Barcelos,M.Batista,AMartins,A.Nogueira,Geodesic path based digital inpainting,J.Appl.Math.Comput.,vol.18,no.2,pp.1662-1674,2007
[67]V.Caselles,R.Kimmel,GSapiro,Geodesic active contours,Int.J.Comp.Vision,vol.22,no.l,pp.61-79,1997
[68]S.Osher,R.PFedkiw,Level set methods and dynamic implicit surfaces,New York:Springer-Verlag,2002
[69]杨新,图像偏微分方程的原理与应用,上海交通大学出版社,2003
[70]R.A.Hummel.Representations based on zero-crossings in scale-space.Proc.Int.Cont.Comput.Vis.Pattern Recogn.Miami,USA,pp.204-209,1986
[71]J.Koenderink,The structure of images,Biol.Cyberm.,vol.50,pp.363-370,1984
[72]T.F.Chan,J.Shen,Non-texture inpainting by curvature-driven diffusions(CDD),J.Vis.Commun.Image Representation,vol.4,no.12,pp.436-449,2001
[73]D.Adalsteinsson,J.A.Sethian,The fast construction of extension velocities in level set methods,J.Comput.Physics,vol.148,pp.2-22,1999
[74]W.Yin,D.Goldfarb,S.Osher,Image Cartoon-Texture Decomposition and Feature Selection using The Total Variation Regularized L1 Functional,Proc.Variational,Geom.,Level Set Methods Comput.Vis.,Lecture Notes in Computer Science,Springer,pp.73-84,2005
[75]W.Yin,D.Goldfarb,S.Osher,The Total Variation Regularized L1 Model for Multiscale Decomposition,SIAM J.Multiscale Model.Simul.,vol.6,no.1,pp.190-211,2006
[76]M.Y.Zou,Deconvolution and signal recovery,Beijing:National Defence Industry Press,2001
[77]A.N.Tikhonov,Regularization of incorrectly posed problems,Soviet Math.,Doklady,vol.4,pp.1624-1627,1963
[78]T.F.Chan,S.Osher,J.Shen,The digital TV filter and nonlinear denoising,IEEE Trans.Image Process.,vol.10,no.10,pp.231-241,2001
[79]T.F.Chan,J.Shen,Variational image inpainting,Commun.Pure Appl.Math.,vol.58,no.5,pp.579-619,2005
[80]T.F.Chan,J.Shen,H.M.Zhou,Total variation wavelet inpainting,J.Math.Imaging Vis.,vol.25,no.1,pp.107-125,2006
[81]GSapiro,Geometric partial differential equations and image analysis,Cambridge University Press,New York,NY,USA,2001
[82]S.Osher,L.Rudin,Feature-oriented image enhancement using shock filters,SIAM J.Num.Anal.vol.27,no.4,pp.919-940,1990
[83]G.Gilboa,Y.YZeevi,N.Sochen,Anisotropic selective inverse diffusion for signal enhancement in the presence of noise,Proc.IEEE Int.Conf.Acoust.,Speech,Signal Process.(ICASSP),Istanbul,Turkey,vol 1,pp.221-224,2000
[84]N.Sochen,G.Gilboa,Y,Y,Zeevi,Color image enhancement by a forward-and-backward adaptive Beltrami flow,AFPAC-2000,LNCS188,New York:Springer-Verlag,pp.319-328,2000
[85]GAubert,L.Vese,A variational method in image recovery,SIAM J.Number.Anal.,vol.34,pp.1948-1979,1997
[86]A.N.Tikhonov,V.Y.Arsenin,Solutions of ill-posed problems,Winston and Sons,Washington,D.C.,1997
[87]T.F.Chan,P.Mulet,On the convergence of the lagged diffusivity fixed point method in total variation image restoration,SIAM J.Numer.Anal.,vol.36,pp.354-367,1999
[88]T.F.Chan,S.Osher,J.Shen,The digital TV filter and nonlinear denoising,IEEE Trans.Image Process.,vol.10,no.2,pp.231-241,2000
[89]T.F.Chan,J.Shen,Variational restoration of non-flat image features:models and algorithms,SIAM J.Appl.Math.,vol.61,no.4,pp.1338-1361,2000
[90]P.Mrazek,Selection of optimal stopping time for nonlinear diffusion filtering,Proc.IEEE Wkshp.Scale-Space Morphology Comput.Vis.,Vancouver,Canada,pp.290-298,2001
[91]P.Mrazek,J.Weickert,GSteidl and M.Welk,On iterations and scales of nonlinear filters,Proc.Comput.Vis.Winter Wkshp.,Valtice,Czech Republic,pp.61-66,2003
[92]Y.You,M.Kaveh,W.Xu,and A.Tannenbaum,Analysis and design of anisotropic diffusion for image processing,Proc.Int.Conf.Image Process.,vol.2,pp.497-501,1994
[93]T.Brox,M.Welk,GSteidl,J.Weickert,Equivalence results for TV diffusion and TV regularization,Scale Space Methods Comput.Vis.,Lecture Notes in Computer Science,2695,Springer,Berlin,vol.99,pp.86-100,2003
[94]L.A.Vese,S.J.Osher,Modeling textures with total variation minimization and oscillating patterns in image processing,J.Sci.Comput,vol.19,no.1,pp.553-572
[95]S.Osher,A.Sole,L.Vese,Image decomposition and restoration using total variation minimization and the h-1 norm,J.Multiscale Model.Simul.,vol.1,no.3,pp.349-370,2003
[96]L.A.Vese,S.J.Osher,Image denoising and decomposition with total variation minimization and oscillatory functions,Math.Imaging Vis.,vol.20,pp.7-18,2004
[97]T.F.Chan,H M.Zhou,Optimal constructions of wavelet coefficients using total variation regularization in image compression,CAM Report,No.00-27,Dept.of Math,UCLA,July 2000
[98]G.Steidl,J.Weickert,T.Brox,On the equivalence of soft wavelet shrinkage,total variation diffusion,total variation regularization,and SIDEs,SIAM.J.Numer.Anal.,vol.42,no.2,pp.686-713,2004
[99]Y.D.Wu,S.X.Sun,A new hybrid image de-noising algorithm based on 2D wavelet shrinkage and nonlinear diffusion,Acta Electronica Sinica,vol.34,no.1,pp 163-166,2006
[100]D.H.Jiang,X.C.Feng,G.X.Song,An anisotropic diffusion equation based on nonlinear wavelet shrinkage,Acta Electronica Sinica,vol.34,no.1,pp.170-172,2006
[101]刘来福,高鑫,基于水平集曲率的图像滤噪与增强,北京师范大学学报(自然科学版),vol.37,no.1,pp.5-9,2001
[102]耿芮芮,蔡安妮,孙景鳌,一种非线性扩散线形纹理图像增强的方法,计算机辅助设计与图形学学报,vol.14,no.2,pp 140-143,2002
[103]付树军,阮秋琦,王文洽,基于特征驱动的双向耦合扩散方程的图像去噪和边缘锐化,光学精密工程,vol.14,no.2,pp.315-319,2006
[104]S.Robert,Cognitive Psychology Fourth Edition,Thomas Wadsworth,2006
[105]T.F.Chan,S.H.Kang,Error analysis on image inpainting problems,J.Math.Imaging Vis.,vol.26,pp.85-103,2006
[106]Chanmbolle,P.L.Lions,Image recovery via total variational minimization and related problems,Numer.Math.,vol.76,pp.167-188,1997
[107]P.Charbonnier,L.B.Feraud,G Aubert,M.Barlaud,Deterministic edge-preserving regularization in computed imaging,IEEE Trans.Image Process.,vol.6,no.2,pp.298-310,1997
[108]C.Price,P.Wambacq,A.Ooosterlinck,Applications of reaction-diffusion equations to image processing,Proc.Int.Cont.Image Process.Appl.,Warwick,UK,pp.49-53,1989
[109]M.Turk,A.Pentland,Eigenfaces for recognition,J.Cogn.Neurosci.,vol.3,pp.72-86,1991
[110]D.M.Strong,PBlomgren,T.F.Chan,Spatially adaptive local feature-driven total variation minimizing image restoration,Proc.SPIE,vol.3167,1997
[111]D.M.Strong,T.F.Chan,Spatially and scale adaptive total variation based regularization and anisotropic diffusion in image processing,UCLA CAM Report 96-46,Nov 1996
[112]G.Aubert,P.Kornprobst,Mathematical problems in image processing:partial differential equations and the calculus of variations(second edition),New York:Springer-Verlag,2006
[113]M.Frazier,B.Jawerth,GWeiss,Littlewood-paley theory and the study of function spaces,CBMS Regional Conf.Series,vol.79,Providence,Amer.Math.Soc.,1991
[114]Daubechies,Orthonormal Bases of Compactly Supported Wavelets,Comm.Pure Appl.Math.,vol.41,pp.906-966,1988
[115]Daubechies,Orthonormal bases of compactly support wavelets:II variations on a theme,SIAM J.Math.Anal.,vol.24,pp.499-519,1993
[116]S.Mallat,S.Zhong,Characterization of signals from multiscale edges,IEEE Trans.Pattern Anal.Mach.Intell.,vol.14,no.7,pp.710-732,1992
[117]S.Mallat,W.L.Hwang,Singularity detection and processing with wavelets,IEEE Trans.Info.Theory,vol.38,pp.617-643,1992
[118]T.D.Bui,GChen,Translation invariant de-noising using multi-wavelets,1EEE Trans.Signal Process.,vol.46,no.12,pp.3414-3420,1998
[119]C.Taswell,Specifications and standards for reproducibility of wavelet transforms,Proc.Int.Conf.Signal Process.Appl.Techn.,Miller Freeman,pp.1923-1927,1996
[120]戴维,于盛林,孙枪,基于Contourlet变换自适应阈值的图像去噪算法,电子学报,vol.35,no.10,pp 1939-1943,2007
[121]陈莹,纪志成,韩崇昭,基于小波域加权阈值的图像去噪方法,计算机工程,vol.33,no.19,pp.183-185,2007
[122]D.L.Donoho,I,M.Johnstone,Adapting to unknown smoothness via wavelet shrinkage,J.Am.Stat.Assoc.,vol.90,no.432,pp.1200-1224,1995
[123]D.L.Donoho,I.M.Johnstone,GKerkyacharian,D.Picard,Wavelet shrinkage:Asymptopia?With discussion,J.R.Statis.Soc.,Series B,vol.57,no.2,pp.301-369,1995
[124]K.Chandrawansa,F.H.Ruymgaart,A.C.M.Wan Rooij,Controlling the Gibbs phenomenon in noisy deconvolution of irregular multivariable input signals,J.Appl.Math.Stochastic Anal.vol.13,no.1,pp.1-14,2000
[125]J.W.Gibbs,Letter to the editor,Nature 59,p.200
[126]J.WGibbs,Letter to the editor,Nature 59,p.606
[127]X.P.Shen,Gibbs phenomenon in orthogonal wavelet expansion,J.Math.Study,vol.35,no.4,1919.343-357,2002
[128]高清维,李海鹰,庄镇泉,王涛,基于平稳小波变换的心电信号噪声消除方法,电子学报,vol.31,no.2,pp.1-3,2003
[129]J.W.Woods,Two-dimensional discrete Markovian Fields,IEEE Trans.Inf.Theory,vol.18,pp.232-240,1972
[130]E.Ising,Zeitschrift Physik,vol.31,P.253
[131]H.S.Hou,H.CAndrews,Cubic splines for image interpolation and digital filtering,IEEE Trans.Acoust.,Speech & Signal Process.,vo126,no.6,pp.508-517,1978
[132]S.K.Park,RASchowengerdt,Image reconstruction by parametric cubic convolution,Comput.Vis.Graph.Image Process.,vol.23,pp258-272,1983
[133]R.Keys,Cubic convolution interpolation for digital image processing,IEEE Trans.Acoustics,Speech & Signal Proc.,voI.ASSP-29,no.6,pp.1153-1160,1981
[134]S.EReichenbach,F.Geng,Two-dimensional cubic convolution,IEEE Trans.Image Process., vol.12,no.8,pp.857-865,2003
[135]C.Boor,A practical guide to splines,Springer-Verlag,New York,1978
[136]P Haeberli,D.Voorhies,Image Processing by Linear Interpolation and Extrapolation,IRIS Universe Magazine,no.28,Silicon Graphics,1994
[137]李天倩,吴援明,杨建军等,两种新图像放大算法研究,信号处理,Vol.19,no.3,pp 234-236,2003
[138]K.Revathy,G.Raju,S.R.Prabhakran Nayar,Image zooming by wavelets,fractals,Fractals-complex geometry patterns and scaling in nature and society,vol.8,no.3,pp.247-253,2000
[139]K.Jensen,D.Anastassiou,Subpixel edge localization and the interpolation of still images,IEEE Trans.Image Process.,vol.4,pp.285-295,1995
[140]X.Li,M.T.Orchard,New edge directed interpolation,Proc.IEEE Int.Conf.Image Process.,Vancouver,BC,Canada,vol.2,pp.311-314,2000
[141]X.Li,M.T.Orchard,New edge-directed interpolation,IEEE Trans.Image Process.,vol.10,no.10,pp.1521-1527,2001
[142]B.Antoni,C.Bartomeu,J.M.Morel,On image denoising methods,CMLA Preprint,CMLA,2004
[143]B.Antoni,C.Bartomeu,J.MMorel,Denoising image sequences does not require motion estimation,Proc.IEEE Conf.Advanced Video and Signal Based Surveillance(AVSS'05),Teatro Sociale,Como,Italy,pp.70-74,2005
[144]T.Wittman,Mathematical techniques for image interpolation,Oral Exam Paper,July 2005
[145]S.J.Fu,Q.Q.Ruan,W.Q.Wang,J.N.Chen,Feature preserving nonlinear image interpolation,Proc.Int.Conf.Signal Process.,Guilin,China,2006
[146]S.Walden,The ravished image,St.Martin's Press,New York,1985
[147]M.Bertalmio,A.L.Bertozzi,GSapiro,Navier-Stokes,fluid dynamics,and image and video inpainting,Proc.IEEE int.conf.Comput.Vis.Pattern Recogn.,Hawaii,USA,vol.1,pp.355-362,2001
[148]C.A.Z.Barcelos,M.A.Batista,Image inpainting and denoising by nonlinear partial differential equations,Proc.Brazilian Symp.Comput.Graph.Image Process.(SIBGRAPI),Brazil,pp.287-293,2003
[149]M.M.Oliveira,B.Bowen,R.McKenna,YS.Chang,Fast digital image inpainting,Proc.Int.Conf.Vis.image Image Process.,Marbella,Spain,pp.261-266,2001
[150]S.Esedoglu,J.Shen,Digital image inpainting by the Mumford-Shah-Euler image model,European J.Appl.Math.,vol.13,pp.353-370,2002
[151]S.Osher,J.A.Sethian,Front propagating with curvature dependent speed:algorithms based on Hamilton-Jacobi formulations,J Comput.Phys.,vol.79,pp.12-49,1988
[152]Z.N.Dong,Inviscid fluid mechanics,Beijing:Tsinghua University Press,2003
[153]Rares,M.J.T.Reinders,J.Biemond,Image sequence restoration in the presence of pathological motion and severe artifacts,Proc.Int.Conf.Acoust.Speech Signal Process.,Orlando,vol.4,pp.3365-3368,2002
[154]Rares,M.J.T.Reinders,J.Biemond,R.L.Lagendijk,A spatiotemporal image sequence restoration algorithm,Proc Int.Conf.Image Process,Rochester,New York,USA,vol.2,pp.857-860,2002
[155]J.J.Gibson,The perception of the visual world,Houghton Mifflin,Boston,Massachusetts,1950
[156]B.Julesz,Visual pattern discrimination,IEEE Trans.Inf.Theory,vol.8,no.2,pp.84-92,1962
[157]M.Tran,A.Datta,Synthesising textures using variable neighborhood searching,Proc.Int.Conf.Digital Image Comput.Techn.Appl.,Sydney,pp.643-652,2003
[158]T.Y.Ng,C.Wen,T.S.Tan,X.Zhang,Y J.Kim,Generating an w-tile set for texture synthesis,Proc.Comput.Graph.Int.,Stony Brook,NY,USA,pp.177-184,2005
[159]D.J.Heeger,J.R.Bergen,Pyramid-based texture analysis/synthesis,Proc.ACM SIGGRAPH,Los Angeles,California,pp.229-238,1995
[160]J.Potilla,E.PSimoncelli,A parametric texture model based on joint statistics of complex wavelet coefficients,Int.J.Comput.Vis.,vol.40,no.1,pp.49-71,2000
[161]Efros,T.Leung,Texture synthesis by nonparametric sampling,Proc.Int.Conf.Comput.Vis.,Greece,pp.1033-1038,1999
[162]L.Y.Wei,M.Levoy,Fast texture synthesis using tree-structured vector quantization,Proc.SIGGRAPH2000,San Antonio,pp.479-488,2000
[163]P.Harrison,A non-hierarchical procedure for re-synthesis of complex textures,Proc.Int.Conf.Central Europe Comput.Graph.Vis.(WSCG 2001),Plzen,Czech Republic,pp.190-197,2001
[164]M.Ashikhmin,Synthesizing Natural Textures,Proc.ACM Symp.Interactive 3D Graphics,Research Triangle Park,NorthCarolina,pp.217-226,2001
[165]Efros,W.F.Freeman,Image quilting for texture synthesis and transfer,Proc.ACM Conf.Comput.Graph.(SIGGRAPH),Los Angeles,pp.341-346,2001
[166]R.Bornard,E.Lecam,L.Laborelli,Missing data correction in still images and image sequences,Proc.ACM.Multimedia,Juan-les-Pins,France,pp.355-361,2002
[167]P.Perez,M.Gangnet,A.Blake,Patch Works:example-based region tiling for image editing,Microsoft Research Report MSR-TR-2004-04,2004
[168]D.Drori,O.Cohen,H.Yeshurun,Fragment-based image completion,ACM Trans.Graph.,vol.22,no.3,pp.303-312,2003
[169]J.Sun,L.Yuan,J.Jia,H.Y.Shum,Image completion with structure propagation,ACM Trans.Graph.,vol.24,no.3,pp.861-868,2005
[170]Criminisi,P.Perez,and K.Toyama,Region filling and object removal by exemplar-based image inpainting,IEEE.Trans.Image Process.,vol.13,no.9,pp.1200-1212,2004
[171]Dewdney,A potpourri of programmed prose and prosody,Scientific America,122-TK,June 1989
[172]K.Popat,R.W.Picard,Novel cluster-based probability model for texture synthesis,classification,and compression,Proc.SPIE Vis.Comm.Image Process.,USA,pp.756-768,1993
[173]J.S.D.Bonet,Multiresolution sampling procedure of analysis and synthesis of texture images.Proc.SIGGRAPH'97,Los Angeles,CA,USA,pp.361-368,1997
[174]J.Portilla,E.PSimoncelli,Texture representation and synthesis using correlation of complex wavelet coefficient magnitudes,TR 54,CSIC,Madrid,April 1999
[175]E.PSimoncelli,J.Portilla,Texture characterization via joint statistics of wavelet coefficient magnitudes,Proc.Int.Conf.Image Process.,Chicago,vol.1,pp.62-66,1998
[176]S.C.Zhu,YWu,D.Mumford,Filters,random fields and maximum entropy(frame),Int.J.Comput.Vis.,vol.27,no.2,pp.1-20,1998
[177]J.Davis,Mosaics of scenes with moving objects,Proc.IEEE Conf.on Comput.Visi.Pattern Recogn.,Santa Barbara,CA,USA,pp.354-360,1998
[178]Criminisi,PPerez,K.Toyama,Object removal by exemplar-based inpainting,Proc.Int.Conf.Comput.Vis.Pattern Recogn.,Madison,WI,vol.2,pp.721-728,2003
[179]阮秋琦,阮宇智等译,电子工业出版社,北京,2007
[180]阮秋琦,数字图像处理学(第二版),电子工业出版社,北京,2008
[181]R.C.Gonzalez,R.EWoods,Digital image processing,Addison-Wesley,Reading,Mass,1992
[182]T.F.Chan,A.Marquina,P.Mulet,Second order differential functionals in total variation-based image restoration,CAM 97-56,1998
[183]M.Kirby,L.Sirovich,Application of the Karhunen-Loeve procedure for the characterization of human faces,IEEE Trans.Pattern Anal.Mach Intell.,vol.12,no.1,pp.103-108,1990
[184]L.Sirovich,M.Kirby,Low-dimensional procedure for the characterization of human faces,J.Opt.Soc.Amer.,vol.4 no.3,pp.519-524,1987
[185]R.A.Fisher,The statistical utilization of multiple measurements,Ann.Eugen.,vol.8,pp.376-386,1938
[186]B.Moghaddam,A.Pentland,Probabilistic visual learning for object representation,IEEE Trans.Pattern Anal.Mach Intell.,vol.19,pp.696-710,1997
[187]P J.Phillips,Support vector machines applied to face recognition,Adv.Neural Inform.Process.Syst.,vol.11,pp.803-809,1998
[188]MS.Bartlett,J.RMovellan,T.J.Sejnowski,Face recognition by independent component analysis,IEEE Trans.Neural Netw,vol.13,no.6,pp.1450-1464,2002
[189]B.Sch(o|¨)kopf,A.Smola,K.R.Müller,Nonlinear component analysis as a kernel eigenvalue problem,Neural Comput.,vol.10,pp.1299-1319,1998
[190]C.J.Liu,Gabor-based kernel PCA with fractional power polynomial models for face recognition,IEEE Trans.Pattern Anal.Mach.Intell.,vol.26,pp.572-581,2004
[191]J.Yang,X.Gao,D.Zhang,J.Yang,Kernel ICA:An alternative formulation and its application to face recognition,Pattern Recogn.,vol.38,pp.1784-1787,2005
[192]S.Mika,GRatsch,J.Weston,B.Scholkopf,K.Muller,Fisher discriminant analysis with kernels,Proc.IEEE Wkshp.Neural Netw.Signal Process.,Madison,Wisconsin,USA,vol.9,pp.41-48,1999
[193]A.L.Yuille,D.S.Cohen,Feature extraction from faces using deformable templates,Int.J.Comput.r Vis.,vol.8,no.2,pp.99-111,1992
[194]Lanitis,C.J.Taylor,T.FCootes,Automatic interpretation and coding of face images using flexible models,IEEE Trans.Pattern Anal.Mach.Intell.,vol.19,no.7,pp.743-756,1997
[195]T.F.Cootes,GJ.Edwards,C.J.Taylor,Advances in active appearance models,Proc.Int.Conf.Comput.Vis.,Kerkyra,Corfu,Greece,pp.137-142,1999
[196]L.D.Hamon,The recognition of faces,Sci.Am.,vol.229,pp.71-82,1973
[197]J.Sergent,Microgenesis of face perception,In Aspects of Face Processing.,H.D.Ellis,M.A.,Jeeves,F.Newcombe,and A.Young,Eds.A Young(Dordrecht:Martinus Nijhoff),1986
[198]W.Zhao,R.Chellappa,P.J.Phillips,A.Rosenfeld,Face recognition:a literature survey,ACM Comput.Surv.,vol.35,no.4,pp.399-458,2003
[199]王蕴红,范伟,谭铁牛,融合全局与局部特征的子空间人脸识别算法计算机学报,vol 28,no.10,pp 1657一1663,2005
[200]H.Bernd,S.Thomas,P.Massimiliano,V.Thomas,P.Tomaso,Categorization by learning and combining object parts,Proc.Advances in Neural Information Processing systems NIPS),Vancouver,Canada,pp.1239-1245,2002
[201]Y.C.Fang,T.NTan,Y.H.Wang,Fusion of global and local features for face verification,Proc.IEEE Int.Conf.Pattern Recogn.,Quebec,Canada,vol.2,pp.382-385,2002
[202]J.Huang,P.C.Yuen,J.H.Lai,C.H.Li,Face recognition using local and global features, EURASIP J.Appl.Signal Process.,vol.4,pp.530-541,2004
[203]Martinez,A.Kak,PCA versus LDA,IEEE Trans.Pattern Anal.Mach Intell.,vol.23,no.2,pp.228-233,2001
[204]Pentland,B.Moghaddam,T.Starner,View-based and modular eigenspaces for face recognition,Proc.IEEE Int.Conf.Comput.Vis.Pattern Recogn.,ilton Head,SC,USA,pp.84-91,1994
[205]Y.Adini,Y.Moses,S.Ullman,Face recognition:the problem of compensating for changes in illumination direction,IEEE Trans.Pattern Anal.Mach.Intell.,vol.19,no.7,pp.721-732,July 1997
[206]T.Sim,T.Kanade,Combining models and exemplars for face recognition:an illuminating example,Proc.Wkshp.Model.Versus Exemplars Comput.Vis.,Hawaii,USA,pp.1-10,2001
[207]P.W.Hallinan,A low-dimensional representation of human faces for arbitrary lighting conditions,Proc.Int.Cone Comp.Vis.Pattern Recogn.,Seattle,WA,USA,pp.995-999,1994
[208]R.Basri,D.Jacobs,Lambertian reflectance and linear subspaces,Proc.Int.Conf.Compu.Vis.(ICCV),Vancouver,Canada,pp.383-390,2001
[209]R.Ramamoorthi,PHanrahan,On the relationship between radiance and irradianc:Determining the illumination from images of a convex Lambertian object,J.Opt.Soc.Am.,A,vol.18,no.10,pp.2448-2459,2001
[210]Y.K.Hu,Z.F.Wang,Face recognition under different illuminations,J.Image Graph.,vol.10,no.7,pp.844-849,2005
[211]卿来云,山势光,陈熙霖,高文,基于球面谐波基图像的任意光照下的人脸识别,计算机学报,vol.29,no.5,pp.760-768,2006
[212]P.N.Belhumeur,D.J.Kriegman,What is the set of images of an object under all possible lighting conditions? Proc.IEEE Int.Conf.Comput.Vis.Pattern Recogn.,San Francisco,pp.270-277,1996
[213]A.S.Georghiades,P.N.Belhumeur,D.J.Kriegman,From few to many:Illumination cone models for face recognition under differing pose and lighting,IEEE Trans.Pattern Anal.Mach.Intell.,vol.23,pp.643-660,2001
[214]S.G.Shan,WGao,B.Cao,D.Zhao,Illumination normalization for robust face recognition against varying lighting conditions,Proc.IEEE Int.Wkshp.Anal.Model.Faces Gestures Recogn.,Nice,France,pp.157-164,2003
[215]Shashua,T.Riklin-Raviv,The quotient image:class-based re-rendering and recognition with varying illuminations,IEEE Trans.Pattern Anal.Mach.Intell.,voi.23,no.2,pp.129-139,2001
[216]W.Zhao,R.Chellappa,Illumination-insensitive face recognition using symmetric shape-from-shading,Proc.Int.Cone Comput.Vis.Pattern Recogn.,South Carolina,vol.1,pp. 286-293,2000
[217]K.Okada,C.Malsburg,Pose-invariant face recognition with parametric linear subspaces,Proc.Int.Conf.Aut.Face Gesture Recogn.,Southampton,UK,pp.71-76,2002
[218]W.Gao,S.Shan,X.Chai,X.Fu,Virtual face image generation for illumination and pose insensitive face recognition,Proc.IEEE Int.Conf.Acoust.Speech,Signal Process,Hong Kong,vol.Ⅳ,pp.776-779,2003
[219]T.Chen,W.Yin,X.S.Zhou,D.Comaniciu,T.S.Huang,Total Variation Models for Variable Lighting Face Recognition,IEEE Trans.Pattern Anal Mach.Intell.,vol 28,pp.1519-1524,2006
[220]P.J.Phlips,Y.Vardi,Efficient illumination normalization of facial images,Pattern Recogn.Lett.,vol.17,pp.921-927,1996
[221]X.Xie,K.M.Lam,An efficient illumination normalization method for face recognition,Pattern Recogn.Lett.,vol.27,pp.609-617,2006
[222]Shashua,T Riklin-Raviv,The quotient image:class-based re-rendering and recognition with varying illuminations,IEEE Trans.Pattern Anal.Mach.Intell.,vol.23,no.2,pp.129-139,2001
[223]H.Wang,S.Z.Li,Y.Wang,Generalized quotient image,Proc.IEEE Int.Conf.Comput.Vis.Pattern Recogn.,Washington,DC,USA.vol.2,pp.498-505,2004
[224]D.J.Jobson,Z.Rahman,Properties and performance of a center/surround retinex,IEEE Trans.Image Process.,vol.6,no.3,pp.451-462,1997
[225]T.Chen,WYin,X.S.Zhou,D.Comaniciu,T.S.Huang,Illumination Normalization for Face Recognition and Uneven Background Correction Using Total Variation Based Image Models,Proc.IEEE Int.Conf.Comput.Vis.Pattern Recogn.,San Diego,CA,USA,vol.2,pp.532-539,2005
[226]Witkin,Scale-space filtering,Proc.Int.Joint Conf.Artif.Intell.,Karlsruhe,Germany,pp.1019-1022,1983
[227]J.F.Aujol,G Gilboa,T.Chan,S.Osher,Structure-texture image decomposition-modeling,algorithms,and parameter selection,Int.J.of Comput.Vis.,vol.67,no.1,pp.111-136,2006
[228]Y.Meyer,Oscillating patterns in image processing and nonlinear evolution equations,The Fifteenth Dean Jacquelines B.Lewis Memorial Lectures,2001
[229]W.Yin,D.Goldfarb,S.Osher,Total variation based image cartoon-texture decomposition,Columbia University CORC Report TR-2005-01,UCLA CAM Report 05-27,2005
[230]T.Chan,S.Esedoglu,Aspects of total variation regularized L1 function approximation,SIAM J.Appl.Math.,vol.65,pp.1817-1837,2004
[231]M.M.Meendonca,J.GDenipote,A.S.Ricardo,F.M.Stela,V.Paiva,Illumination normalization methods for face recognition,sibgrapi.sid.inpe.br/col/sid.inpe.br/sibgrapi@80/2007/09.19.15.08/doc/ArtigoSIBGRAPI_2007_Ingles.Final.pdf
[232]X.Xie,K.M.Lam,Face recognition under varying illumination based on a 2D face shape model,Pattern Recogn.,vol.38,no.2,pp.221-230,2005
[233]A.A.Ross,K.Nandakumar,A K.Jain,Handbook of multibiometncs,Springer,2006
[234]K.Delac,M.Grgic,S.Grgic,Independent Comparative Study of PCA,ICA,and LDA on the FERET Data Set,Technical Report,University of Zagreb,2004
[235]K.C.Lee,J.Ho,D.Knegman,Acquiring linear subspaces for face recognition under variable lighting,IEEE Trans.Pattern Anal.Mach.Intell.,vol.27,no.5,pp.684-698,2005
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