基于各向异性扩散的数字图像处理研究
|
摘要
随着社会的数字化与信息化,数字图像处理正在成为一门越来越重要的学科。基于偏微分方程的数字图像处理因其具有强大的理论支撑,获得了学术界普遍的关注。各向异性扩散作为现行的一种非常流行的偏微分方程数字图像处理技术,是由传统的Gaussian滤波发展而来的,其特点是可以在平滑的同时保持边缘特征,由于这种优良的特性,使其得到了深入的研究和广泛的应用。
本文主要研究各向异性扩散的基本理论及各向异性扩散方法和思想在图像平滑、去噪、增强和图像分割方面的应用。本文的主要工作和贡献如下:
首先,本文对各向异性扩散的理论进行了介绍与分析,介绍了几个重要的对于P-M各向异性扩散模型的改进。分析了各向异性扩散模型中的扩散系数,并给出了一个新的扩散系数的选取准则,在实验中取得了良好的效果。
在对各向异性扩散模型的讨论研究之后,本文研究了各向异性扩散在图像平滑、去噪和增强方面的应用。分析了可以用于图像增强的各向异性扩散的改进形式:前向—后向扩散;研究了用于相干斑噪声去除的各向异性扩散方法;提出了一种将各向异性扩散与平稳小波变换结合的图像去噪方法;提出了一种基于视觉特性的各向异性扩散方法,在平滑的同时加入图像细节的因子,提高了扩散的视觉效果。
最后,本文探讨了如何将各向异性扩散的方法和思想应用到图像分割中。我们介绍了经典的分水岭分割算法,并使用前向—后向扩散对图像进行处理从而减少过分割;介绍了活动轮廓模型和它的改进GVF Snake,并分析了如何用各向异性扩散的思想对GVF Snake模型进行改进,从而得到新的GGVF Snake模型。
With the informationization and digitalization over the society, digital image processing is becoming a more and more important subject. Partial differential equations based digital image processing received widely attention by academia because of its’strongly mathematical theoretical support. Anisotropic diffusion is a prevalent partial differential equations based digital image processing method. It developed from traditional Gaussian filter. The trait of anisotropic diffusion is to keeping characteristic of edge information of the image. Because of its good effects, anisotropic diffusion has been in-depth study and widely application.
In this dissertation, we mainly study theory of anisotropic diffusion and the application of the technology and idea of anisotropic diffusion in image smooth, denoise, enhancement and segmentation. The main work includes:
At first, we discuss the theory of anisotropic diffusion. The theory of Perona-Malik anisotropic diffusion are introduced and analyzed. Several important improved anisotropic diffusion methods to Perona-Malik anisotropic diffusion are led in. We make an assay of diffusion coefficient of anisotropic diffusion, and give a new principle to choose diffusion coefficient. The new choosing principle achieves better results in the experiment.
After the foregoing discussion, we research the application of anisotropic diffusion in image smooth, denoise and enhancement. The Forward-and-Backward diffusion is introduced. It can smooth the image and enhance the edge feature. The Speckle Reduced Anisotropic Diffusion is recommended for remove speckle noise. A new denoising method to use anisotropic diffusion in stationary wavelet domain is raised. We introduce vision mask to anisotropic diffusion, and improve it. A new improved vision mask based anisotropic diffusion is raised and it can effectively remove noise in accordance with human vision.
At last, this dissertation investigates how to use method and idea of anisotropic diffusion to image segmentation. The classic watershed for image segmentation is introduced and use Forward-and-Backward diffusion to reduce over-segmentation of watershed. The active contour model (Snake) and GVF snake model are introduced and we introduce how to improve GVF snake model using idea of anisotropic diffusion, thus a new method GGVF snake model is raised, it can be achieve better segmentation result.
本文主要研究各向异性扩散的基本理论及各向异性扩散方法和思想在图像平滑、去噪、增强和图像分割方面的应用。本文的主要工作和贡献如下:
首先,本文对各向异性扩散的理论进行了介绍与分析,介绍了几个重要的对于P-M各向异性扩散模型的改进。分析了各向异性扩散模型中的扩散系数,并给出了一个新的扩散系数的选取准则,在实验中取得了良好的效果。
在对各向异性扩散模型的讨论研究之后,本文研究了各向异性扩散在图像平滑、去噪和增强方面的应用。分析了可以用于图像增强的各向异性扩散的改进形式:前向—后向扩散;研究了用于相干斑噪声去除的各向异性扩散方法;提出了一种将各向异性扩散与平稳小波变换结合的图像去噪方法;提出了一种基于视觉特性的各向异性扩散方法,在平滑的同时加入图像细节的因子,提高了扩散的视觉效果。
最后,本文探讨了如何将各向异性扩散的方法和思想应用到图像分割中。我们介绍了经典的分水岭分割算法,并使用前向—后向扩散对图像进行处理从而减少过分割;介绍了活动轮廓模型和它的改进GVF Snake,并分析了如何用各向异性扩散的思想对GVF Snake模型进行改进,从而得到新的GGVF Snake模型。
With the informationization and digitalization over the society, digital image processing is becoming a more and more important subject. Partial differential equations based digital image processing received widely attention by academia because of its’strongly mathematical theoretical support. Anisotropic diffusion is a prevalent partial differential equations based digital image processing method. It developed from traditional Gaussian filter. The trait of anisotropic diffusion is to keeping characteristic of edge information of the image. Because of its good effects, anisotropic diffusion has been in-depth study and widely application.
In this dissertation, we mainly study theory of anisotropic diffusion and the application of the technology and idea of anisotropic diffusion in image smooth, denoise, enhancement and segmentation. The main work includes:
At first, we discuss the theory of anisotropic diffusion. The theory of Perona-Malik anisotropic diffusion are introduced and analyzed. Several important improved anisotropic diffusion methods to Perona-Malik anisotropic diffusion are led in. We make an assay of diffusion coefficient of anisotropic diffusion, and give a new principle to choose diffusion coefficient. The new choosing principle achieves better results in the experiment.
After the foregoing discussion, we research the application of anisotropic diffusion in image smooth, denoise and enhancement. The Forward-and-Backward diffusion is introduced. It can smooth the image and enhance the edge feature. The Speckle Reduced Anisotropic Diffusion is recommended for remove speckle noise. A new denoising method to use anisotropic diffusion in stationary wavelet domain is raised. We introduce vision mask to anisotropic diffusion, and improve it. A new improved vision mask based anisotropic diffusion is raised and it can effectively remove noise in accordance with human vision.
At last, this dissertation investigates how to use method and idea of anisotropic diffusion to image segmentation. The classic watershed for image segmentation is introduced and use Forward-and-Backward diffusion to reduce over-segmentation of watershed. The active contour model (Snake) and GVF snake model are introduced and we introduce how to improve GVF snake model using idea of anisotropic diffusion, thus a new method GGVF snake model is raised, it can be achieve better segmentation result.
引文
[Alvarez 1992] L. Alvarez, P. L. Lions, J.M. Morel, Image selective smoothing and edge detection by nonlinear diffusion. II[J]. SIAM Journal on Numerical Analysis, 1992, 29(3): 845-866.
[Anderson 1976] G. L. Anderson, A. N. Netravali. Image restoration based on a subjective criterion [J]. IEEE Transactions on System, Man, and Cybernetics, 1976, SMC26: 845-853.
[Black 1998] M. J. Black, G Sapiro, D. H. Marimont. Robust anisotropic diffusion[J],IEEE Transactions on Image Processing,1998,7(3): 421-432.
[Carmona 1998] R. A. Carmona, S. Zhong. Adaptive Smoothing Respecting Feature Directions[J]. IEEE Transactions on Image Processing,1998,7(3): 353-358.
[Catté1992] F. Catté, P. L. Lions, J. M. Morel, T. Coll. Image selective smoothing and edge detection by nonlinear diffusion[J]. SIAM Journal on Numerical Analysis. 1992,29(1): 182-193
[Cayley 1859] A. Cayley. On contour and slope lines[J]. The London, Edinburgh, and Dublin Philosophical Magazine and J. of Science 18, Oct. 1859 (120), 264–268
[Chen 2000] Y. Chen, B. C. Vemuri, L. Wang. Image denoising and segmentation via nonlinear diffusion[J]. Computers and Mathematics with applications, 2000,39(5-6): 131-149
[Cohen 1984] M. A. Cohen, S. Grossberg. Neural dynamics of brightness perception - Features, boundaries, diffusion, and resonance[J], Perception and Psychophysics, 1984,36: 428-456.
[Daubechies 1992] Daubechies, Ten Lectures on Wavelets[M]. New York: SIAM, 1992.
[Digabel 1977] H. Digabel, C. Lantuejoul. Iterative algorithms, Actes du Second Symposium Europeen d'Analyse Quantitative des Microstructures en Sciences des Materiaux, Biologie et Medecine, Caen, 4-7 October 1977.
[Domg 2001] Y. Domg, A. K. Milne, B. C. Forster. Toward edge sharpening: a SAR speckle filtering algorithm [J]. IEEE Transactions on Geosciences and Remote Sensing, 2001, 39(4): 851-863.
[Frost 1982] V. S. Frost, J. A. Stiles, K. S. Shanmugan and J. C. Holtzman, A model for radar images and its application to adaptive digital filtering of multiplicative noise. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-4, pp. 157-165, 1982
[Gabor 1965] D. Gabor. Information theory in electron microscopy[J]. Laboratory Investigation, 1965, 14(6): 801-807.
[Gilboa 2002] G. Gilboa, N. Sochen, Y. Y. Zeevi. Forward-and-backward diffusion processes for adaptive image enhancement and denoising[J].IEEE Transaction on Image Processing, 2002, 11(7): 689-703.
[Gilboa 2004] G. Gilboa, N. A. Sochen, Y. Y. Zeevi. Image enhancement and denoising by complex diffusion processes [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, 26(8): 1020-1036
[Guichard 2003] F. Guichard, J. M. Morel. Image iterative smoothing and PDE's[M], Book in preparation, 2003.
[H?llig 1982] K. H?llig, J. Nohel, A diffusion equation with a nonmonotone constitutive function[M], Systems of Nonlinear Partial Differential Equations, Oxford, 1982
[Hummel 1987] R. A. Hummel, B. Kimia, S. W. Zucker. Deblurring Gaussian blur[J]. Computer vision, graphics, and image processing, 1987(38): 66-80.
[Jain 1981] J. R. Jain, A. K. Jain. Displacement measurement and its application in interframe image coding[J]. IEEE Transactions on Communications, 1981,29(12): 1799-1808.
[Kass 1988] M. Kass, A. Witkin, D. Terzopoulos. Snakes: Active contour models. International Journal of Computer Vision,1988,1(4):321~331.
[Katsaggelos 1991] A. K. Katsaggelos, J. Biemond, R. W. Schafer, R.M. Mersereau. A regularized iterative image restoration algorithm[J]. IEEE Transaction on Signal Processing, 1991, 39(4): 914 - 929.
[Koenderink 1984] J. J. Koenderink. The Structure of Image[J]. Biological Cybernetics, 1984, 50: 363-370.
[Kuan 1987] D. T. Kuan, A. A. Sawchuk, T. C. Strand and P. Chavel, Adaptive restoration of image with speckle. IEEE Transactions on Acoustics, Speech, Signal Processing, Vol. ASSP-35, pp. 373-383,1987
[Lee 1980] J. S. Lee,Digital image enhancement and noise filtering by using local statistics[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI 1-2,1980, 165-168
[Lin 1999] Z. Lin, Q. Shi. An anisotropic diffusion PDE for noise reduction and thin edge preservation[C]. IEEE Tenth International Conference on Image Analysis and Processing, Venice, Italy, 1999.
[Lindeberg 1994] T. Lindeberg. Scale-space theory in computer vision[M], KLUWER ACADEMIC PUBLISHERS GROUP, 1994.
[Malladi 2002] R. Malladi (Ed.), Geometric Methods in Bio-Medical Image Processing[M], Springer, Berlin, 2002.
[Mallat 1989a] S. G. Mallat. A theory for multiresolution signal decomposition: the waveletrepresentation [J]. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1989.7, 11(7): 674-693.
[Mallat 1989b] S. G. Mallat. Multiresolution approximations and wavelet orthonormal bases of L2 (R). Trans.Amer.Math.Soc.,1989.9,315:69-87
[Mallat 1989c] S. G. Mallat. Multi-frequency channel decomposition of images and wavelet[J]. IEEE Transaction on ASSP.1989.12(37):2091-2110
[Maxwell 1870] J. C. Maxwell. On hills and dales. The London, Edinburgh, and Dublin Philosophical Magazine and J. of Science 4th Series 40, Dec. 1870 (269), 421–425
[Nago 1979] M. Nagao, T. Matsuyama. Edge preserving smoothing[J]. Computer Graphics and Image Processing, 1979, September: 394-407.
[Nason 1995] G. P. Nason, B. W. Silverman, The Stationary Wavelet Transform and some Statistical Applications[M]. Germany: SPRINGER VERLAG KG, 1995
[Perona 1990] P. Perona, J. Malik. Scale-space and edge detection using anisotropic diffusion[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990, 12(7): 629-639.
[Perona 1998] P. Perona. Orientation Diffusions[J]. IEEE Transactions on Image Processing, 1998, 7(3): 357-365.
[Pollak 2000] I. Pollak, A. S. Willsky, H. Krim. Image segmentation and edge enhancement with stabilized inversediffusion equations[J]. IEEE Transactions on Image Processing, 2000, 9(2): 256-266.
[Rudin 1987] L. Rudin, Images, Numerical Analysis of Singularities, and Shock Filters[D]: [Ph.D. thesis]. Computer Science Department, California Institute of Technology, Pasadena, CA, 1987.
[Segall 1997] C. A. Segall, S. T. Acton, Morphological Anisotropic Diffusion[C]. IEEEProceedings: International Conference on Image Processing. 1997, 3(3): 348-351.
[Shih 2003] A. C. C. Shih, H. Y. M. Liao, C. S. Lu. A new iterated two-band diffusion equation: theory and its application[J]. IEEE Transactions on Image Processing, 2003, 12(4): 466-476.
[Sochen 1998] N. Sochen, R. Kimmel, R. Malladi. A General Framework for Low Level Vision[J]. IEEE Transactions on Image Processing, 1998, 7(3):310-318.
[Torkamani-Azar 1996] F. Torkamani-Azar, K. E. Tait. Image recovery using the anisotropic diffusion equation[J]. IEEE Transactions on Image Processing, 1996, 5(11): 1573-1578.
[Vincent 1991] L. Vincent, P. Soille. Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations[J]. IEEE Transactions on Pattern Analysis and Machine Inteligence, 1991; 13:583～598
[Voci 2004] F. Voci, S. Eiho, N. Sugimoto, H. Sekibuchi, Estimating the gradient in the Perona-Malik equation[J]. IEEE Signal Processing Magazine, May 2004, 21(3), 39-65.
[Wang 2004] Z. Wang, A. C. Bovik, H. R. Sheikh, E. P. Simoncelli, Image Quality Assessment: From Error Visibility to Structural Similarity[J]. IEEE Transactions on Image Processing, 2004, 13(4): 600-612.
[Weickert 1998] J. Weickert. Anisotropic Diffusion in Image Processing[M]. Teubner Verlag, Stuttgart, 1998.
[Witkin 1987] A. P. Witkin. Scale-space filtering[P]. US Patent 4,658,372, 1987.
[Xu 1998a] C. Xu, J. L. Prince. Snakes, shapes and gradient vector flow[J]. IEEE Transactions on Imaging Processing. 1998, 7(3): 359-369.
[Xu 1998b] C. Xu, J. L. Prince. Generalized gradient vector flow external forces for active contours [J]. International Journal of Signal Processing, 1998, 71(2): 131-139.
[Yezzi 1998] A. Yezzi Jr. Modified Curvature Motion for Image Smoothing and Enhancement[J]. IEEE Transactions on Image Processing, 1998, 7(3): 345-351.
[You 1996a] Y. L. You, W. Xu, A. Tannenbaum, M. Kaveh. Behavioral analysis of anisotropic diffusion in image processing[J]. IEEE Transactions on Image Processing, 1996, 5(11): 1539-1553.
[You 1996b] Y. L. You, M. Kaveh. Blind Image Restoration by Anisotropic Regularization[J]. IEEE Transactions on Image Processing,1999,8(3): 396-407.
[You 2000] Y. L. You, M Kaveh and Kaveh M. Fourth-Order Partial Differential Equations for Noise Removal[J], IEEE Transactions on Image Processing, 2000, 9(10):1723-1730.
[Yu 2002] Y. Yu, S. T. Acton. Speckle reducing anisotropic diffusion[J].IEEE Transactions on Image Processing,2002,11(11): 1260-1270.
[丛舸1997]丛舸。计算机视觉中的非线性尺度空间理论[博士学位论文]。中国科学院自动化研究所,北京,1997。
[崔景泰1995]崔景泰。小波分析导论[M]。西安:西安交通大学出版社,1995。
[崔屹2000]崔屹。图像处理与分析数学形态学方法及应用[M]。科学出版社,2000。
[李培华2000]李培华,张田文。主动轮廓线模型(蛇模型)综述[J]。软件学报,2000, 11 (6) : 751-757。
[林宙辰1999]林宙辰,石青云。一个能去噪和保持真实感的各向异性扩散方程[J]。计算机学报.。Vol.22,No.11,Nov.1999:1133-1137。
[杨福生2000]杨福生。小波变换的工程分析与应用[M]。科学出版社,2000。
[余庆军2004]余庆军,谢胜利。基于人类视觉系统的各向异性扩散图像平滑方法[J]。电子学报,2004,32(1):17- 20。
[张禀2004]张禀,陈刚。基于偏微分方程的图象处理[M]。北京:高等教育出版社。2004。
[Anderson 1976] G. L. Anderson, A. N. Netravali. Image restoration based on a subjective criterion [J]. IEEE Transactions on System, Man, and Cybernetics, 1976, SMC26: 845-853.
[Black 1998] M. J. Black, G Sapiro, D. H. Marimont. Robust anisotropic diffusion[J],IEEE Transactions on Image Processing,1998,7(3): 421-432.
[Carmona 1998] R. A. Carmona, S. Zhong. Adaptive Smoothing Respecting Feature Directions[J]. IEEE Transactions on Image Processing,1998,7(3): 353-358.
[Catté1992] F. Catté, P. L. Lions, J. M. Morel, T. Coll. Image selective smoothing and edge detection by nonlinear diffusion[J]. SIAM Journal on Numerical Analysis. 1992,29(1): 182-193
[Cayley 1859] A. Cayley. On contour and slope lines[J]. The London, Edinburgh, and Dublin Philosophical Magazine and J. of Science 18, Oct. 1859 (120), 264–268
[Chen 2000] Y. Chen, B. C. Vemuri, L. Wang. Image denoising and segmentation via nonlinear diffusion[J]. Computers and Mathematics with applications, 2000,39(5-6): 131-149
[Cohen 1984] M. A. Cohen, S. Grossberg. Neural dynamics of brightness perception - Features, boundaries, diffusion, and resonance[J], Perception and Psychophysics, 1984,36: 428-456.
[Daubechies 1992] Daubechies, Ten Lectures on Wavelets[M]. New York: SIAM, 1992.
[Digabel 1977] H. Digabel, C. Lantuejoul. Iterative algorithms, Actes du Second Symposium Europeen d'Analyse Quantitative des Microstructures en Sciences des Materiaux, Biologie et Medecine, Caen, 4-7 October 1977.
[Domg 2001] Y. Domg, A. K. Milne, B. C. Forster. Toward edge sharpening: a SAR speckle filtering algorithm [J]. IEEE Transactions on Geosciences and Remote Sensing, 2001, 39(4): 851-863.
[Frost 1982] V. S. Frost, J. A. Stiles, K. S. Shanmugan and J. C. Holtzman, A model for radar images and its application to adaptive digital filtering of multiplicative noise. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-4, pp. 157-165, 1982
[Gabor 1965] D. Gabor. Information theory in electron microscopy[J]. Laboratory Investigation, 1965, 14(6): 801-807.
[Gilboa 2002] G. Gilboa, N. Sochen, Y. Y. Zeevi. Forward-and-backward diffusion processes for adaptive image enhancement and denoising[J].IEEE Transaction on Image Processing, 2002, 11(7): 689-703.
[Gilboa 2004] G. Gilboa, N. A. Sochen, Y. Y. Zeevi. Image enhancement and denoising by complex diffusion processes [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, 26(8): 1020-1036
[Guichard 2003] F. Guichard, J. M. Morel. Image iterative smoothing and PDE's[M], Book in preparation, 2003.
[H?llig 1982] K. H?llig, J. Nohel, A diffusion equation with a nonmonotone constitutive function[M], Systems of Nonlinear Partial Differential Equations, Oxford, 1982
[Hummel 1987] R. A. Hummel, B. Kimia, S. W. Zucker. Deblurring Gaussian blur[J]. Computer vision, graphics, and image processing, 1987(38): 66-80.
[Jain 1981] J. R. Jain, A. K. Jain. Displacement measurement and its application in interframe image coding[J]. IEEE Transactions on Communications, 1981,29(12): 1799-1808.
[Kass 1988] M. Kass, A. Witkin, D. Terzopoulos. Snakes: Active contour models. International Journal of Computer Vision,1988,1(4):321~331.
[Katsaggelos 1991] A. K. Katsaggelos, J. Biemond, R. W. Schafer, R.M. Mersereau. A regularized iterative image restoration algorithm[J]. IEEE Transaction on Signal Processing, 1991, 39(4): 914 - 929.
[Koenderink 1984] J. J. Koenderink. The Structure of Image[J]. Biological Cybernetics, 1984, 50: 363-370.
[Kuan 1987] D. T. Kuan, A. A. Sawchuk, T. C. Strand and P. Chavel, Adaptive restoration of image with speckle. IEEE Transactions on Acoustics, Speech, Signal Processing, Vol. ASSP-35, pp. 373-383,1987
[Lee 1980] J. S. Lee,Digital image enhancement and noise filtering by using local statistics[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI 1-2,1980, 165-168
[Lin 1999] Z. Lin, Q. Shi. An anisotropic diffusion PDE for noise reduction and thin edge preservation[C]. IEEE Tenth International Conference on Image Analysis and Processing, Venice, Italy, 1999.
[Lindeberg 1994] T. Lindeberg. Scale-space theory in computer vision[M], KLUWER ACADEMIC PUBLISHERS GROUP, 1994.
[Malladi 2002] R. Malladi (Ed.), Geometric Methods in Bio-Medical Image Processing[M], Springer, Berlin, 2002.
[Mallat 1989a] S. G. Mallat. A theory for multiresolution signal decomposition: the waveletrepresentation [J]. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1989.7, 11(7): 674-693.
[Mallat 1989b] S. G. Mallat. Multiresolution approximations and wavelet orthonormal bases of L2 (R). Trans.Amer.Math.Soc.,1989.9,315:69-87
[Mallat 1989c] S. G. Mallat. Multi-frequency channel decomposition of images and wavelet[J]. IEEE Transaction on ASSP.1989.12(37):2091-2110
[Maxwell 1870] J. C. Maxwell. On hills and dales. The London, Edinburgh, and Dublin Philosophical Magazine and J. of Science 4th Series 40, Dec. 1870 (269), 421–425
[Nago 1979] M. Nagao, T. Matsuyama. Edge preserving smoothing[J]. Computer Graphics and Image Processing, 1979, September: 394-407.
[Nason 1995] G. P. Nason, B. W. Silverman, The Stationary Wavelet Transform and some Statistical Applications[M]. Germany: SPRINGER VERLAG KG, 1995
[Perona 1990] P. Perona, J. Malik. Scale-space and edge detection using anisotropic diffusion[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990, 12(7): 629-639.
[Perona 1998] P. Perona. Orientation Diffusions[J]. IEEE Transactions on Image Processing, 1998, 7(3): 357-365.
[Pollak 2000] I. Pollak, A. S. Willsky, H. Krim. Image segmentation and edge enhancement with stabilized inversediffusion equations[J]. IEEE Transactions on Image Processing, 2000, 9(2): 256-266.
[Rudin 1987] L. Rudin, Images, Numerical Analysis of Singularities, and Shock Filters[D]: [Ph.D. thesis]. Computer Science Department, California Institute of Technology, Pasadena, CA, 1987.
[Segall 1997] C. A. Segall, S. T. Acton, Morphological Anisotropic Diffusion[C]. IEEEProceedings: International Conference on Image Processing. 1997, 3(3): 348-351.
[Shih 2003] A. C. C. Shih, H. Y. M. Liao, C. S. Lu. A new iterated two-band diffusion equation: theory and its application[J]. IEEE Transactions on Image Processing, 2003, 12(4): 466-476.
[Sochen 1998] N. Sochen, R. Kimmel, R. Malladi. A General Framework for Low Level Vision[J]. IEEE Transactions on Image Processing, 1998, 7(3):310-318.
[Torkamani-Azar 1996] F. Torkamani-Azar, K. E. Tait. Image recovery using the anisotropic diffusion equation[J]. IEEE Transactions on Image Processing, 1996, 5(11): 1573-1578.
[Vincent 1991] L. Vincent, P. Soille. Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations[J]. IEEE Transactions on Pattern Analysis and Machine Inteligence, 1991; 13:583～598
[Voci 2004] F. Voci, S. Eiho, N. Sugimoto, H. Sekibuchi, Estimating the gradient in the Perona-Malik equation[J]. IEEE Signal Processing Magazine, May 2004, 21(3), 39-65.
[Wang 2004] Z. Wang, A. C. Bovik, H. R. Sheikh, E. P. Simoncelli, Image Quality Assessment: From Error Visibility to Structural Similarity[J]. IEEE Transactions on Image Processing, 2004, 13(4): 600-612.
[Weickert 1998] J. Weickert. Anisotropic Diffusion in Image Processing[M]. Teubner Verlag, Stuttgart, 1998.
[Witkin 1987] A. P. Witkin. Scale-space filtering[P]. US Patent 4,658,372, 1987.
[Xu 1998a] C. Xu, J. L. Prince. Snakes, shapes and gradient vector flow[J]. IEEE Transactions on Imaging Processing. 1998, 7(3): 359-369.
[Xu 1998b] C. Xu, J. L. Prince. Generalized gradient vector flow external forces for active contours [J]. International Journal of Signal Processing, 1998, 71(2): 131-139.
[Yezzi 1998] A. Yezzi Jr. Modified Curvature Motion for Image Smoothing and Enhancement[J]. IEEE Transactions on Image Processing, 1998, 7(3): 345-351.
[You 1996a] Y. L. You, W. Xu, A. Tannenbaum, M. Kaveh. Behavioral analysis of anisotropic diffusion in image processing[J]. IEEE Transactions on Image Processing, 1996, 5(11): 1539-1553.
[You 1996b] Y. L. You, M. Kaveh. Blind Image Restoration by Anisotropic Regularization[J]. IEEE Transactions on Image Processing,1999,8(3): 396-407.
[You 2000] Y. L. You, M Kaveh and Kaveh M. Fourth-Order Partial Differential Equations for Noise Removal[J], IEEE Transactions on Image Processing, 2000, 9(10):1723-1730.
[Yu 2002] Y. Yu, S. T. Acton. Speckle reducing anisotropic diffusion[J].IEEE Transactions on Image Processing,2002,11(11): 1260-1270.
[丛舸1997]丛舸。计算机视觉中的非线性尺度空间理论[博士学位论文]。中国科学院自动化研究所,北京,1997。
[崔景泰1995]崔景泰。小波分析导论[M]。西安:西安交通大学出版社,1995。
[崔屹2000]崔屹。图像处理与分析数学形态学方法及应用[M]。科学出版社,2000。
[李培华2000]李培华,张田文。主动轮廓线模型(蛇模型)综述[J]。软件学报,2000, 11 (6) : 751-757。
[林宙辰1999]林宙辰,石青云。一个能去噪和保持真实感的各向异性扩散方程[J]。计算机学报.。Vol.22,No.11,Nov.1999:1133-1137。
[杨福生2000]杨福生。小波变换的工程分析与应用[M]。科学出版社,2000。
[余庆军2004]余庆军,谢胜利。基于人类视觉系统的各向异性扩散图像平滑方法[J]。电子学报,2004,32(1):17- 20。
[张禀2004]张禀,陈刚。基于偏微分方程的图象处理[M]。北京:高等教育出版社。2004。