图上的正则化扩散图像分割方法研究
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摘要
全监督图像分割方法由于能够提供用户影响分割效果的能力而越来越受到人们的重视,传统方法通过比较未标记点与种子点的相似程度来判断未标记点的所属类别,存在判断相似程度的标准单一问题而导致分割方法不理想的问题。近年来,图上的正则化扩散方法由于其离散性和适定性在图像去噪方面取得了良好的效果,本文从正则化扩散的物理意义出发,将其应用在全监督图像分割中,提出了一种基于图论正则化扩散的图像分割方法。
将离散的正则化扩散框架应用到全监督的图像分割领域中;使用非下采样轮廓波变换提取图像的多方向多尺度几何特征,结合HSI分解产生的图像颜色特征,使用高斯核函数公式构造图中各顶点特征之间的权重,并使用以8连接为基础,跨度为2 k , k = 0,1,2,3的拓扑结构构造图,进而将这些特征统一到离散的正则化框架中,并将其应用于全监督彩色图像分割领域。实验结果证明:与基于图谱理论的Random Walker和Lazy Snapping图像分割方法相比,本方法具有抗噪声能力强,对边缘细节保留完整,对具有纹理不一致的图像区域分割能力强的优点。
从核方法的算法框架出发,可以把正则化扩散理解为一种核方法,Morlet小波核是以Morlet小波为基础构而成的一种平移不变核,使用Morlet小波核构造算法中的核产生一种新的图像分割方法。本文从Morlet小波核在扩散去噪中所表现出的保留复杂边缘能力强的特点出发,通过分析扩散框架中的权重构造的特点,对标准的Morlet小波核形式加以改造,将Morlet小波核函数代替高斯核函数构造图中各顶点特征之间的权重,并进行全监督图像分割,通过与已知模式进行对比的量化分析方式证明了:与使用高斯核函数的图像分割算法相比,使用Morlet小波核函数的图像分割算法具有在较少的特征支持下可以达到与前者相当甚至更好的图像分割效果,尤其在复杂边缘细节的保留上,使用Morlet小波核函数的图像分割算法具有明显的优势。
Supervised image segmentation which provide the user with the ability of interacting with the algorithm is gradually worth paying more attentions, conventional method use the similarity between unknown pixel and the seed pixel to decide the label of the unknown pixel, but these kind of methods are not always producing good results because of the insufficient criteria of the similarity. These days, with the characteristics like discrete and well-posed, regularized diffusion method perform good in the filed of image denoising, we propose a new digital image segmentation method on graph based on regularized diffusion by analysising the essence of the regularized diffusion.
We apply a regularized diffusion framework to solve the supervised learning image segmentation problem. The weight of the graph is generated by using Gaussian Kernel Function, combining with the geometric feature extracted from the image by using contourlet transform and the color feature by HSI decomposition. The graph topology structure is an improved 8-connection topology which step is 2 k , k = 0,1,2,3.
Experimental results have shown that compared with some graph spectral theory based image segmentation algorithm, such as random walker and the Lazy Snapping, the proposed method is robust on noisy pictures, which can reserve a more complete boundary and have a better performance on the section with inconsistent texture. .One can consider the diffusion method as a kernel method. Morlet wavelet kernel is a translation invariant function based on Morlet wavelet transform, which make a terrific performance of reserving the complex boundary of the object on the denoise by diffusion. So by analysing the construction property of the weight of the diffusion framework, one can modify the formulation of the standard Morlet wavelet kernel function to apply it on the supervised learning image segmentation problem instead of using Gaussian Kernel Function. By computing the difference between the segment result and the known pattern, experimental results have shown that compared with algorithm using Gaussian Kernel Function, the algorithm using Morlet wavelet kernel function can do a better job with less feature supports, especially on the problem of reserving complex boundary section.
将离散的正则化扩散框架应用到全监督的图像分割领域中;使用非下采样轮廓波变换提取图像的多方向多尺度几何特征,结合HSI分解产生的图像颜色特征,使用高斯核函数公式构造图中各顶点特征之间的权重,并使用以8连接为基础,跨度为2 k , k = 0,1,2,3的拓扑结构构造图,进而将这些特征统一到离散的正则化框架中,并将其应用于全监督彩色图像分割领域。实验结果证明:与基于图谱理论的Random Walker和Lazy Snapping图像分割方法相比,本方法具有抗噪声能力强,对边缘细节保留完整,对具有纹理不一致的图像区域分割能力强的优点。
从核方法的算法框架出发,可以把正则化扩散理解为一种核方法,Morlet小波核是以Morlet小波为基础构而成的一种平移不变核,使用Morlet小波核构造算法中的核产生一种新的图像分割方法。本文从Morlet小波核在扩散去噪中所表现出的保留复杂边缘能力强的特点出发,通过分析扩散框架中的权重构造的特点,对标准的Morlet小波核形式加以改造,将Morlet小波核函数代替高斯核函数构造图中各顶点特征之间的权重,并进行全监督图像分割,通过与已知模式进行对比的量化分析方式证明了:与使用高斯核函数的图像分割算法相比,使用Morlet小波核函数的图像分割算法具有在较少的特征支持下可以达到与前者相当甚至更好的图像分割效果,尤其在复杂边缘细节的保留上,使用Morlet小波核函数的图像分割算法具有明显的优势。
Supervised image segmentation which provide the user with the ability of interacting with the algorithm is gradually worth paying more attentions, conventional method use the similarity between unknown pixel and the seed pixel to decide the label of the unknown pixel, but these kind of methods are not always producing good results because of the insufficient criteria of the similarity. These days, with the characteristics like discrete and well-posed, regularized diffusion method perform good in the filed of image denoising, we propose a new digital image segmentation method on graph based on regularized diffusion by analysising the essence of the regularized diffusion.
We apply a regularized diffusion framework to solve the supervised learning image segmentation problem. The weight of the graph is generated by using Gaussian Kernel Function, combining with the geometric feature extracted from the image by using contourlet transform and the color feature by HSI decomposition. The graph topology structure is an improved 8-connection topology which step is 2 k , k = 0,1,2,3.
Experimental results have shown that compared with some graph spectral theory based image segmentation algorithm, such as random walker and the Lazy Snapping, the proposed method is robust on noisy pictures, which can reserve a more complete boundary and have a better performance on the section with inconsistent texture. .One can consider the diffusion method as a kernel method. Morlet wavelet kernel is a translation invariant function based on Morlet wavelet transform, which make a terrific performance of reserving the complex boundary of the object on the denoise by diffusion. So by analysing the construction property of the weight of the diffusion framework, one can modify the formulation of the standard Morlet wavelet kernel function to apply it on the supervised learning image segmentation problem instead of using Gaussian Kernel Function. By computing the difference between the segment result and the known pattern, experimental results have shown that compared with algorithm using Gaussian Kernel Function, the algorithm using Morlet wavelet kernel function can do a better job with less feature supports, especially on the problem of reserving complex boundary section.
引文
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[2] Grady L. Random walk for image segmentation[J].IEEE Transactions Pattern Analysis and Machine Intelligence,2006, 28(11): 1768-1783.
[3] Shi J , Malik J . Normalized cuts and image segmentation[J]. IEEE Transactions on Pattern Analysis Machine Intelligence , 2000 , 22 (8) : 888-905.
[4] Couprie C, Grady L, Najman L,et al. Power watersheds: A new image segmentation framework extending graph cuts,random walker and optimal spanning forest[C]//the Twelfth IEEE International Conference on Computer Vision(ICCV2009),Dep 29 to Oct 2,2009,Kyoto,Japan.Institute of Electrical and Electronics Engineers Inc,2009:731-738.
[5] Lezoray O,Elmoataz A,Bougleux S. Graph regularization for color image processing[J]. Computer Vision and Image Understanding,2006, 107(11):38-55.
[6] Zhang F,Hancock E R.Graph spectral image smoothing using the heat kernel[J].Pattern Recognition,2008,41(11): 3328-3342.
[7] Szlam A D,Maggioni M,Coifman R R. Regularization on Graphs with Function adapted Diffusion Processes[J].Journal of Machine Learning Research,2008,9:1711–1739.
[8] Mercer J. Functions of positive and negative type and their connection with the theory of integral equations[J]. Philos. Trans. Roy. Soc. London, 1909, 209: 415-446.
[9] Mitchell T M.Machine Learning[M]. New York :McGraw-Hill,1997
[10] Vapnik V N.统计学习理论的本质[M].北京:清华大学出版社,2000.
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[12] Sinop A K, Grady L.A Seeded Image Segmentation Framework Unifying Graph Cuts And Random Walker Which Yields A New Algorithm[C]// the eleventh IEEE International Conference on Computer Vision(ICCV2007), October 14 to 20,2007,Rio de Janeiro, Brazil. Institute of Electrical and Electronics Engineers Inc.2007:1-8.
[13] CattéF, Lions P, Morel J,et al.Image selective smoothing and edge detection by nonlinear diffusion[J]. SIAM Journal on Numerical Analysis,1992,29(1):182-193.
[14] Alvarez L, Lions P, Morel J,Image selective smoothing and edge detection by nonlinear diffusion[J].SIAM Journal on Numerical Analysis,1992,29(3):845--866.
[15] Bakushinsky A,Goncharsky A.Ill-Posed Problems:Theory and Applications[M].Kluwer Academic Publishers,1994.
[16] Tikhonov A N, Goncharsky A, Stepanov V V, et al. Numerical Methods for the Solution of Ill-Posed Problems[M].Kluwer Academic Publishers,1995.
[17] Chambolle A. Partial differential equations and image processing[C]//IEEE International Conference on Image Processing,Nov 13 to 16,1994,Austin,Texas,USA: Institute of Electrical and Electronics Engineers Inc.1994:16–20.
[18] Perona P , Malik J.Scale-space and edge detection using anisotropic diffusion[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence ,1990 ,12 (7) :629– 639.
[19] Elmoataz A,Lezoray O,Bougleux S.Nonlocal Discrete Regularization on Weighted Graphs:a Framework for Image and Manifold Processing[J]. IEEE Transactions on Image Processing, 2008,17(7):1047-1060.
[20] Buades A, Coll B, Morel J. A non-local algorithm for image denoising[C]//2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05),Jun 20 to 26,2005,San Diego,USA.2005:60-65.
[21]焦李成,谭山.图像的多尺度几何分析:回顾和展望[J].电子学报, .2003,31(12A):1975-1981.
[22] Do M N,Vetterli M. The contourlet transform: an efficient directional multiresolution image representation[J]. IEEE Transaction on Image Processing,2005, 14(12):2091-2106.
[23] Burt P J,Adelson E H. The laplacian pyramid as a compact image code[J]. IEEE. Trans.Communications, 1983, 31(4): 532-540.
[24] Bamberger R H, Smith M J T. A filter bank for the directional decomposition of images: Theory and design[J]. IEEE Transactions on Signal Processing,1992, 40(4):882-893.
[25] da Cunha A L,Jianping Zhou.The nonsubsampled contourlet transform: theory, design, and applications[J].IEEE Transaction on Image Processing,2006,15(10): 3089-3101.
[26] Taylor J S, Cristianini N.Kernel Methid for Pattern Analysis[M].北京:机械工业出版社,2005.
[27] Smola A, Scholkopf B, Müller K R. The Connection between Regularization Operators and Support Vector Kernels[J].Neural Networks, 1998, 11(4):637-649.
[28] Shaoming Zhang,Ying Chen. Image Denoising Based on Wavelet Support Vector Machine[C].//IEEE International Conference on Cybernetics and Intelligent Systems (CIS 2006),Nov 3 to 6,2006,Guangzhou China.2006: 963– 971.
[29] Yin Li,Jian Sun,Chi-Keung Tang,et al.Lazy snapping[C]//The 31st international conference on computer graphics and interactive techniques(Siggraph 2004), Aug 8 to 12,2004,LosAngeles, California, USA.2004:303-308.
[30] Jedynak B,Karakos D. Unigram Language Models using Diffusion Smoothing over Graphs[C]//2007 Workshop on Graph-based Methods for Natural Language Processing, April 26, 2007,New York,USA.2007:TextGraphs-2.
[31] Levin A,Acha A R,Lischinski D. Spectral Matting[C]//2007 IEEE Conference on Computer Vision and Pattern Recognition(CVPR'07), June 17 to 22,2007, Minneapolis, Minnesota, USA .2007:1-8.
[32]武方方,赵银亮.一种基于Morlet小波核的约简支持向量机[J].控制与决策, 2006,21(8):848-856.
[33]汪鼎文,李元香.基于HSI颜色空间的X射线彩色图像分割[J].计算机工程与设计,2006,27(1):139-141.
[2] Grady L. Random walk for image segmentation[J].IEEE Transactions Pattern Analysis and Machine Intelligence,2006, 28(11): 1768-1783.
[3] Shi J , Malik J . Normalized cuts and image segmentation[J]. IEEE Transactions on Pattern Analysis Machine Intelligence , 2000 , 22 (8) : 888-905.
[4] Couprie C, Grady L, Najman L,et al. Power watersheds: A new image segmentation framework extending graph cuts,random walker and optimal spanning forest[C]//the Twelfth IEEE International Conference on Computer Vision(ICCV2009),Dep 29 to Oct 2,2009,Kyoto,Japan.Institute of Electrical and Electronics Engineers Inc,2009:731-738.
[5] Lezoray O,Elmoataz A,Bougleux S. Graph regularization for color image processing[J]. Computer Vision and Image Understanding,2006, 107(11):38-55.
[6] Zhang F,Hancock E R.Graph spectral image smoothing using the heat kernel[J].Pattern Recognition,2008,41(11): 3328-3342.
[7] Szlam A D,Maggioni M,Coifman R R. Regularization on Graphs with Function adapted Diffusion Processes[J].Journal of Machine Learning Research,2008,9:1711–1739.
[8] Mercer J. Functions of positive and negative type and their connection with the theory of integral equations[J]. Philos. Trans. Roy. Soc. London, 1909, 209: 415-446.
[9] Mitchell T M.Machine Learning[M]. New York :McGraw-Hill,1997
[10] Vapnik V N.统计学习理论的本质[M].北京:清华大学出版社,2000.
[11] Schlkopf B,Smola A J.Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond (Adaptive Computation and Machine Learning)[M]. The MIT Press,2001.
[12] Sinop A K, Grady L.A Seeded Image Segmentation Framework Unifying Graph Cuts And Random Walker Which Yields A New Algorithm[C]// the eleventh IEEE International Conference on Computer Vision(ICCV2007), October 14 to 20,2007,Rio de Janeiro, Brazil. Institute of Electrical and Electronics Engineers Inc.2007:1-8.
[13] CattéF, Lions P, Morel J,et al.Image selective smoothing and edge detection by nonlinear diffusion[J]. SIAM Journal on Numerical Analysis,1992,29(1):182-193.
[14] Alvarez L, Lions P, Morel J,Image selective smoothing and edge detection by nonlinear diffusion[J].SIAM Journal on Numerical Analysis,1992,29(3):845--866.
[15] Bakushinsky A,Goncharsky A.Ill-Posed Problems:Theory and Applications[M].Kluwer Academic Publishers,1994.
[16] Tikhonov A N, Goncharsky A, Stepanov V V, et al. Numerical Methods for the Solution of Ill-Posed Problems[M].Kluwer Academic Publishers,1995.
[17] Chambolle A. Partial differential equations and image processing[C]//IEEE International Conference on Image Processing,Nov 13 to 16,1994,Austin,Texas,USA: Institute of Electrical and Electronics Engineers Inc.1994:16–20.
[18] Perona P , Malik J.Scale-space and edge detection using anisotropic diffusion[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence ,1990 ,12 (7) :629– 639.
[19] Elmoataz A,Lezoray O,Bougleux S.Nonlocal Discrete Regularization on Weighted Graphs:a Framework for Image and Manifold Processing[J]. IEEE Transactions on Image Processing, 2008,17(7):1047-1060.
[20] Buades A, Coll B, Morel J. A non-local algorithm for image denoising[C]//2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05),Jun 20 to 26,2005,San Diego,USA.2005:60-65.
[21]焦李成,谭山.图像的多尺度几何分析:回顾和展望[J].电子学报, .2003,31(12A):1975-1981.
[22] Do M N,Vetterli M. The contourlet transform: an efficient directional multiresolution image representation[J]. IEEE Transaction on Image Processing,2005, 14(12):2091-2106.
[23] Burt P J,Adelson E H. The laplacian pyramid as a compact image code[J]. IEEE. Trans.Communications, 1983, 31(4): 532-540.
[24] Bamberger R H, Smith M J T. A filter bank for the directional decomposition of images: Theory and design[J]. IEEE Transactions on Signal Processing,1992, 40(4):882-893.
[25] da Cunha A L,Jianping Zhou.The nonsubsampled contourlet transform: theory, design, and applications[J].IEEE Transaction on Image Processing,2006,15(10): 3089-3101.
[26] Taylor J S, Cristianini N.Kernel Methid for Pattern Analysis[M].北京:机械工业出版社,2005.
[27] Smola A, Scholkopf B, Müller K R. The Connection between Regularization Operators and Support Vector Kernels[J].Neural Networks, 1998, 11(4):637-649.
[28] Shaoming Zhang,Ying Chen. Image Denoising Based on Wavelet Support Vector Machine[C].//IEEE International Conference on Cybernetics and Intelligent Systems (CIS 2006),Nov 3 to 6,2006,Guangzhou China.2006: 963– 971.
[29] Yin Li,Jian Sun,Chi-Keung Tang,et al.Lazy snapping[C]//The 31st international conference on computer graphics and interactive techniques(Siggraph 2004), Aug 8 to 12,2004,LosAngeles, California, USA.2004:303-308.
[30] Jedynak B,Karakos D. Unigram Language Models using Diffusion Smoothing over Graphs[C]//2007 Workshop on Graph-based Methods for Natural Language Processing, April 26, 2007,New York,USA.2007:TextGraphs-2.
[31] Levin A,Acha A R,Lischinski D. Spectral Matting[C]//2007 IEEE Conference on Computer Vision and Pattern Recognition(CVPR'07), June 17 to 22,2007, Minneapolis, Minnesota, USA .2007:1-8.
[32]武方方,赵银亮.一种基于Morlet小波核的约简支持向量机[J].控制与决策, 2006,21(8):848-856.
[33]汪鼎文,李元香.基于HSI颜色空间的X射线彩色图像分割[J].计算机工程与设计,2006,27(1):139-141.