基于支持向量机的图像分割研究综述
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摘要
图像分割和目标分类是数字图像处理领域中两个重要的研究课题。建立在统计学理论基础之上的传统学习分类方法在这两个研究课题中得到了广泛的应用。传统学习分类方法是以经验风险最小化取代期望风险最小化,即渐进理论,但这种取代只有当训练样本数趋于无穷时,最小化经验风险与最小化期望风险之间的偏差才能达到理论上的最小。然而在实际应用中,训练样本数趋于无穷这一前提条件往往得不到满足,特别当问题处在高维空间时更是如此。因此,一些理论上非常优秀的学习分类方法在实际应用中的表现却可能不尽人意。
与传统统计学相比,统计学习理论是一种专门研究小样本情况下机器学习规律的理论。该理论针对小样本学习问题建立了一套新的理论体系,在这种体系下的统计推理规则不仅考虑了对渐进性的要求,而且追求在现有有限信息的条件下得到最优结果。建立在统计学习理论的VC维理论和结构风险最小化原理基础上的支持向量机方法已经被看作是对传统学习分类方法的一个好的替代,特别在小样本、高维非线性情况下,具有较好的泛化性能。
支持向量机是Vapnik及其研究小组提出的一种全新的模式识别技术。在使用结构风险最小化原则替代经验风险最小化原则的基础上,支持向量机综合了统计学习、机器学习和神经网络等方面的技术,并被证明在最小化结构风险的同时,有效地提高算法的推广能力。由于其完备的理论基础和良好的实验结果,支持向量机日渐引起研究人员的重视。目前将其应用于图像分割的方法研究还比较肤浅,有待深入研究和进一步完善。现有的基于支持向量机的图像分割方法大多都是针对具体图像提出的,比较零散。为此,本论文对支持向量机方法及其在图像分割中的应用研究进行了系统综述,以期能为对基于支持向量机方法进行图像分割感兴趣的读者提供参考。
本论文首先从支持向量机的发展背景、基本思想、基本算法以及方法特点进行了详细综述,然后对基于支持向量机的图像分割方法进行了系统综述和分析。
本论文的主要内容安排如下:第一章综述了课题背景,综述了图像分割的相关概念、图像分割技术以及发展趋势;第二章概述了统计学习理论的主要内容;第三章综述了支持向量机的基本思想、基本算法以及支持向量机方法的特点;第四章详细综述了基于支持向量机的图像分割方法;第五章做了总结和展望。
Image segmentation and object classification are two important topics of digital image processing. Traditional classification approaches based on statistical theory have been extensively applied in the two research areas. Traditional classification approaches, which are based on the principle of Experiential Risk Minimization instead of Expected Risk Minimization, achieve the best, when the number of training samples is infinite. Because the number of training samples is often limited and data dimension is high, the performance of traditional classification approaches is often unsatisfied in practice.
Compared with statistical theory, statistical learning theory focuses on the machine learning of small sample size and can trade off between the complexity of models and generalization performance. Support vector machines, which are based on Vapnik-Chervonenkis (VC) dimension theory and Structural Risk Minimization principle, are considered good candidates because of their high generalization performance without the need to add a priori knowledge, even when the dimension of the input space is very high and the problem is nonlinear.
Support vector machine(SVM) is a new sort of recognizing technology. Based on the principle of structural risk minimization instead of the principle of experiential risk minimization, combining the techniques of statistical learning, machines learning and neural networks etc, support vector machines has good capability of generalization. Because of having self-contained theories and good experimental results, Support vector machines are coming researched by more and more researcher.
This dissertation surveys of study on image segmentation based on support vector machines. The main contents are as follows:
The background of the dissertation is introduced in chapter 1. The definitions and techniques of image segmentation are also summarized. The main statistical learning theory is given in chapter 2. Chapter 3 surveys the support vector machine such as its basic ideas, algorithms, and characters. The methods of image segmentation based on support vector machine are expounded in chapter 4. At last, tags are made in chapter 5.
与传统统计学相比,统计学习理论是一种专门研究小样本情况下机器学习规律的理论。该理论针对小样本学习问题建立了一套新的理论体系,在这种体系下的统计推理规则不仅考虑了对渐进性的要求,而且追求在现有有限信息的条件下得到最优结果。建立在统计学习理论的VC维理论和结构风险最小化原理基础上的支持向量机方法已经被看作是对传统学习分类方法的一个好的替代,特别在小样本、高维非线性情况下,具有较好的泛化性能。
支持向量机是Vapnik及其研究小组提出的一种全新的模式识别技术。在使用结构风险最小化原则替代经验风险最小化原则的基础上,支持向量机综合了统计学习、机器学习和神经网络等方面的技术,并被证明在最小化结构风险的同时,有效地提高算法的推广能力。由于其完备的理论基础和良好的实验结果,支持向量机日渐引起研究人员的重视。目前将其应用于图像分割的方法研究还比较肤浅,有待深入研究和进一步完善。现有的基于支持向量机的图像分割方法大多都是针对具体图像提出的,比较零散。为此,本论文对支持向量机方法及其在图像分割中的应用研究进行了系统综述,以期能为对基于支持向量机方法进行图像分割感兴趣的读者提供参考。
本论文首先从支持向量机的发展背景、基本思想、基本算法以及方法特点进行了详细综述,然后对基于支持向量机的图像分割方法进行了系统综述和分析。
本论文的主要内容安排如下:第一章综述了课题背景,综述了图像分割的相关概念、图像分割技术以及发展趋势;第二章概述了统计学习理论的主要内容;第三章综述了支持向量机的基本思想、基本算法以及支持向量机方法的特点;第四章详细综述了基于支持向量机的图像分割方法;第五章做了总结和展望。
Image segmentation and object classification are two important topics of digital image processing. Traditional classification approaches based on statistical theory have been extensively applied in the two research areas. Traditional classification approaches, which are based on the principle of Experiential Risk Minimization instead of Expected Risk Minimization, achieve the best, when the number of training samples is infinite. Because the number of training samples is often limited and data dimension is high, the performance of traditional classification approaches is often unsatisfied in practice.
Compared with statistical theory, statistical learning theory focuses on the machine learning of small sample size and can trade off between the complexity of models and generalization performance. Support vector machines, which are based on Vapnik-Chervonenkis (VC) dimension theory and Structural Risk Minimization principle, are considered good candidates because of their high generalization performance without the need to add a priori knowledge, even when the dimension of the input space is very high and the problem is nonlinear.
Support vector machine(SVM) is a new sort of recognizing technology. Based on the principle of structural risk minimization instead of the principle of experiential risk minimization, combining the techniques of statistical learning, machines learning and neural networks etc, support vector machines has good capability of generalization. Because of having self-contained theories and good experimental results, Support vector machines are coming researched by more and more researcher.
This dissertation surveys of study on image segmentation based on support vector machines. The main contents are as follows:
The background of the dissertation is introduced in chapter 1. The definitions and techniques of image segmentation are also summarized. The main statistical learning theory is given in chapter 2. Chapter 3 surveys the support vector machine such as its basic ideas, algorithms, and characters. The methods of image segmentation based on support vector machine are expounded in chapter 4. At last, tags are made in chapter 5.
引文
铩?.C.Yan,N.Sang and T.Zhang.Local entropy-based transition region extraction andthresholding.Patter Recognition Letters,2003,24:2935-2941
2.X.Li,Z.Liu and K.Leung.Detection of vehicles from traffic scenes using fuzzyintegrals.Pattern Recognition,2002,35:967-980
3.M.D.Jolly,S.Lakshmanan and A.K.Jain.Vehicle segmentation and classificationusing deformable templates.IEEE Trans.PAMI,1996,18(3):293-308
4.D.M.Ha,J.M.Lee and Y D.Kim.Neural-edge-based vehicle detection and trafficparameter extraction.Image Vision Computing,2004,22:899907
5.陈寅鹏,丁晓青.复杂车辆图像中的车牌定位与字符分割方法.红外与激光上程,2004,33(1):29-33
6.C.Tsai,B.S.Manjunath and R.Jagadeesan.Automated segmentation of brain MRimages.Pattern Recognition,1995,28(12):1825-1837
7.X.M.Pardo,E Radeva and D.Cabello.Discriminant snakes for 3D reconstruction ofanatomical organs.Medical Image Analysis,2003,7(3):293-310
8.L.Xu.Segmentation of skin cancer images.Image and Vision Computing,1999,17(1):65-74
9.薛景浩,章毓晋,林行刚.SAR图像基于Rayleigh分布假设的最小误差阈值化分割.电子科学学刊,1999,21(2):219-225
10.李国宽,彭嘉雄.基于小波变换的红外成像弱小目标检测方法.华中理工大学学报,2000,28(5):69-71
11.B.Tian,M.A.Shaikh,S.Azimi,et al.A study of cloud classification with neuralnetworks using spectral and textural features.IEEE Trans.Neural Networks,1999,10(1):138-151
12.C.Y Wang,S.J.Liao and L.W Chang.Wavelet image coding using variableblocksize vector quantization with optimal quadtree segmentation.SignalProcessing:Image Communication,2000,15:879-890
13.E.EI-Qawasmeh.A quadtree-based representation technique for indexing and retrievalof image databases Journal of Visual Communication and Image Representation,2003,14(3):340-357
14.T.Zhang,J.Peng and Z.Li.An adaptive image segmentation method with visual nonlinearity characteristics.IEEE Transactions on Systems,Man and
Cybernetics-part B:Cybernetics,1996,26(4):619-627
铩?5.章毓晋.图像分割.北京:科学出版社,2001
16.J.M.S.Prewitt and M.L.Mendelsohn.The analysis of cell images.In Ann.NewYork Acad.Sci.,1966,128:1035-1053
17.A.Rosenfeld and P.D.Tome.Histogram concavity analysis as an aid in thresholdselection.IEEE Trans.Syst.Man Cybern.,1983,SMC-13:231-235
18.N.A.Otsu:A threshold selection method from gray-level histogram.IEEE Trans.System Man Cybernetics,1979,SMC-9(1):62-66
19.T.Pun.Entropic,thresholding:a new approach.Computer Vision,Graphics andImage processing,1981,16:210-239
20.I.Hannah,D.Patel and E.R.Davies.The use of variance and entropic thresholdingmethods for image segmentation.Pattern Recognition,1995,28(8):1135-1144
21.A.D.Brink.Thresholding of digital images using two-dimensional entropies.PatternRecognition,1992,25(8):803-808
22.H.D.Cheng,J.R.Cheng and J.G.Li.Threshold selection based on fuzzy c-partitionentropy approach.Pattern Recognition,1998,31(7):857-870
23.P Sahoo,C.Wilkins and J.Yeager.Threshold selection using Renyi's entropy.PatternRecognition,1997,30(1):71-84
24.W.H.Tsai.Moment-preserving thresholding:a new approach.ComputerVision,Graphics,and Image Processing,1985,29:377-393
25.J.M.Beaulieu,M.Goldberg.Hierarchy in picture segmentation:a stepwiseoptimization approach.IEEE-PAMI,1989,11(2):150-163
26.王润生.图像理解.长沙:国防科技大学出版社,1995
27.桑农,张天序,曹治国.基于边缘约束的红外目标图像松弛分割技术.电子学报,2002,30(7):1027-1031
28.Y J.Zhang and J.J.Gerbrands.Transition region determination based thresholding.Pattern Recognition Letters,1991,12:13-23
29.章毓晋.过渡区和图像分割.电子学报,1996,24(1):12-17
30.J.F.Mangin,V Frouin,I.Bloch et al.From 3D magnetic resonance images tostructural representations of the cortex topography preserving deformations.J.MathImag.Vis.,1995,5:297-318
31.I.N.Manousakas,P E.Undrill,G.G.Cameron et al.Split-and-merge segmentation of magnetic resonance medical images:performance evaluation and extension to three
dimensions.Computers and Biomedical Research,1998,31:393-412
铩?2.S.Geman and D.Geman.Stochastic relaxation,Gibbs distributions,and the Bayesianrestoration of images.IEE Trans.PAMI,1984,PAMI-6(6):721-741
33.边肇祺,张学工.模式识别.北京:清华大学出版社,2000
34.R.A.Reyna and M.Cattoen.Segmenting images with support vector machines.IEEE Int.Conf.Image Proc.,2000:820-823
35.F.Xu,X.Li and Q.Yan.Aerial images segmentation based on SVM.Proceedings ofthe second international conference on machine learning and cybernetics,2003:2207-2211
36.V Vapnik.The nature of statistics learning theory.New York:Springer Verlag,1995.
37.V Vapnik.Statistical learning theory,New York:J.Wiley,1998
38.D.L.Pham and J.L.Prince.An adaptive fuzzy c-means algorithm for imagesegmentation in the presence of intensity inhomogeneities.Pattern RecognitionLetters,1999,20(1):57-68
39.Z.Liang,J.R.MacFall and D.E Harrington.Parameter estimation and tissuesegmentation from multi-spectral MR imaging.IEEE Trans.Medical Imaging,1994,13(3):441-449
40.V S.Nalwa and T.O.Binford.On detecting edges.IEEE Trans.PAMI,1986,PAMI-8(6):699-714
41.J.Canny.A computational approach to edge detection.IEEE Trans.PAMI,1986,PAMI-8(6):679-698
42.E Perona and J.Malik.Scale space and edge detection using anisotropic diffusion.IEEE Trans.PAMI,1990,PAMI-12(7):629-639
43.W T.Freeman and E.H.Adelson.The design and use of steerable filters.Trans.PAMI,1991,PAMI-13(9):891-906
44.K.H.Liang,T.Tjahajadi and Y H.Yang.Roof edge detection using regularized cubicB-spline fitting.Pattern Recognition,1997,30(5):719-728
45.Vapnik V N.An overview of statistical learning theory[J].IEEE Transaction onNeural Network,1999 10(5):988-999
46.Boser B,Guyon I,Vapnik V.A training algorithm for optimal margin classifiers[C].Fifth Annual Workshop on Computational Learning Theory Pittsburgh:ACMPress,1992.144-152
铩?7.ConesC,Vapnik V.Support-vector networks[J].Machine Learning,1995,20:273-297
48.许建华,张学上,李衍达.支持向量机的新发展[J].控制与决策,2004 19(5):481-484
49.郑红军,周旭,毕笃彦.统计学习理论及支持向量机概述.现代电子技术.2003,4:59-61
50.谭东宁,谭东汉.小样本机器学习理论:统计学习理论.南京理上大学学报.2001,1(25):108-112
51.I.Middleton and R.I.Damper.Segmentation of magnetic resonance images using acombination of neural networks and active contour models.Medical Engineering&Physics,2004,26:71-86
52.K.L.Vincken,A.S.E.Koster,M.A.Viergever.Probabilistic multiscale imagesegmentation.IEEE Trans.PAMI,1997,PAMI-19(2):109-120
53.E Perona and J.Malik.Scale space and edge detection using anisotropic diffusion.IEEE Trans.PAMI,1990,PAMI-12(7):629-639
54.M.G.Genton.Classes of kernels for machine learning:a statistics perspective.Journal of Machine Learning Research,2001,2:299-312
55.张铃.基于核函数的SVM机与三层前向神经网络的关系.计算机学报,2002 25(7):696-700
56.徐海祥,基于支持向量机方法的图像分割与目标分类,华中科技大学博士论文,2005.6
57.K.R.Muller,S.Mika,G.Ratsch,K.Tsuda and B.Scholkopf.An introductiontoKernel-based learning algorithm.IEEE Transactions on Neural Networks,2001,12(2):181-201
58.阎威武,邵惠鹤.支持向量机和最小二乘支持向量机的比较及应用研究.控制与决策.2003(3)
59.朱家元,郭基联,张恒喜,张喜斌.多元分类LS-SVM设计与装备保障性评估.装备指挥技术学院学报.2003(3)
60.朱家元,昊伟,张恒喜,董彦非一种新型的多元分类支持向量机.计算机工程.2003(17)
61.阎威武,朱宏栋,邵惠鹤.基于最小二乘支持向量机的软测量建模.系统仿真学报.2003(10)
62.Pontil;A Verri:ProPerties of Support Vector Machines.Neural Computation.VoL.10, 1998:955-974
铩?3.袁亚湘,孙文瑜.最优化理论与方法.科技出版社,2001
64.徐芳,航空影像分割的支持向量机方法,武汉大学博士论文,2004.4
65.许磊,支持向量机和模糊理论在遥感图像分类中的应用,江南大学,2006.3
66.蒋林,基于支持向量机的特征提取方法研究与应用,湖南大学,2006.10
67.张翔,支持向量机及其在医学图像分割中的应用,华中科技大,2004.3
2.X.Li,Z.Liu and K.Leung.Detection of vehicles from traffic scenes using fuzzyintegrals.Pattern Recognition,2002,35:967-980
3.M.D.Jolly,S.Lakshmanan and A.K.Jain.Vehicle segmentation and classificationusing deformable templates.IEEE Trans.PAMI,1996,18(3):293-308
4.D.M.Ha,J.M.Lee and Y D.Kim.Neural-edge-based vehicle detection and trafficparameter extraction.Image Vision Computing,2004,22:899907
5.陈寅鹏,丁晓青.复杂车辆图像中的车牌定位与字符分割方法.红外与激光上程,2004,33(1):29-33
6.C.Tsai,B.S.Manjunath and R.Jagadeesan.Automated segmentation of brain MRimages.Pattern Recognition,1995,28(12):1825-1837
7.X.M.Pardo,E Radeva and D.Cabello.Discriminant snakes for 3D reconstruction ofanatomical organs.Medical Image Analysis,2003,7(3):293-310
8.L.Xu.Segmentation of skin cancer images.Image and Vision Computing,1999,17(1):65-74
9.薛景浩,章毓晋,林行刚.SAR图像基于Rayleigh分布假设的最小误差阈值化分割.电子科学学刊,1999,21(2):219-225
10.李国宽,彭嘉雄.基于小波变换的红外成像弱小目标检测方法.华中理工大学学报,2000,28(5):69-71
11.B.Tian,M.A.Shaikh,S.Azimi,et al.A study of cloud classification with neuralnetworks using spectral and textural features.IEEE Trans.Neural Networks,1999,10(1):138-151
12.C.Y Wang,S.J.Liao and L.W Chang.Wavelet image coding using variableblocksize vector quantization with optimal quadtree segmentation.SignalProcessing:Image Communication,2000,15:879-890
13.E.EI-Qawasmeh.A quadtree-based representation technique for indexing and retrievalof image databases Journal of Visual Communication and Image Representation,2003,14(3):340-357
14.T.Zhang,J.Peng and Z.Li.An adaptive image segmentation method with visual nonlinearity characteristics.IEEE Transactions on Systems,Man and
Cybernetics-part B:Cybernetics,1996,26(4):619-627
铩?5.章毓晋.图像分割.北京:科学出版社,2001
16.J.M.S.Prewitt and M.L.Mendelsohn.The analysis of cell images.In Ann.NewYork Acad.Sci.,1966,128:1035-1053
17.A.Rosenfeld and P.D.Tome.Histogram concavity analysis as an aid in thresholdselection.IEEE Trans.Syst.Man Cybern.,1983,SMC-13:231-235
18.N.A.Otsu:A threshold selection method from gray-level histogram.IEEE Trans.System Man Cybernetics,1979,SMC-9(1):62-66
19.T.Pun.Entropic,thresholding:a new approach.Computer Vision,Graphics andImage processing,1981,16:210-239
20.I.Hannah,D.Patel and E.R.Davies.The use of variance and entropic thresholdingmethods for image segmentation.Pattern Recognition,1995,28(8):1135-1144
21.A.D.Brink.Thresholding of digital images using two-dimensional entropies.PatternRecognition,1992,25(8):803-808
22.H.D.Cheng,J.R.Cheng and J.G.Li.Threshold selection based on fuzzy c-partitionentropy approach.Pattern Recognition,1998,31(7):857-870
23.P Sahoo,C.Wilkins and J.Yeager.Threshold selection using Renyi's entropy.PatternRecognition,1997,30(1):71-84
24.W.H.Tsai.Moment-preserving thresholding:a new approach.ComputerVision,Graphics,and Image Processing,1985,29:377-393
25.J.M.Beaulieu,M.Goldberg.Hierarchy in picture segmentation:a stepwiseoptimization approach.IEEE-PAMI,1989,11(2):150-163
26.王润生.图像理解.长沙:国防科技大学出版社,1995
27.桑农,张天序,曹治国.基于边缘约束的红外目标图像松弛分割技术.电子学报,2002,30(7):1027-1031
28.Y J.Zhang and J.J.Gerbrands.Transition region determination based thresholding.Pattern Recognition Letters,1991,12:13-23
29.章毓晋.过渡区和图像分割.电子学报,1996,24(1):12-17
30.J.F.Mangin,V Frouin,I.Bloch et al.From 3D magnetic resonance images tostructural representations of the cortex topography preserving deformations.J.MathImag.Vis.,1995,5:297-318
31.I.N.Manousakas,P E.Undrill,G.G.Cameron et al.Split-and-merge segmentation of magnetic resonance medical images:performance evaluation and extension to three
dimensions.Computers and Biomedical Research,1998,31:393-412
铩?2.S.Geman and D.Geman.Stochastic relaxation,Gibbs distributions,and the Bayesianrestoration of images.IEE Trans.PAMI,1984,PAMI-6(6):721-741
33.边肇祺,张学工.模式识别.北京:清华大学出版社,2000
34.R.A.Reyna and M.Cattoen.Segmenting images with support vector machines.IEEE Int.Conf.Image Proc.,2000:820-823
35.F.Xu,X.Li and Q.Yan.Aerial images segmentation based on SVM.Proceedings ofthe second international conference on machine learning and cybernetics,2003:2207-2211
36.V Vapnik.The nature of statistics learning theory.New York:Springer Verlag,1995.
37.V Vapnik.Statistical learning theory,New York:J.Wiley,1998
38.D.L.Pham and J.L.Prince.An adaptive fuzzy c-means algorithm for imagesegmentation in the presence of intensity inhomogeneities.Pattern RecognitionLetters,1999,20(1):57-68
39.Z.Liang,J.R.MacFall and D.E Harrington.Parameter estimation and tissuesegmentation from multi-spectral MR imaging.IEEE Trans.Medical Imaging,1994,13(3):441-449
40.V S.Nalwa and T.O.Binford.On detecting edges.IEEE Trans.PAMI,1986,PAMI-8(6):699-714
41.J.Canny.A computational approach to edge detection.IEEE Trans.PAMI,1986,PAMI-8(6):679-698
42.E Perona and J.Malik.Scale space and edge detection using anisotropic diffusion.IEEE Trans.PAMI,1990,PAMI-12(7):629-639
43.W T.Freeman and E.H.Adelson.The design and use of steerable filters.Trans.PAMI,1991,PAMI-13(9):891-906
44.K.H.Liang,T.Tjahajadi and Y H.Yang.Roof edge detection using regularized cubicB-spline fitting.Pattern Recognition,1997,30(5):719-728
45.Vapnik V N.An overview of statistical learning theory[J].IEEE Transaction onNeural Network,1999 10(5):988-999
46.Boser B,Guyon I,Vapnik V.A training algorithm for optimal margin classifiers[C].Fifth Annual Workshop on Computational Learning Theory Pittsburgh:ACMPress,1992.144-152
铩?7.ConesC,Vapnik V.Support-vector networks[J].Machine Learning,1995,20:273-297
48.许建华,张学上,李衍达.支持向量机的新发展[J].控制与决策,2004 19(5):481-484
49.郑红军,周旭,毕笃彦.统计学习理论及支持向量机概述.现代电子技术.2003,4:59-61
50.谭东宁,谭东汉.小样本机器学习理论:统计学习理论.南京理上大学学报.2001,1(25):108-112
51.I.Middleton and R.I.Damper.Segmentation of magnetic resonance images using acombination of neural networks and active contour models.Medical Engineering&Physics,2004,26:71-86
52.K.L.Vincken,A.S.E.Koster,M.A.Viergever.Probabilistic multiscale imagesegmentation.IEEE Trans.PAMI,1997,PAMI-19(2):109-120
53.E Perona and J.Malik.Scale space and edge detection using anisotropic diffusion.IEEE Trans.PAMI,1990,PAMI-12(7):629-639
54.M.G.Genton.Classes of kernels for machine learning:a statistics perspective.Journal of Machine Learning Research,2001,2:299-312
55.张铃.基于核函数的SVM机与三层前向神经网络的关系.计算机学报,2002 25(7):696-700
56.徐海祥,基于支持向量机方法的图像分割与目标分类,华中科技大学博士论文,2005.6
57.K.R.Muller,S.Mika,G.Ratsch,K.Tsuda and B.Scholkopf.An introductiontoKernel-based learning algorithm.IEEE Transactions on Neural Networks,2001,12(2):181-201
58.阎威武,邵惠鹤.支持向量机和最小二乘支持向量机的比较及应用研究.控制与决策.2003(3)
59.朱家元,郭基联,张恒喜,张喜斌.多元分类LS-SVM设计与装备保障性评估.装备指挥技术学院学报.2003(3)
60.朱家元,昊伟,张恒喜,董彦非一种新型的多元分类支持向量机.计算机工程.2003(17)
61.阎威武,朱宏栋,邵惠鹤.基于最小二乘支持向量机的软测量建模.系统仿真学报.2003(10)
62.Pontil;A Verri:ProPerties of Support Vector Machines.Neural Computation.VoL.10, 1998:955-974
铩?3.袁亚湘,孙文瑜.最优化理论与方法.科技出版社,2001
64.徐芳,航空影像分割的支持向量机方法,武汉大学博士论文,2004.4
65.许磊,支持向量机和模糊理论在遥感图像分类中的应用,江南大学,2006.3
66.蒋林,基于支持向量机的特征提取方法研究与应用,湖南大学,2006.10
67.张翔,支持向量机及其在医学图像分割中的应用,华中科技大,2004.3