基于图像的焊接缺陷提取与识别方法研究
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摘要
射线检测是广泛使用的焊接质量检测方式,在获得焊缝的射线检测图像后,通常采用人工方式对焊缝检测图像进行分析来评定焊接质量。为了保证焊接质量评定的可靠性和稳定性,减少人工评定差异,国内外研究人员在焊接缺陷的自动提取和识别方面开展了比较广泛的研究,已取得了不少研究成果,但是仍未达到可以应用的水平,存在的主要问题包括不均匀背景下微小缺陷的准确检出、各种缺陷的有效特征描述及分类识别等。考虑到射线胶片照相检测使用的普遍性,以及各种射线检测方式所得到图像的相似性,本文以数字化的射线检测底片图像为对象,对焊接缺陷的提取和识别方法进行了比较深入的研究。首先,设计了完整实用的焊接缺陷提取流程,并分别开展了焊缝区域确定、非裂纹类焊接缺陷提取、裂纹类焊接缺陷提取方面的研究;然后,进行了焊接缺陷的特征描述和特征选择的研究;最后,进行了焊接缺陷的分类识别的研究。本文的主要工作和创新体现在以下几个方面:
(1)针对焊缝区域确定问题,提出了一种逐级细化确定焊缝区域的方法。该方法首先通过条带特征检测确定焊缝所在大致区域;然后基于线灰度曲线相邻间隔点数计算快速确定准确的焊缝边界。结果表明,该方法受图像亮度不均匀以及焊缝在图像中位置和分布变化等影响较小,能够较好地确定出焊缝边界,具有较强的适应性和实用性。
(2)针对非裂纹类焊接缺陷提取问题,立足于图像分割的偏微分方程理论,将“加速收缩项”引入IAC模型得到加速IAC模型,在此基础上,提出了基于加速IAC模型的非裂纹类焊接缺陷提取方法。该方法首先使用形态学变换去除焊缝区域图像的背景;然后通过亮度变换缩小图像灰度范围,并以多阈值的方式将一幅图像变换为一组矢量图像;再采用概率松弛法降低图像区域模糊度并减少局部矛盾;最后应用加速IAC模型对焊接区域图像逐块分割提取缺陷,并进行适当的后处理。结果表明,该方法能够有效提取气孔、夹杂、未熔合、未焊透等非裂纹类焊接缺陷,且加速IAC模型的应用有效减少了普通IAC模型所需的迭代次数,具有较好的通用性。
(3)针对裂纹类焊接缺陷提取问题,立足于多尺度几何分析中的Beamlet理论,提出了基于Beamlet分析的裂纹类焊接缺陷提取方法。该方法首先使用形态学变换去除焊缝区域图像的背景同时屏蔽图像中可能包含的非裂纹类焊接缺陷;然后逐块进行亮度变换处理,并通过Beamlet分析及最优BD-RDP来确定符合条件的若干beamlet作为裂纹特征检测结果;最后使用形态学膨胀、细化等操作进行适当的后处理。结果表明,该方法能够有效提取纵向裂纹、横向裂纹、放射状裂纹等裂纹类焊接缺陷,可以较好地反映裂纹类缺陷的形状和延展特点,具有较好的实用性。
(4)在焊接缺陷的特征描述和特征选择方面,本文首先结合常见的描绘方法和专家经验初步确定了9个用于描述焊接缺陷的特征;然后为了挑选出描述焊接缺陷的最有效的特征,提出并应用了一种类内方差与相关度结合的特征选择算法(WVCMFS算法),从初步确定的特征中挑选出5个描述焊接缺陷的最有效特征。其中被去除的4个特征中,平坦性(FLT)、对称性(SYM)和不尖锐性(USP)特征是加藤雄平等基于经验提出并经常采用的特征,而本文的特征选择结果表明这些特征属于无效或冗余特征,对焊接缺陷的分类并不具有明显作用。
(5)在焊接缺陷的分类识别方面,立足于支持向量机理论,提出采用嵌入WVCMFS的二叉树SVM方法进行焊接缺陷分类识别,并通过实验确定了该方法的最有效结构。为了进一步提高其分类性能,本文从两个方面进行改进,包括提出并使用一种统计不相关特征变换算法(LUFT和NLUFT),以及提出并使用一种可用于不平衡数据分类的模糊支持向量机(IC-FSVM)。结果表明,采用本文确定的特征进行焊接缺陷描述时,使用嵌入WVCMFS的二叉树IC-FSVM方法即可获得较好的焊接缺陷分类性能;若采用更多新特征进行焊接缺陷描述,则可以考虑使用嵌入WVCMFS和NLUFT的二叉树IC-FSVM方法。
Radiographic testing is a widely used method of welding quality control. With the radiographic testing weld image is acquired, it is manually analyzed to evaluate the welding quality. Extensive research has been developed on automatic extraction and recognition of welding defects, in order to ensure the reliability and stability of evaluation, and reduce the artificial differences of evaluation. However, the research results can not meet the practical application. The main problems include the accurate extraction of small welding defects, effective feature description and accurate classification of welding defects. Considering the generalized application of radiography testing, as well as the similarity among images obtained using all kinds of radiographic testing methods, the methods are studied in depth to extract and recognize the welding defects from digital radiograph images. First of all, a complete and practical extraction process of welding defects was designed, and then we did some research on the location of weld zone, extraction of non-crack welding defects, as well as extraction of crack welding defects; Secondly, we studied on the feature description and selection of welding defects; last but not least, we studied on the classification of welding defects. The chief work and innovation of present study can be drawn as follows.
(1) To determine the weld zone on the radiograph image, a step-refining location method of weld zone was proposed. That is to say, firstly, locate the rough weld zone through the characteristic detection of strip region; then rapidly locate the weld boundaries based on points calculating of adjacent intervals of line gray curves. It is suggested that the present method can accurately locate the weld boundaries, besides its better adaption and practicability, which is less affected by the non-uniform image brightness and the change of weld position and distribution.
(2) To extract non-crack welding defects, based on the PDE theory of image segmentation, the accelerated IAC model was obtained by introducing accelerated contraction item into IAC model, and then an extraction method of non-crack welding defects using the accelerated IAC model was proposed. At first, morphological transform was applied to remove the background of weld image; secondly, the range of image gray was narrowed through brightness transform and an image was transformed into a set of vector images by multi-threshold way; thirdly, the probabilistic relaxation method was adopted to reduce the local ambiguity; finally, the accelerated IAC model was applied to block-by-block extract non-crack welding defects, with combining proper post-processing. It is shown that the present method can effectively extract the non-crack welding defects, such as porosity, slag inclusion, incomplete fusion and incomplete penetration, and the application of the accelerated IAC model can effectively reduce the needed number of iterative loops, which is quite practicable.
(3) To extract crack welding defects, based on the Beamlet theory of multi-scale geometric analysis, an extraction method of crack welding defects lying on the Beamlet analysis was put forward. For one thing, morphological transform was brought to remove the background of weld image and shield the non-crack welding defects; for another, brightness transform was processed block-by-block, and Beamlet analysis and optimal BD-RDP were applied to determine several proper beamlets as the detection result of crack welding defects; in the end, appropriate post-processing was adopted by using morphological dilation, thinning and other operations. It is shown that the present method can effectively extract crack welding defects, such as longitudinal crack, transversal crack and radiate crack. The result with wide practicability can reflect the shape and extension of crack welding defects.
(4) As for the feature description and selection of welding defects, the paper combining the common description method and expert experience, preliminarily determined nine features for describing welding defect. In order to select the most effective features, a feature selection algorithm was proposed and applied which combine within-class variance with correlation measure; subsequently, the most effective five features were selected from the nine to describe welding defect. In the four removed features, the flatness (FLT), symmetry (SYM) and unsharpness (USP) were presented by KATOH Y according to experience and commonly used by others. While the result of feature selection gives explanation that the removed features are invalid or redundant, with unobvious effect on classification of welding defects.
(5) In the classification of welding defects, based on the support vector machine theory, the binary tree SVM algorithm embedded WVCMFS was adopted for classification of welding defects, and then the most effective structure was determined experimentally. In order to further improve the classification performance, the paper improves from two aspects, which are including the proposition and use of an uncorrelated feature transform algorithm (LUFT and NLUFT), as well as a kind of fuzzy support vector machine for imbalanced data classification (IC-FSVM). The result shown that the binary tree IC-FSVM algorithm embedded WVCMFS has better classification performance when adopts the features determined in this paper to describe welding defects. If more new features are applied to describe welding defects, the binary tree IC-FSVM algorithm embedded WVCMFS and NLUFT could be considered.
(1)针对焊缝区域确定问题,提出了一种逐级细化确定焊缝区域的方法。该方法首先通过条带特征检测确定焊缝所在大致区域;然后基于线灰度曲线相邻间隔点数计算快速确定准确的焊缝边界。结果表明,该方法受图像亮度不均匀以及焊缝在图像中位置和分布变化等影响较小,能够较好地确定出焊缝边界,具有较强的适应性和实用性。
(2)针对非裂纹类焊接缺陷提取问题,立足于图像分割的偏微分方程理论,将“加速收缩项”引入IAC模型得到加速IAC模型,在此基础上,提出了基于加速IAC模型的非裂纹类焊接缺陷提取方法。该方法首先使用形态学变换去除焊缝区域图像的背景;然后通过亮度变换缩小图像灰度范围,并以多阈值的方式将一幅图像变换为一组矢量图像;再采用概率松弛法降低图像区域模糊度并减少局部矛盾;最后应用加速IAC模型对焊接区域图像逐块分割提取缺陷,并进行适当的后处理。结果表明,该方法能够有效提取气孔、夹杂、未熔合、未焊透等非裂纹类焊接缺陷,且加速IAC模型的应用有效减少了普通IAC模型所需的迭代次数,具有较好的通用性。
(3)针对裂纹类焊接缺陷提取问题,立足于多尺度几何分析中的Beamlet理论,提出了基于Beamlet分析的裂纹类焊接缺陷提取方法。该方法首先使用形态学变换去除焊缝区域图像的背景同时屏蔽图像中可能包含的非裂纹类焊接缺陷;然后逐块进行亮度变换处理,并通过Beamlet分析及最优BD-RDP来确定符合条件的若干beamlet作为裂纹特征检测结果;最后使用形态学膨胀、细化等操作进行适当的后处理。结果表明,该方法能够有效提取纵向裂纹、横向裂纹、放射状裂纹等裂纹类焊接缺陷,可以较好地反映裂纹类缺陷的形状和延展特点,具有较好的实用性。
(4)在焊接缺陷的特征描述和特征选择方面,本文首先结合常见的描绘方法和专家经验初步确定了9个用于描述焊接缺陷的特征;然后为了挑选出描述焊接缺陷的最有效的特征,提出并应用了一种类内方差与相关度结合的特征选择算法(WVCMFS算法),从初步确定的特征中挑选出5个描述焊接缺陷的最有效特征。其中被去除的4个特征中,平坦性(FLT)、对称性(SYM)和不尖锐性(USP)特征是加藤雄平等基于经验提出并经常采用的特征,而本文的特征选择结果表明这些特征属于无效或冗余特征,对焊接缺陷的分类并不具有明显作用。
(5)在焊接缺陷的分类识别方面,立足于支持向量机理论,提出采用嵌入WVCMFS的二叉树SVM方法进行焊接缺陷分类识别,并通过实验确定了该方法的最有效结构。为了进一步提高其分类性能,本文从两个方面进行改进,包括提出并使用一种统计不相关特征变换算法(LUFT和NLUFT),以及提出并使用一种可用于不平衡数据分类的模糊支持向量机(IC-FSVM)。结果表明,采用本文确定的特征进行焊接缺陷描述时,使用嵌入WVCMFS的二叉树IC-FSVM方法即可获得较好的焊接缺陷分类性能;若采用更多新特征进行焊接缺陷描述,则可以考虑使用嵌入WVCMFS和NLUFT的二叉树IC-FSVM方法。
Radiographic testing is a widely used method of welding quality control. With the radiographic testing weld image is acquired, it is manually analyzed to evaluate the welding quality. Extensive research has been developed on automatic extraction and recognition of welding defects, in order to ensure the reliability and stability of evaluation, and reduce the artificial differences of evaluation. However, the research results can not meet the practical application. The main problems include the accurate extraction of small welding defects, effective feature description and accurate classification of welding defects. Considering the generalized application of radiography testing, as well as the similarity among images obtained using all kinds of radiographic testing methods, the methods are studied in depth to extract and recognize the welding defects from digital radiograph images. First of all, a complete and practical extraction process of welding defects was designed, and then we did some research on the location of weld zone, extraction of non-crack welding defects, as well as extraction of crack welding defects; Secondly, we studied on the feature description and selection of welding defects; last but not least, we studied on the classification of welding defects. The chief work and innovation of present study can be drawn as follows.
(1) To determine the weld zone on the radiograph image, a step-refining location method of weld zone was proposed. That is to say, firstly, locate the rough weld zone through the characteristic detection of strip region; then rapidly locate the weld boundaries based on points calculating of adjacent intervals of line gray curves. It is suggested that the present method can accurately locate the weld boundaries, besides its better adaption and practicability, which is less affected by the non-uniform image brightness and the change of weld position and distribution.
(2) To extract non-crack welding defects, based on the PDE theory of image segmentation, the accelerated IAC model was obtained by introducing accelerated contraction item into IAC model, and then an extraction method of non-crack welding defects using the accelerated IAC model was proposed. At first, morphological transform was applied to remove the background of weld image; secondly, the range of image gray was narrowed through brightness transform and an image was transformed into a set of vector images by multi-threshold way; thirdly, the probabilistic relaxation method was adopted to reduce the local ambiguity; finally, the accelerated IAC model was applied to block-by-block extract non-crack welding defects, with combining proper post-processing. It is shown that the present method can effectively extract the non-crack welding defects, such as porosity, slag inclusion, incomplete fusion and incomplete penetration, and the application of the accelerated IAC model can effectively reduce the needed number of iterative loops, which is quite practicable.
(3) To extract crack welding defects, based on the Beamlet theory of multi-scale geometric analysis, an extraction method of crack welding defects lying on the Beamlet analysis was put forward. For one thing, morphological transform was brought to remove the background of weld image and shield the non-crack welding defects; for another, brightness transform was processed block-by-block, and Beamlet analysis and optimal BD-RDP were applied to determine several proper beamlets as the detection result of crack welding defects; in the end, appropriate post-processing was adopted by using morphological dilation, thinning and other operations. It is shown that the present method can effectively extract crack welding defects, such as longitudinal crack, transversal crack and radiate crack. The result with wide practicability can reflect the shape and extension of crack welding defects.
(4) As for the feature description and selection of welding defects, the paper combining the common description method and expert experience, preliminarily determined nine features for describing welding defect. In order to select the most effective features, a feature selection algorithm was proposed and applied which combine within-class variance with correlation measure; subsequently, the most effective five features were selected from the nine to describe welding defect. In the four removed features, the flatness (FLT), symmetry (SYM) and unsharpness (USP) were presented by KATOH Y according to experience and commonly used by others. While the result of feature selection gives explanation that the removed features are invalid or redundant, with unobvious effect on classification of welding defects.
(5) In the classification of welding defects, based on the support vector machine theory, the binary tree SVM algorithm embedded WVCMFS was adopted for classification of welding defects, and then the most effective structure was determined experimentally. In order to further improve the classification performance, the paper improves from two aspects, which are including the proposition and use of an uncorrelated feature transform algorithm (LUFT and NLUFT), as well as a kind of fuzzy support vector machine for imbalanced data classification (IC-FSVM). The result shown that the binary tree IC-FSVM algorithm embedded WVCMFS has better classification performance when adopts the features determined in this paper to describe welding defects. If more new features are applied to describe welding defects, the binary tree IC-FSVM algorithm embedded WVCMFS and NLUFT could be considered.
引文
[1] GRAY J, TILLACK G R. X-ray imaging methods over the last 25 years - new advances and capabilities [C]. 7th Annual Review of Progress in Quantitative Nondestructive Evaluation, Ames, USA, 2001: 16-32.
[2]张天鹏.射线检测[M].北京:中国劳动社会保障出版社, 2007.
[3]机械工程学会无损检测分会.射线检测[M].北京:机械工业出版社, 2004.
[4] GAYER A, SAYA A, SHILOH A. Automatic recognition of welding defects in real-time radiography [J]. NDT&E International, 1990, 23(3): 131-136.
[5] HYATT R, KECHTER G E, NAGASHIMA S. A method for segmentation in digital radiographic of pipe line girth welds [J]. Materials Evaluation, 1996, 54(8): 925-928.
[6]孙忠诚,李鹤歧,陶维道,等.焊缝X射线实时探伤数字图象处理方法研究[J].无损检测, 1992, 14(2): 37-40.
[7] LIAO T W, LI Y M. Automated radiographic NDT system for weld inspection: Part II - flaw detection [J]. NDT&E International, 1998, 31(3): 183-192.
[8] LIAO T W, LI D M, LI Y M. Detection of welding flaws from radiographic images with fuzzy clustering methods [J]. Fuzzy Sets and Systems, 1999, 108: 145-158.
[9] LASHKIA V. Defect detection in X-ray images using fuzzy reasoning [J]. Image and Vision Computing, 2001, 19: 261-269.
[10]孙怡,孙洪雨,白鹏,等. X射线焊缝图像中缺陷的实时检测方法[J].焊接学报, 2004, 25(2): 115-118.
[11] TIAN Y, DU D, CAI G R, et al. Automatic defect detection in X-ray images using image data fusion [J]. Tsinghua Science and Technology, 2006, 11(6): 720-724.
[12] FELISBERTO M K, LOPES H S, CENTENO T M, et al. An object detection and recognition system for weld bead extraction from digital radiographs [J]. Computer Vision and Image Understanding, 2006, 102: 238–249.
[13]刚铁,王东华.基于自适应形态学滤波的X射线图像的缺陷提取[J].机械工程学报, 2001, 37(5): 85-89.
[14]罗爱民.基于数学形态学的射线检测数字图像处理技术[D].成都:四川大学制造科学与工程学院, 2007.
[15] ALAKNANDA, ANAND R S, KUMAR P, et al. Flaw detection in radiographic weld images using morphological approach [J]. NDT&E International, 2006, 39: 29-33.
[16] ALAKNANDA, ANAND R S, KUMAR P, et al. Flaw detection in radiographic weldment images using morphological watershed segmentation technique [J]. NDT&EInternational, 2009, 42: 2-8.
[17] JACOBSEN C, ZSCHERPEL U, BAM, et al. Automated evaluation of digitized radiographs with neuronal methods [C]. Proceedings of Computerized Tomography for Industrial Applications and Image Processing in Radiology, Berlin, Germany, 1999: 141-152.
[18]张晓光,徐健健,任世锦.基于字典的概率松弛法对焊缝图像中裂纹缺陷的提取[J].华东理工大学学报, 2004, 30(5): 605-608.
[19] WANG Y, SUN Y, LV P, et al. Detection of line weld defects based on multiple thresholds and support vector machine [J]. NDT&E International, 2008, 41: 517-524.
[20]加藤雄平,等.放射線透過写真の自動合否判定システムの開発(第1报)—画像处理によゐ欠陷像の抽出[J].非破壞検查, 1992, 41(4): 186-195.
[21]何怡,杨永才,王海鹏.焊缝底片计算机辅助识别的研究[J].无损检测, 2000, 22(12): 548-550.
[22]戴明,吴林,李岩.基于势函数法的铝合金焊缝缺陷识别[J].机器人, 2001, 23(7): 701-704.
[23] WANG G, LIAO T W. Automatic identification of different types of welding defects in radiographic images [J]. NDT&E International, 2002, 35: 519-528.
[24] ZHANG X G, ZHU Z C, XU J H, et al. The classification algorithm of defects in weld image based on asymmetrical SVMs [C]. Proceedings of International Conference on Control and Automation, Budapest, Hungary, 2005(2): 1215-1219.
[25] NACEREDDINE N, TRIDI M, LTSI, et al. Statistical tools for weld defect evaluation in radiographic testing [C]. Proceedings of European NDT Conference, Berlin, Germany, 2006: 1-22.
[26]刚铁,王东华. X射线检测图象中缺陷的自动提取和分割[J].焊接, 2001, (5): 6-9.
[27]张晓光,高顶.射线检测焊接缺陷的提取和自动识别[M].北京:国防工业出版社, 2004.
[28] GONZALES R C, WOODS R E.数字图像处理[M].阮秋琦,阮宇智,等译.北京:电子工业出版社, 2006: 460-514.
[29] SONKA M, HLAVAC V, BOYLE R.图像处理、分析与机器视觉[M].艾海舟,武勃,等译.北京:人民邮电出版社, 2003: 83-155.
[30]王爱民,沈兰荪.图像分割研究综述[J].测控技术, 2000, 19(5): 1-6.
[31] BARASH D, SCHLICK T. Multiplicative operator splittings in nonlinear diffusion: from spatial splitting to multiple timesteps [J]. Journal of Mathematical Image and Vision, 2003, 19(1): 33-48.
[32] CASELLES V, LISANI J L, MOREL J M, et al. Shape preserving local histogram modification [J]. IEEE Transactions on Image Processing, 1999, 8(2): 220-230.
[33] AUBERT G, VESE L. A variational method in image recovery [J]. SIAM Journal on Numerical Analysis, 1997, 34(5): 1948-1979.
[34] SUMENGEN B, MANJUNATH B S. Edgeflow-driven variational image segmentation: theory and performance evolution [J]. IEEE Transactions on PAMI, 2005, 8: 1-35.
[35] KASS M, WITKIN A, TERZOPOLOS D. Snakes: active contour models [J]. International Journal of Computer Vision, 1988, (1): 321-331.
[36] CASELLES V, MOREL J M, SAPIRO G. Geodesic active contours [J]. International Journal of Computer Vision, 1997, 22: 61-79.
[37] MUMFORD D, SHAH J. Boundary detection by minimizing functionals [C]. Proceedings of International Conference on Computer Vision and Pattern Recognition, San Francisco, USA, 1985: 22-26.
[38] MUMFORD D, SHAH J. Optimal approximations by piecewise smooth functions and associated variational problems [J]. Communications on Pure and Applied Mathematics, 1989, XLII: 577-685.
[39] CHAN T F, VESE L A. Active contours without edges [J]. IEEE Transactions on Image Processing, 2001, 10(2): 266-277.
[40] SAGIV C, SOCHEN N A, ZEEVI Y Y. Integrated active contours for texture segmentation [J]. IEEE Transactions on Image Processing, 2006, 15(6): 1633-1646.
[41] POGGIO T. Marr’s computational approach to vision [J]. Trends in NeuroSciences, 1981, 4(10): 258-262.
[42]李国友.基于广义模糊集及主动轮廓线模型的图像分割方法研究[D].秦皇岛:燕山大学电气工程学院, 2006.
[43]王大凯,侯榆青,彭进业.图像处理的偏微分方程方法[M].北京:科学出版社, 2008.
[44]华东师范大学数学系.数学分析[M].北京:高等教育出版社, 2001.
[45]贾迪野.基于偏微分方程的图像平滑与分割研究[D].哈尔滨:哈尔滨工程大学计算机科学与技术学院, 2005.
[46]周昌雄.基于活动轮廓模型的图像分割方法研究[D].南京:南京航空航天大学自动化学院, 2005.
[47] OSHER S. Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations [J]. Journal of Computational Physics, 1988, 79(1): 12-49.
[48] ZHAO H K, CHAN T, MERRIMAN B, et al. A variational level set approach tomultiphase motion [J]. Journal of Computational Physics, 1996, 127: 179-195.
[49]段先华.核磁共振图像分割与运动分析若干技术研究[D].南京:南京理工大学计算机科学与技术学院, 2005.
[50] SAPIRO G.几何偏微分方程和图像分析[M].北京:世界图书出版社, 2003.
[51] CHUNG D H, SAPIRO G. On the level lines and geometry of vector-valued images [J]. IEEE Signal Processing Letters, 2000, 7(9): 241-243.
[52] SOILLE P.形态学图像分析原理与应用[M].王小鹏,等译.北京:清华大学出版社, 2008: 89-93.
[53]高木干雄,下田阳久.图像处理技术手册[M].孙卫东,等译.北京:科学出版社, 2007: 1335-1344.
[54] PELEG S. A new probabilistic relaxation scheme [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1980, 2(4): 362-369.
[55] BHANU B, FAUGERAS O D. Segmentation of images having unimodal distributions [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1982, 4(3): 408-419.
[56]焦李成,侯彪,王爽,等.图像多尺度几何分析理论与应用-后小波分析理论与应用[M].西安:西安电子科技大学出版社, 2008.
[57] CANDES E J. Ridgelets: theory and application [D]. Department of Statistics, Stanford University, Stanford, California, 1998.
[58] DONOHO D L. Orthonormal ridgelets and linear singularities [R]. Department of Statistics, Stanford University, Stanford, California, 1998.
[59] CANDES E J. Monoscale ridgelets for the representation of images with edges [R]. Department of Statistics, Stanford University, Stanford, California, 1999.
[60] CANDES E J, DONOHO D L. Curvelets - a surprisingly effective nonadaptive representation for objects with edges [R]. Department of Statistics, Stanford University, Stanford, California, 1999.
[61] DONOHO D L, DUNCAN M R. Digital curvelet transform: strategy, implementation, and experiments [C]. Proceedings of the International Society for Optical Engineering, Orlando, USA, 2000, 4056: 12-30.
[62] CANDES E, DEMANET L, DONOHO D, et al. Fast discrete curvelet transforms [J]. Multiscale Modeling and Simulation, 2006, 5(3): 861-899.
[63] MEYER F G, COIFMAN R R. Brushlets: a tool for directional image analysis and image compression [J]. Applied and Computational Harmonic Analysis, 1997, 4(2): 147-187.
[64] MEYER F G, COIFMAN R R. Directional image compression with brushlets [C], Processing of the IEEE-SP International Symposium on Time-Frequency and Time-ScaleAnalysis, 1996, 189-192.
[65] DONOHO D L. Wedgelets: nearly minimax estimation of edges [J]. Annals of Statistics, 1999, 27(3), 859-897.
[66] ROMBERG J K, WAKIN M, BARANIUK R. Multiscale wedgelet image analysis: fast decompositions and modeling [C]. Proceedings of IEEE International Conference on Image Processing, Rochester, USA, 2002(3): 585-588.
[67] DONOHO D L, HUO X M. Beamlets and multiscale image analysis [J]. Lecture Notes in Computational Science and Engineering, 2002, 20: 149-196.
[68] DONOHO D L. Beamlet Pramids: a new form of multiresolution analysis, suited for extracting lines, curves, and objects from very noisy image data [C]. Proceedings of the International Society for Optical Engineering, San Diego, USA, 2000, 4119, 434-444.
[69] HUO X M, DONOHO D. Recovering filamentary objects in severely degraded binary images using beamlet-driven partitioning [C]. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, Orlando, USA, 2002, 2: 1265-1268.
[70] Beamlab website: http://www-stat.stanford.edu/~beamlab/.
[71] DO M N, MARTIN, V. Contourlet: a new directional multiresolution image representation [C]. Conference on Signal, Systems and Computers, Pacific Groove, USA, 2002: 497-501.
[72] DO M N. Contourlets and sparse image expansions [C]. Proceedings of the International Society for Optical Engineering, San Diego, USA, 2003, 5207: 560-570.
[73] LU Y, DO M N. CRISP - contourlet: a critically sampled directional multiresolution image representation [C]. Proceedings of the International Society for Optical Engineering, San Diego, USA, 2003, 5207: 655-665.
[74] CUNHA A L, ZHOU J P, DO M N. The nonsubsampled contourlet transform: theory, design, and applications [J]. IEEE Transactions on Image Processing, 2006, 15(10), 3089-3101.
[75] PENNEC E L, MALLAT S. Image compression with geometrical wavelets [C]. Proceedings of IEEE International Conference on Image Processing, Vancouver, Canada, 2000, 1: 661-664.
[76] PENNEC E L, MALLAT S. Bandelet image approximation and compression [J]. Multiscale Modeling and Simulation, 2005, 4(3): 992-1039.
[77] PENNEC E L, MALLAT S. Sparse geometric image representation with bandelets [J]. IEEE Transaction on Image Processing, 2003, 14(4): 423-438.
[78] VELISAVLJEVIC V, BEFERULL-LOZANO B, VETTERLI M, et al. Directionlets: anisotropic multidirectional representation with separable filtering [J]. IEEE Transactions on Image Processing, 2006, 15(7): 1916-1933.
[79] VELISAVLJEVIC V, BEFERULL-LOZANO B, VETTERLI M. Space-frequency quantization using directionlets [C]. Proceedings of IEEE International Conference on Image Processing, San Antonio, USA, 2007, 1: 161-164.
[80] LABATE D, LIM W Q, KUYNIOK G, et al. Sparse multidimensional representation using shearlets [C]. Proceedings of the International Society for Optical Engineering, 2005, 5914: 1-9.
[81] GUO K, LABATE D. Optimally sparse multidimensional representation using shearlets [J]. SIAM Journal on Mathematical Analysis, 2007, 39(1): 298-318.
[82] EASLEY G, LABATE D, LIM W Q. Sparse directional image representations using the discrete shearlet transform [J]. Applied and Computational Harmonic Analysis, 2008, 25(1): 25-46.
[83]屈庆春,彭玉华,杨明强.基于Beamlet变换的线特征检测[J].中国图象图形学报, 2007, 12(3): 500-504.
[84]秦襄培. MATLAB图像处理与界面编程宝典[M].北京:电子工业出版社, 2009: 470-493.
[85]林克正.基于小波分析的焊缝图象处理与识别的研究[D].哈尔滨:哈尔滨工程大学自动化学院, 2001: 81-91.
[86] LIU H, YU L A. Toward integrating feature selection algorithms for classification and clustering [J]. IEEE Transactions on Knowledge and Data Engineering, 2005, 17(4): 491-502.
[87] NARENDRA P M, FUKUNAGA K. A branch and bound algorithm for feature subset selection [J]. IEEE Transactions on Computers, 1977, 26(9): 917-922.
[88] HAMAMOTO Y, UCHIMURA S, MATSUURA Y, et al. Evaluation of the branch and bound algorithm for feature selection [J]. Pattern Recognition Letters, 1990, 11(7): 453-456.
[89] CHEN X W. An improved branch and bound algorithm for feature selection [J]. Pattern Recognition Letters, 2003, 24(12): 1925-1933.
[90] MAO K Z. Fast orthogonal forward selection algorithm for feature subset selection [J]. IEEE Transactions on Neural Networks, 2002, 13(5): 1218-1224.
[91] PARSONS L, HAQUE E, LIU H. Subspace clustering for high dimensional data: a review [J]. ACM SIGKDD Explorations Newsletter, 2004, 6(1): 90-105.
[92] FURLANELLO C, SERAFINI M, MERLER S, et al. An accelerated procedure for recursive feature ranking on microarray data [J]. Neural Networks, 2003, 16(5-6): 641-648.
[93] TSYMBAL A, PUURONEN S, PATTERSON D W. Ensemble feature selection with the simple Bayesian classification [J]. Information Fusion, 2003, 4(2): 87-100.
[94] SUN Z H, BEBIS G, MILLER R. Object detection using feature subset selection [J]. Pattern Recognition, 2004, 37(11): 2165-2176.
[95] CHIANG L H, PELL R J. Genetic algorithms combined with discriminant analysis for key variable identification [J]. Journal of Process Control, 2004, 14(2): 143-155.
[96]毛勇.基于支持向量机的特征选择方法的研究与应用[D].杭州:浙江大学信息科学与工程学院, 2006.
[97] LIU H, MOTODA H, DASH M. A monotonic measure for optimal feature selection[C]. Proceedings of the 10th European Conference on Machine Learning, Chemnitz, Germany, 1998: 101-106.
[98] KONONENKO I. Estimating attributes: analysis and extensions of RELIEF[C]. Proceedings of the 7th European Conference on Machine Learning, Catania, Italy, 1994: 171-182.
[99] HALL M A. Correlation-based feature selection for machine learning[D]. Hamilton: University of Waikato, 1999.
[100] KIRA K, RENDELL L A. A practical approach to feature selection [C]. Proceedings of the 9th European Conference on Machine Learning, Aberdeen, Scotland, 1992: 249-256.
[101]詹德川,周志华.基于相关投影分的特征选择算法[J].计算机科学与探索, 2007, 1(2): 138-145.
[102] DY J G, BRODLEY C E. Feature subset selection and order identification for unsupervised learning [C]. Proceedings of the 17th International Conference on Machine Learning, Stanford, USA, 2000: 247-254.
[103] XIONG M, FANG X, ZHAO J. Biomarker identification by feature wrappers [J]. Genome Research, 2001, 11: 1878-1887.
[104] VERIKAS A, BACAUSKIENE M. Feature selection with neural networks [J]. Pattern Recognition Letters, 2002, 23(11): 1323-1335.
[105] GUYON I, WESTON J, BARNHILL S, et al. Gene selection for cancer classification using support vector machines [J]. Machine Learning, 2002, 46(1-3): 389-422.
[106] HSU W H. Genetic wrappers for feature selection in decision tree induction and variable ordering in Bayesian network structure learning [J]. Information Sciences, 2004, 163(1-3):103-122.
[107] HUANG Y, SHIAN-SHYONG T, WU G, et al. A two-phase feature selection method using both filter and wrapper [C]. Proceedings of IEEE International Conference on Systems, Man, and Cybernetics, Tokyo, Japan, 1999, 2: 132-136.
[108] DAS S. Filters, wrappers and a boosting-based hybrid for feature selection [C]. Proceedings of the 18th International Conference on Machine Learning, Williamstown, USA, 2001: 74-81.
[109] XING E P, JORDAN M I, KARP R M. Feature selection for high-dimensional genomic microarry data [C]. Proceedings of the 18th International Conference on Machine Learning, Williamstown, USA, 2001: 601-608.
[110]刘成林,谭铁牛.模式识别研究进展[EB/OL]. http://liama.ia.ac.cn/wiki/.
[111] UCI Machine Learning Repository [DB/OL]. http://archive.ics.uci.edu/ml/.
[112] ZHOU Z H, YU Y. Ensembling local learners through multimodal perturbation [J]. IEEE Transactions on Systems, Man and Cybemetics-B, 2005, 35(4): 725-735.
[113] CHAWLA N V, JAPKOWICZ N, KOTCZ A. Editorial: special issue on learning from imbalanced data sets [J]. ACM SIGKDD Explorations, 2004, 6(1): 1-6.
[114] WEISS G M. Mining with rarity: a unifying framework [J]. ACM SIGKDD Explorations, 2004, 6(1): 7-19.
[115]叶志飞,文益民,吕宝粮.不平衡分类问题研究综述[J].智能系统学报, 2009, 4(2): 148-156.
[116] CHAWLA N V, BOWYER K W, HALL L O, et al. SMOTE: synthetic minority over-sampling technique [J]. Journal of Artificial Intelligence Research, 2002, 16: 321-357.
[117] LEE S S. Noisy replication in skewed binary classification [J]. Computational Statistics and Data Analysis, 2000, 34: 165-191.
[118] KUBAT M, HOLTE R, MATWIN S. Learning when negative examples abound [J]. Learning when negative examples abound [C]. Proceedings of the 9th European Conference on Machine Learning, Prague, Czechoslovakia, 1997: 146-153.
[119] KUBAT M, MATWIN S. Addressing the curse of imbalanced training sets: one-sided selection [C]. Proceedings of the 14th International Conference on Machine Learning, San Francisco, 1997: 179-186.
[120] DRUMMOND C, HOLTE R C. C4.5, class imbalance, and cost sensitivity: why under-sampling beats over-sampling [C]. Workshop on Learning from Imbalanced Data Sets II, International Conference on Machine Learning, Washington DC, 2003: 152-154.
[121] CHEN X, GERLACH B, CASASENT D. Pruning support vectors for imbalance data classification [C]. Proceedings of the International Joint Conference on Neural Networks, Montreal, 2005: 1883-1888.
[122] KOTSIANTIS S B, PINTELAS P E. Mixture of expert agents for handling imbalanced data sets [J]. Annals of Mathematics, Computing & Teleinformatics, 2003, 1(1): 46-55.
[123] ESTABROOKS A, TAEHO J, JAPKOWICZ N. A multiple resampling method for learning from imbalanced data sets [J]. Computational Intelligence, 2004, 20(1): 18-36.
[124] CHEW H G, CRISP D J, BOGNER R E, et al. Target detection in radar imagery using support vector machines with training size biasing [C]. Proceedings of the 6th International Conference on Control, Automation, Robotics and Vision, Singapore, 2000.
[125] CHEW H G, LIM C C, BOGNER R E. Dual-nu support vector machines applications in multi-class image recognition [J]. Proceedings of the International Conference on Optimization Techniques and Applications, Ballarat, 2004: 1-11.
[126] VAPNIK V N. The Nature of Statistical Learning Theory [M]. New York: Springer-Verlag, 1995.
[127] VAPNIK V N. An overview of statistical learning theory [J]. IEEE Transactions on Neural Networks, 1999, 10(5): 988-998.
[128]张学工.关于统计学习理论与支持向量机[J].自动化学报, 2000, 26(1): 32-42.
[129] DUDA R O, HART P E, STORK D G.模式分类[M].李宏东,姚天翔,等译.北京:机械工业出版社, 2003: 177-183.
[130] THEODORIDIS S, KOUTROUMBAS K.模式识别[M].李晶皎,王爱侠,张广渊,等译.北京:电子工业出版社, 2006: 60-68
[131] FRIESS T T, CRISTIANINI N, CAMPBELL C. The kernel-adatron algorithm: a fast and simple learning procedure for support vector machines [C]. Proceedings of the 15th International Conference on Machine Learning, Madison, 1998: 188-196.
[132] SCHOLKOPF B, SMOLA A J, WILLIAMSON, et al. New support vector algorithms [J]. Neural Computation, 2000, 12(5): 1207-1245.
[133] SUYKENS J A K, VANDEWALLE J. Least square support vector machine classifiers [J]. Neural Processing Letters, 1999, 9: 293-300.
[134] SCHOLKOPF B, PLATT J C, SHAWE T J, et al. Estimating the support of a high-dimensional distribution [J]. Neural Computation, 2001, 13(7): 1443-1471.
[135] LEE Y J, MANGASARIAN O L. RSVM: reduced support vector machines [C]. Proceedings of the First SIAM International Conference on Data Mining, 2001.
[136] CHEW H G, BOGNER R E, LIM C C. Dual-nu support vector machine with error rateand training size biasing [C]. Proceedings of the 26th IEEE International Conference on Acoustics, Speech, and Signal Processing, Salt Lake City, 2001: 1269-1272.
[137] LIN C F, WANG S. Fuzzy support vector machines [J]. IEEE Transactions on Neural Networks, 2002, 13(2): 464-471.
[138]张翔,肖小玲,徐光祐.基于样本之间紧密度的模糊支持向量机方法[J].软件学报, 2006, 17(5): 951-958.
[139]唐浩,廖与禾,孙峰,等.具有模糊隶属度的模糊支持向量机算法[J].西安交通大学学报, 2009, 43(7): 40-43.
[140] WESTON J, WATKINS C. Support vector machines for multi-class pattern recognition [C]. Proceedings of the 7th European Symposium on Artificial Neural Networks, Bruges, 1999: 219-224.
[141]唐发明.基于统计学习理论的支持向量机算法研究[D].武汉:华中科技大学控制科学与工程系, 2005.
[142]应自炉,唐京海,李景文,等.支持向量鉴别分析及在人脸表情识别中的应用[J].电子学报, 2008, 36(4): 725-730.
[143]杨健.线性投影分析的理论与算法及其在特征抽取中的应用研究[D].南京:南京理工大学计算机科学与技术学院, 2002.
[144] JIN Z, YANG J, TANG Z, et al. A theorem on the uncorrelated optimal discriminant vectors [J]. Pattern Recognition, 2001, 34(10): 2041-2047.
[145] JIN Z, YANG J, HU Z, et al. Face recognition based on the uncorrelated discriminant transformation [J]. Pattern Recognition, 2001, 34(7): 1405-1416.
[146] XIANG C, FAN X, LEE T H. Face recognition using recursive fisher linear discriminant [J]. IEEE Transactions on Image Processing, 2006, 15(8): 2097-2105.
[147] TAO Q, CHU D, WANG J. Recursive support vector machines for dimensionality reduction [J]. IEEE Transactions on Neural Networks, 2008, 19(1): 189-193.
[148] YE J, XIONG T. Computational and theoretical analysis of null space and orthogonal linear discriminant analysis [J]. Journal of Machine Learning Research, 2006, 7(7): 1183-1204.
[149] TAO Q, WU G, WANG J. The theoretical analysis of FDA and applications [J]. Pattern Recognition, 2006, 39(6): 1199-1204.
[150]章万锋.基于PCA与LDA的说话人识别研究[D].杭州:浙江大学计算机科学与技术学院, 2004.
[151] ZAFEIRIOU S, TEFAS A, PITAS I. Minimum class variance support vector machines [J]. IEEE Transactions on Image Processing, 2007, 16(10): 2551-2564.
[2]张天鹏.射线检测[M].北京:中国劳动社会保障出版社, 2007.
[3]机械工程学会无损检测分会.射线检测[M].北京:机械工业出版社, 2004.
[4] GAYER A, SAYA A, SHILOH A. Automatic recognition of welding defects in real-time radiography [J]. NDT&E International, 1990, 23(3): 131-136.
[5] HYATT R, KECHTER G E, NAGASHIMA S. A method for segmentation in digital radiographic of pipe line girth welds [J]. Materials Evaluation, 1996, 54(8): 925-928.
[6]孙忠诚,李鹤歧,陶维道,等.焊缝X射线实时探伤数字图象处理方法研究[J].无损检测, 1992, 14(2): 37-40.
[7] LIAO T W, LI Y M. Automated radiographic NDT system for weld inspection: Part II - flaw detection [J]. NDT&E International, 1998, 31(3): 183-192.
[8] LIAO T W, LI D M, LI Y M. Detection of welding flaws from radiographic images with fuzzy clustering methods [J]. Fuzzy Sets and Systems, 1999, 108: 145-158.
[9] LASHKIA V. Defect detection in X-ray images using fuzzy reasoning [J]. Image and Vision Computing, 2001, 19: 261-269.
[10]孙怡,孙洪雨,白鹏,等. X射线焊缝图像中缺陷的实时检测方法[J].焊接学报, 2004, 25(2): 115-118.
[11] TIAN Y, DU D, CAI G R, et al. Automatic defect detection in X-ray images using image data fusion [J]. Tsinghua Science and Technology, 2006, 11(6): 720-724.
[12] FELISBERTO M K, LOPES H S, CENTENO T M, et al. An object detection and recognition system for weld bead extraction from digital radiographs [J]. Computer Vision and Image Understanding, 2006, 102: 238–249.
[13]刚铁,王东华.基于自适应形态学滤波的X射线图像的缺陷提取[J].机械工程学报, 2001, 37(5): 85-89.
[14]罗爱民.基于数学形态学的射线检测数字图像处理技术[D].成都:四川大学制造科学与工程学院, 2007.
[15] ALAKNANDA, ANAND R S, KUMAR P, et al. Flaw detection in radiographic weld images using morphological approach [J]. NDT&E International, 2006, 39: 29-33.
[16] ALAKNANDA, ANAND R S, KUMAR P, et al. Flaw detection in radiographic weldment images using morphological watershed segmentation technique [J]. NDT&EInternational, 2009, 42: 2-8.
[17] JACOBSEN C, ZSCHERPEL U, BAM, et al. Automated evaluation of digitized radiographs with neuronal methods [C]. Proceedings of Computerized Tomography for Industrial Applications and Image Processing in Radiology, Berlin, Germany, 1999: 141-152.
[18]张晓光,徐健健,任世锦.基于字典的概率松弛法对焊缝图像中裂纹缺陷的提取[J].华东理工大学学报, 2004, 30(5): 605-608.
[19] WANG Y, SUN Y, LV P, et al. Detection of line weld defects based on multiple thresholds and support vector machine [J]. NDT&E International, 2008, 41: 517-524.
[20]加藤雄平,等.放射線透過写真の自動合否判定システムの開発(第1报)—画像处理によゐ欠陷像の抽出[J].非破壞検查, 1992, 41(4): 186-195.
[21]何怡,杨永才,王海鹏.焊缝底片计算机辅助识别的研究[J].无损检测, 2000, 22(12): 548-550.
[22]戴明,吴林,李岩.基于势函数法的铝合金焊缝缺陷识别[J].机器人, 2001, 23(7): 701-704.
[23] WANG G, LIAO T W. Automatic identification of different types of welding defects in radiographic images [J]. NDT&E International, 2002, 35: 519-528.
[24] ZHANG X G, ZHU Z C, XU J H, et al. The classification algorithm of defects in weld image based on asymmetrical SVMs [C]. Proceedings of International Conference on Control and Automation, Budapest, Hungary, 2005(2): 1215-1219.
[25] NACEREDDINE N, TRIDI M, LTSI, et al. Statistical tools for weld defect evaluation in radiographic testing [C]. Proceedings of European NDT Conference, Berlin, Germany, 2006: 1-22.
[26]刚铁,王东华. X射线检测图象中缺陷的自动提取和分割[J].焊接, 2001, (5): 6-9.
[27]张晓光,高顶.射线检测焊接缺陷的提取和自动识别[M].北京:国防工业出版社, 2004.
[28] GONZALES R C, WOODS R E.数字图像处理[M].阮秋琦,阮宇智,等译.北京:电子工业出版社, 2006: 460-514.
[29] SONKA M, HLAVAC V, BOYLE R.图像处理、分析与机器视觉[M].艾海舟,武勃,等译.北京:人民邮电出版社, 2003: 83-155.
[30]王爱民,沈兰荪.图像分割研究综述[J].测控技术, 2000, 19(5): 1-6.
[31] BARASH D, SCHLICK T. Multiplicative operator splittings in nonlinear diffusion: from spatial splitting to multiple timesteps [J]. Journal of Mathematical Image and Vision, 2003, 19(1): 33-48.
[32] CASELLES V, LISANI J L, MOREL J M, et al. Shape preserving local histogram modification [J]. IEEE Transactions on Image Processing, 1999, 8(2): 220-230.
[33] AUBERT G, VESE L. A variational method in image recovery [J]. SIAM Journal on Numerical Analysis, 1997, 34(5): 1948-1979.
[34] SUMENGEN B, MANJUNATH B S. Edgeflow-driven variational image segmentation: theory and performance evolution [J]. IEEE Transactions on PAMI, 2005, 8: 1-35.
[35] KASS M, WITKIN A, TERZOPOLOS D. Snakes: active contour models [J]. International Journal of Computer Vision, 1988, (1): 321-331.
[36] CASELLES V, MOREL J M, SAPIRO G. Geodesic active contours [J]. International Journal of Computer Vision, 1997, 22: 61-79.
[37] MUMFORD D, SHAH J. Boundary detection by minimizing functionals [C]. Proceedings of International Conference on Computer Vision and Pattern Recognition, San Francisco, USA, 1985: 22-26.
[38] MUMFORD D, SHAH J. Optimal approximations by piecewise smooth functions and associated variational problems [J]. Communications on Pure and Applied Mathematics, 1989, XLII: 577-685.
[39] CHAN T F, VESE L A. Active contours without edges [J]. IEEE Transactions on Image Processing, 2001, 10(2): 266-277.
[40] SAGIV C, SOCHEN N A, ZEEVI Y Y. Integrated active contours for texture segmentation [J]. IEEE Transactions on Image Processing, 2006, 15(6): 1633-1646.
[41] POGGIO T. Marr’s computational approach to vision [J]. Trends in NeuroSciences, 1981, 4(10): 258-262.
[42]李国友.基于广义模糊集及主动轮廓线模型的图像分割方法研究[D].秦皇岛:燕山大学电气工程学院, 2006.
[43]王大凯,侯榆青,彭进业.图像处理的偏微分方程方法[M].北京:科学出版社, 2008.
[44]华东师范大学数学系.数学分析[M].北京:高等教育出版社, 2001.
[45]贾迪野.基于偏微分方程的图像平滑与分割研究[D].哈尔滨:哈尔滨工程大学计算机科学与技术学院, 2005.
[46]周昌雄.基于活动轮廓模型的图像分割方法研究[D].南京:南京航空航天大学自动化学院, 2005.
[47] OSHER S. Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations [J]. Journal of Computational Physics, 1988, 79(1): 12-49.
[48] ZHAO H K, CHAN T, MERRIMAN B, et al. A variational level set approach tomultiphase motion [J]. Journal of Computational Physics, 1996, 127: 179-195.
[49]段先华.核磁共振图像分割与运动分析若干技术研究[D].南京:南京理工大学计算机科学与技术学院, 2005.
[50] SAPIRO G.几何偏微分方程和图像分析[M].北京:世界图书出版社, 2003.
[51] CHUNG D H, SAPIRO G. On the level lines and geometry of vector-valued images [J]. IEEE Signal Processing Letters, 2000, 7(9): 241-243.
[52] SOILLE P.形态学图像分析原理与应用[M].王小鹏,等译.北京:清华大学出版社, 2008: 89-93.
[53]高木干雄,下田阳久.图像处理技术手册[M].孙卫东,等译.北京:科学出版社, 2007: 1335-1344.
[54] PELEG S. A new probabilistic relaxation scheme [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1980, 2(4): 362-369.
[55] BHANU B, FAUGERAS O D. Segmentation of images having unimodal distributions [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1982, 4(3): 408-419.
[56]焦李成,侯彪,王爽,等.图像多尺度几何分析理论与应用-后小波分析理论与应用[M].西安:西安电子科技大学出版社, 2008.
[57] CANDES E J. Ridgelets: theory and application [D]. Department of Statistics, Stanford University, Stanford, California, 1998.
[58] DONOHO D L. Orthonormal ridgelets and linear singularities [R]. Department of Statistics, Stanford University, Stanford, California, 1998.
[59] CANDES E J. Monoscale ridgelets for the representation of images with edges [R]. Department of Statistics, Stanford University, Stanford, California, 1999.
[60] CANDES E J, DONOHO D L. Curvelets - a surprisingly effective nonadaptive representation for objects with edges [R]. Department of Statistics, Stanford University, Stanford, California, 1999.
[61] DONOHO D L, DUNCAN M R. Digital curvelet transform: strategy, implementation, and experiments [C]. Proceedings of the International Society for Optical Engineering, Orlando, USA, 2000, 4056: 12-30.
[62] CANDES E, DEMANET L, DONOHO D, et al. Fast discrete curvelet transforms [J]. Multiscale Modeling and Simulation, 2006, 5(3): 861-899.
[63] MEYER F G, COIFMAN R R. Brushlets: a tool for directional image analysis and image compression [J]. Applied and Computational Harmonic Analysis, 1997, 4(2): 147-187.
[64] MEYER F G, COIFMAN R R. Directional image compression with brushlets [C], Processing of the IEEE-SP International Symposium on Time-Frequency and Time-ScaleAnalysis, 1996, 189-192.
[65] DONOHO D L. Wedgelets: nearly minimax estimation of edges [J]. Annals of Statistics, 1999, 27(3), 859-897.
[66] ROMBERG J K, WAKIN M, BARANIUK R. Multiscale wedgelet image analysis: fast decompositions and modeling [C]. Proceedings of IEEE International Conference on Image Processing, Rochester, USA, 2002(3): 585-588.
[67] DONOHO D L, HUO X M. Beamlets and multiscale image analysis [J]. Lecture Notes in Computational Science and Engineering, 2002, 20: 149-196.
[68] DONOHO D L. Beamlet Pramids: a new form of multiresolution analysis, suited for extracting lines, curves, and objects from very noisy image data [C]. Proceedings of the International Society for Optical Engineering, San Diego, USA, 2000, 4119, 434-444.
[69] HUO X M, DONOHO D. Recovering filamentary objects in severely degraded binary images using beamlet-driven partitioning [C]. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, Orlando, USA, 2002, 2: 1265-1268.
[70] Beamlab website: http://www-stat.stanford.edu/~beamlab/.
[71] DO M N, MARTIN, V. Contourlet: a new directional multiresolution image representation [C]. Conference on Signal, Systems and Computers, Pacific Groove, USA, 2002: 497-501.
[72] DO M N. Contourlets and sparse image expansions [C]. Proceedings of the International Society for Optical Engineering, San Diego, USA, 2003, 5207: 560-570.
[73] LU Y, DO M N. CRISP - contourlet: a critically sampled directional multiresolution image representation [C]. Proceedings of the International Society for Optical Engineering, San Diego, USA, 2003, 5207: 655-665.
[74] CUNHA A L, ZHOU J P, DO M N. The nonsubsampled contourlet transform: theory, design, and applications [J]. IEEE Transactions on Image Processing, 2006, 15(10), 3089-3101.
[75] PENNEC E L, MALLAT S. Image compression with geometrical wavelets [C]. Proceedings of IEEE International Conference on Image Processing, Vancouver, Canada, 2000, 1: 661-664.
[76] PENNEC E L, MALLAT S. Bandelet image approximation and compression [J]. Multiscale Modeling and Simulation, 2005, 4(3): 992-1039.
[77] PENNEC E L, MALLAT S. Sparse geometric image representation with bandelets [J]. IEEE Transaction on Image Processing, 2003, 14(4): 423-438.
[78] VELISAVLJEVIC V, BEFERULL-LOZANO B, VETTERLI M, et al. Directionlets: anisotropic multidirectional representation with separable filtering [J]. IEEE Transactions on Image Processing, 2006, 15(7): 1916-1933.
[79] VELISAVLJEVIC V, BEFERULL-LOZANO B, VETTERLI M. Space-frequency quantization using directionlets [C]. Proceedings of IEEE International Conference on Image Processing, San Antonio, USA, 2007, 1: 161-164.
[80] LABATE D, LIM W Q, KUYNIOK G, et al. Sparse multidimensional representation using shearlets [C]. Proceedings of the International Society for Optical Engineering, 2005, 5914: 1-9.
[81] GUO K, LABATE D. Optimally sparse multidimensional representation using shearlets [J]. SIAM Journal on Mathematical Analysis, 2007, 39(1): 298-318.
[82] EASLEY G, LABATE D, LIM W Q. Sparse directional image representations using the discrete shearlet transform [J]. Applied and Computational Harmonic Analysis, 2008, 25(1): 25-46.
[83]屈庆春,彭玉华,杨明强.基于Beamlet变换的线特征检测[J].中国图象图形学报, 2007, 12(3): 500-504.
[84]秦襄培. MATLAB图像处理与界面编程宝典[M].北京:电子工业出版社, 2009: 470-493.
[85]林克正.基于小波分析的焊缝图象处理与识别的研究[D].哈尔滨:哈尔滨工程大学自动化学院, 2001: 81-91.
[86] LIU H, YU L A. Toward integrating feature selection algorithms for classification and clustering [J]. IEEE Transactions on Knowledge and Data Engineering, 2005, 17(4): 491-502.
[87] NARENDRA P M, FUKUNAGA K. A branch and bound algorithm for feature subset selection [J]. IEEE Transactions on Computers, 1977, 26(9): 917-922.
[88] HAMAMOTO Y, UCHIMURA S, MATSUURA Y, et al. Evaluation of the branch and bound algorithm for feature selection [J]. Pattern Recognition Letters, 1990, 11(7): 453-456.
[89] CHEN X W. An improved branch and bound algorithm for feature selection [J]. Pattern Recognition Letters, 2003, 24(12): 1925-1933.
[90] MAO K Z. Fast orthogonal forward selection algorithm for feature subset selection [J]. IEEE Transactions on Neural Networks, 2002, 13(5): 1218-1224.
[91] PARSONS L, HAQUE E, LIU H. Subspace clustering for high dimensional data: a review [J]. ACM SIGKDD Explorations Newsletter, 2004, 6(1): 90-105.
[92] FURLANELLO C, SERAFINI M, MERLER S, et al. An accelerated procedure for recursive feature ranking on microarray data [J]. Neural Networks, 2003, 16(5-6): 641-648.
[93] TSYMBAL A, PUURONEN S, PATTERSON D W. Ensemble feature selection with the simple Bayesian classification [J]. Information Fusion, 2003, 4(2): 87-100.
[94] SUN Z H, BEBIS G, MILLER R. Object detection using feature subset selection [J]. Pattern Recognition, 2004, 37(11): 2165-2176.
[95] CHIANG L H, PELL R J. Genetic algorithms combined with discriminant analysis for key variable identification [J]. Journal of Process Control, 2004, 14(2): 143-155.
[96]毛勇.基于支持向量机的特征选择方法的研究与应用[D].杭州:浙江大学信息科学与工程学院, 2006.
[97] LIU H, MOTODA H, DASH M. A monotonic measure for optimal feature selection[C]. Proceedings of the 10th European Conference on Machine Learning, Chemnitz, Germany, 1998: 101-106.
[98] KONONENKO I. Estimating attributes: analysis and extensions of RELIEF[C]. Proceedings of the 7th European Conference on Machine Learning, Catania, Italy, 1994: 171-182.
[99] HALL M A. Correlation-based feature selection for machine learning[D]. Hamilton: University of Waikato, 1999.
[100] KIRA K, RENDELL L A. A practical approach to feature selection [C]. Proceedings of the 9th European Conference on Machine Learning, Aberdeen, Scotland, 1992: 249-256.
[101]詹德川,周志华.基于相关投影分的特征选择算法[J].计算机科学与探索, 2007, 1(2): 138-145.
[102] DY J G, BRODLEY C E. Feature subset selection and order identification for unsupervised learning [C]. Proceedings of the 17th International Conference on Machine Learning, Stanford, USA, 2000: 247-254.
[103] XIONG M, FANG X, ZHAO J. Biomarker identification by feature wrappers [J]. Genome Research, 2001, 11: 1878-1887.
[104] VERIKAS A, BACAUSKIENE M. Feature selection with neural networks [J]. Pattern Recognition Letters, 2002, 23(11): 1323-1335.
[105] GUYON I, WESTON J, BARNHILL S, et al. Gene selection for cancer classification using support vector machines [J]. Machine Learning, 2002, 46(1-3): 389-422.
[106] HSU W H. Genetic wrappers for feature selection in decision tree induction and variable ordering in Bayesian network structure learning [J]. Information Sciences, 2004, 163(1-3):103-122.
[107] HUANG Y, SHIAN-SHYONG T, WU G, et al. A two-phase feature selection method using both filter and wrapper [C]. Proceedings of IEEE International Conference on Systems, Man, and Cybernetics, Tokyo, Japan, 1999, 2: 132-136.
[108] DAS S. Filters, wrappers and a boosting-based hybrid for feature selection [C]. Proceedings of the 18th International Conference on Machine Learning, Williamstown, USA, 2001: 74-81.
[109] XING E P, JORDAN M I, KARP R M. Feature selection for high-dimensional genomic microarry data [C]. Proceedings of the 18th International Conference on Machine Learning, Williamstown, USA, 2001: 601-608.
[110]刘成林,谭铁牛.模式识别研究进展[EB/OL]. http://liama.ia.ac.cn/wiki/.
[111] UCI Machine Learning Repository [DB/OL]. http://archive.ics.uci.edu/ml/.
[112] ZHOU Z H, YU Y. Ensembling local learners through multimodal perturbation [J]. IEEE Transactions on Systems, Man and Cybemetics-B, 2005, 35(4): 725-735.
[113] CHAWLA N V, JAPKOWICZ N, KOTCZ A. Editorial: special issue on learning from imbalanced data sets [J]. ACM SIGKDD Explorations, 2004, 6(1): 1-6.
[114] WEISS G M. Mining with rarity: a unifying framework [J]. ACM SIGKDD Explorations, 2004, 6(1): 7-19.
[115]叶志飞,文益民,吕宝粮.不平衡分类问题研究综述[J].智能系统学报, 2009, 4(2): 148-156.
[116] CHAWLA N V, BOWYER K W, HALL L O, et al. SMOTE: synthetic minority over-sampling technique [J]. Journal of Artificial Intelligence Research, 2002, 16: 321-357.
[117] LEE S S. Noisy replication in skewed binary classification [J]. Computational Statistics and Data Analysis, 2000, 34: 165-191.
[118] KUBAT M, HOLTE R, MATWIN S. Learning when negative examples abound [J]. Learning when negative examples abound [C]. Proceedings of the 9th European Conference on Machine Learning, Prague, Czechoslovakia, 1997: 146-153.
[119] KUBAT M, MATWIN S. Addressing the curse of imbalanced training sets: one-sided selection [C]. Proceedings of the 14th International Conference on Machine Learning, San Francisco, 1997: 179-186.
[120] DRUMMOND C, HOLTE R C. C4.5, class imbalance, and cost sensitivity: why under-sampling beats over-sampling [C]. Workshop on Learning from Imbalanced Data Sets II, International Conference on Machine Learning, Washington DC, 2003: 152-154.
[121] CHEN X, GERLACH B, CASASENT D. Pruning support vectors for imbalance data classification [C]. Proceedings of the International Joint Conference on Neural Networks, Montreal, 2005: 1883-1888.
[122] KOTSIANTIS S B, PINTELAS P E. Mixture of expert agents for handling imbalanced data sets [J]. Annals of Mathematics, Computing & Teleinformatics, 2003, 1(1): 46-55.
[123] ESTABROOKS A, TAEHO J, JAPKOWICZ N. A multiple resampling method for learning from imbalanced data sets [J]. Computational Intelligence, 2004, 20(1): 18-36.
[124] CHEW H G, CRISP D J, BOGNER R E, et al. Target detection in radar imagery using support vector machines with training size biasing [C]. Proceedings of the 6th International Conference on Control, Automation, Robotics and Vision, Singapore, 2000.
[125] CHEW H G, LIM C C, BOGNER R E. Dual-nu support vector machines applications in multi-class image recognition [J]. Proceedings of the International Conference on Optimization Techniques and Applications, Ballarat, 2004: 1-11.
[126] VAPNIK V N. The Nature of Statistical Learning Theory [M]. New York: Springer-Verlag, 1995.
[127] VAPNIK V N. An overview of statistical learning theory [J]. IEEE Transactions on Neural Networks, 1999, 10(5): 988-998.
[128]张学工.关于统计学习理论与支持向量机[J].自动化学报, 2000, 26(1): 32-42.
[129] DUDA R O, HART P E, STORK D G.模式分类[M].李宏东,姚天翔,等译.北京:机械工业出版社, 2003: 177-183.
[130] THEODORIDIS S, KOUTROUMBAS K.模式识别[M].李晶皎,王爱侠,张广渊,等译.北京:电子工业出版社, 2006: 60-68
[131] FRIESS T T, CRISTIANINI N, CAMPBELL C. The kernel-adatron algorithm: a fast and simple learning procedure for support vector machines [C]. Proceedings of the 15th International Conference on Machine Learning, Madison, 1998: 188-196.
[132] SCHOLKOPF B, SMOLA A J, WILLIAMSON, et al. New support vector algorithms [J]. Neural Computation, 2000, 12(5): 1207-1245.
[133] SUYKENS J A K, VANDEWALLE J. Least square support vector machine classifiers [J]. Neural Processing Letters, 1999, 9: 293-300.
[134] SCHOLKOPF B, PLATT J C, SHAWE T J, et al. Estimating the support of a high-dimensional distribution [J]. Neural Computation, 2001, 13(7): 1443-1471.
[135] LEE Y J, MANGASARIAN O L. RSVM: reduced support vector machines [C]. Proceedings of the First SIAM International Conference on Data Mining, 2001.
[136] CHEW H G, BOGNER R E, LIM C C. Dual-nu support vector machine with error rateand training size biasing [C]. Proceedings of the 26th IEEE International Conference on Acoustics, Speech, and Signal Processing, Salt Lake City, 2001: 1269-1272.
[137] LIN C F, WANG S. Fuzzy support vector machines [J]. IEEE Transactions on Neural Networks, 2002, 13(2): 464-471.
[138]张翔,肖小玲,徐光祐.基于样本之间紧密度的模糊支持向量机方法[J].软件学报, 2006, 17(5): 951-958.
[139]唐浩,廖与禾,孙峰,等.具有模糊隶属度的模糊支持向量机算法[J].西安交通大学学报, 2009, 43(7): 40-43.
[140] WESTON J, WATKINS C. Support vector machines for multi-class pattern recognition [C]. Proceedings of the 7th European Symposium on Artificial Neural Networks, Bruges, 1999: 219-224.
[141]唐发明.基于统计学习理论的支持向量机算法研究[D].武汉:华中科技大学控制科学与工程系, 2005.
[142]应自炉,唐京海,李景文,等.支持向量鉴别分析及在人脸表情识别中的应用[J].电子学报, 2008, 36(4): 725-730.
[143]杨健.线性投影分析的理论与算法及其在特征抽取中的应用研究[D].南京:南京理工大学计算机科学与技术学院, 2002.
[144] JIN Z, YANG J, TANG Z, et al. A theorem on the uncorrelated optimal discriminant vectors [J]. Pattern Recognition, 2001, 34(10): 2041-2047.
[145] JIN Z, YANG J, HU Z, et al. Face recognition based on the uncorrelated discriminant transformation [J]. Pattern Recognition, 2001, 34(7): 1405-1416.
[146] XIANG C, FAN X, LEE T H. Face recognition using recursive fisher linear discriminant [J]. IEEE Transactions on Image Processing, 2006, 15(8): 2097-2105.
[147] TAO Q, CHU D, WANG J. Recursive support vector machines for dimensionality reduction [J]. IEEE Transactions on Neural Networks, 2008, 19(1): 189-193.
[148] YE J, XIONG T. Computational and theoretical analysis of null space and orthogonal linear discriminant analysis [J]. Journal of Machine Learning Research, 2006, 7(7): 1183-1204.
[149] TAO Q, WU G, WANG J. The theoretical analysis of FDA and applications [J]. Pattern Recognition, 2006, 39(6): 1199-1204.
[150]章万锋.基于PCA与LDA的说话人识别研究[D].杭州:浙江大学计算机科学与技术学院, 2004.
[151] ZAFEIRIOU S, TEFAS A, PITAS I. Minimum class variance support vector machines [J]. IEEE Transactions on Image Processing, 2007, 16(10): 2551-2564.