基于Contourlet变换和子空间分析的人脸识别技术研究
|
摘要
在基于生物特征识别技术的身份认证中,人脸识别是最主要的方法之一,已经成为当前模式识别和人工智能领域研究的热点,探索高识别率的人脸识别算法具有重要的理论意义和应用价值。
小波分析是信号处理的有效方式,是目前国际上公认的信息获取与处理领域的新技术。小波能从信号中提取有用的信息成分,是各种信号处理方法(如多尺度分析、时频分析和子带编码)的统一处理框架。小波分析在一维时具有优异的特性,但是,这种优异特性不能简单地推广到二维或更高维。在高维空间中,多尺度几何分析拥有更明显的优势。
Contourlet变换是一种新的多尺度几何分析方法,它不仅具有小波变换的多分辨率特性和时频局域特性,还具有很强的方向性和各向异性。子空间方法具有计算代价小、描述能力强、可分性好等特点,现已经成为人脸识别的主流方法。
本文提出基于Contourlet变换和主成分分析(PCA)的人脸识别方法,研究Contourlet变换的低频系数与PCA相结合的识别率；同时提出基于Contourlet变换和核Fisher判别分析的人脸识别方法,研究Contourlet变换的低频系数、各层高频系数与核Fisher判别分析相结合进行人脸识别的识别率和识别时间。实验表明,Contourlet变换与PCA相结合,可获得优异的识别率；Contourlet变换的低频系数与核Fisher判别分析相结合,在获得优异的识别率的同时也减少了识别时间；高频成分有一定的识别性能,但识别率较低。将低频成分与高频方向子带相结合能获得最优的识别率。
Face recognition is one of main methods of status authentication which based on technology of biologic characters recognition and has become hot topic in the field of patterm recognition and artificial intelligence. Exploring the high recognition rate algorithm for face recognition has great theory significance and application value.
Wavelet analysis is an effective way in the field of signal processing and high-tech in the field of information acquisition and processing. Wavelet is an unified processing framework for various signals processing method, such as muti-scale analysis, time-frequency analysis and sub-band coding. The useful information can be extracted by wavelet transform. Wavelet analysis shows excellent character in the one-dimensional space, but this excellent feature can not be simply extended to two-dimentional space or higher dimentional space. In high dimensional spaces, multiscale geometric analysis has more significant advantages.
Contourlet transform is a new image representation scheme which not only possesses the main features of wavelets (namely, multi-scale and time-frequency localization), but also has directionality and anisotropy. The subspace methods have been the most popular approach owing to their appealing properties, such as low time-consuming, good performance on expression and separation.
In this paper, a method based on contourlet transform and Principal Components Analysis (PCA) for face recognition is proposed. In the method, the features of the low frequency in contourlet transform are extracted and combined with PCA for face recognition. The recognition rate is researched.At the same time, the other method that based on contourlet transform and Kernel Fisher Discriminant Analysis (KFDA) for face recognition is proposed. In this method, the features of the low frequency and high-frequency directional subband each level in contourlet transform are extracted respectively and combined with KFDA for face recognition. The recognition rate and recognition time are researched. The expremental result shows that combining the coefficients of the low frequency with PCA achieve excellent recognition rate and combining the coefficients of the low frequency with KFDA not only achieve higher recognition rate but also decrease the recognition time. High-frequency directional subband is helpful for recognition, but the recognition rate is low. Combining low frequency with high frequency directional subband can optimize the recognition rate.
小波分析是信号处理的有效方式,是目前国际上公认的信息获取与处理领域的新技术。小波能从信号中提取有用的信息成分,是各种信号处理方法(如多尺度分析、时频分析和子带编码)的统一处理框架。小波分析在一维时具有优异的特性,但是,这种优异特性不能简单地推广到二维或更高维。在高维空间中,多尺度几何分析拥有更明显的优势。
Contourlet变换是一种新的多尺度几何分析方法,它不仅具有小波变换的多分辨率特性和时频局域特性,还具有很强的方向性和各向异性。子空间方法具有计算代价小、描述能力强、可分性好等特点,现已经成为人脸识别的主流方法。
本文提出基于Contourlet变换和主成分分析(PCA)的人脸识别方法,研究Contourlet变换的低频系数与PCA相结合的识别率；同时提出基于Contourlet变换和核Fisher判别分析的人脸识别方法,研究Contourlet变换的低频系数、各层高频系数与核Fisher判别分析相结合进行人脸识别的识别率和识别时间。实验表明,Contourlet变换与PCA相结合,可获得优异的识别率；Contourlet变换的低频系数与核Fisher判别分析相结合,在获得优异的识别率的同时也减少了识别时间；高频成分有一定的识别性能,但识别率较低。将低频成分与高频方向子带相结合能获得最优的识别率。
Face recognition is one of main methods of status authentication which based on technology of biologic characters recognition and has become hot topic in the field of patterm recognition and artificial intelligence. Exploring the high recognition rate algorithm for face recognition has great theory significance and application value.
Wavelet analysis is an effective way in the field of signal processing and high-tech in the field of information acquisition and processing. Wavelet is an unified processing framework for various signals processing method, such as muti-scale analysis, time-frequency analysis and sub-band coding. The useful information can be extracted by wavelet transform. Wavelet analysis shows excellent character in the one-dimensional space, but this excellent feature can not be simply extended to two-dimentional space or higher dimentional space. In high dimensional spaces, multiscale geometric analysis has more significant advantages.
Contourlet transform is a new image representation scheme which not only possesses the main features of wavelets (namely, multi-scale and time-frequency localization), but also has directionality and anisotropy. The subspace methods have been the most popular approach owing to their appealing properties, such as low time-consuming, good performance on expression and separation.
In this paper, a method based on contourlet transform and Principal Components Analysis (PCA) for face recognition is proposed. In the method, the features of the low frequency in contourlet transform are extracted and combined with PCA for face recognition. The recognition rate is researched.At the same time, the other method that based on contourlet transform and Kernel Fisher Discriminant Analysis (KFDA) for face recognition is proposed. In this method, the features of the low frequency and high-frequency directional subband each level in contourlet transform are extracted respectively and combined with KFDA for face recognition. The recognition rate and recognition time are researched. The expremental result shows that combining the coefficients of the low frequency with PCA achieve excellent recognition rate and combining the coefficients of the low frequency with KFDA not only achieve higher recognition rate but also decrease the recognition time. High-frequency directional subband is helpful for recognition, but the recognition rate is low. Combining low frequency with high frequency directional subband can optimize the recognition rate.
引文
[1]A.K.Jain, L.Hong. On-Line fingerprint verification [J]. IEEE Trans. On PAMI, 1997,19(4):302-314.
[2]束为,容刚,边肇祺,张大鹏.利用掌纹进行身份自动识别方法的研究[J].清华大学学报(自然科学报),1999,39(1)：95-99.
[3]王蕴红,朱勇,谭铁牛.基于虹膜识别的身份鉴别[J].自动化学报,2002,28(11)：1-10
[4]A.K.Jain, A.Ross, and S.Prabhaker. An Introduction to Biometric Recognition [J]. IEEE Trans. On CSVT, Special Issue on " Image-and Video-Based Biometrics",8,2003.
[5]孙冬梅,裘正定.生物特征识别技术综述[J].电子学报,2001,29(12A)：1744-1748
[6]Vladimir N.Vapnik, The Nature of Statistical Learning Theory [J]. Springer,1995.
[7]边肇祺,张学工.模式识别(第二版)[M].北京：清华大学出版社,1999.
[8]王建文,杨川.基于小波变换的人脸识别系统[J].安徽农业科学,2007,35(16)：5021-5022
[9]Cunjian.chen, Jiashu.zhang. Wavelet Energy Entropy as a New Feature Extractor for Face Recognition [J]. IEEE, Fourth International Conference on Image and Graphics,2007: 616-619.
[10]Bai-Ling Zhang, Haihong Zhang. Face Recognition by Applying Wavelet Subband Representation and Kernel Associative Memory [J]. IEEE, Trans on Neural Networks, vol.15, nol,2004:166-177.
[11]JIE LIN, JIAN-PING LI, MING JI. ROBUST FACE RECOGNITION BY WAVE-LET FEATURES AND MODEL ADAPTATION[C]. IEEE, Proceedings of the 2007 International Conference on Wavelet Analysis and Pattern Recognition, Beijing, China, 2-4 Nov.2007:1638-1643
[12]Rama Chellappa,Charles L.Wilson and Saad Sirohey,Human and machine recognition of faces:a survey,Proceedings of IEEE[J],May 1995, Vol.83,No.5.
[13]Ashok Samal and Prasana A.Iyengar,Automatic recognition and analysis of human faces and facial expression:a survey,Pattern Recognition[J],1992, Vol.25,No.l,pp.65-77.
[14]Dominique Valentin,Herve Abdi,Alice J.O'Toole and Garrison W.Cottrell,Connectionist models of face processing:a survey,Pattern Recognition[J],1994,Vol.27,No.9,pp.1209-1230.
[15]Jun Zhang,Yong Yan and Martin Lades,Face recognition:Eigenface,Elastic matching,and Neural nets, Proceedings of the IEEE[J],September 1997,Vol.85,No.9.
[16]陈绵书.计算机人脸识别方法研究[D].吉林：吉林大学,2003.
[17]林立宇,张友焱等Contourlet变换-影像处理应用[M].北京：科学出版社,2008：15-25
[18]程正兴,杨守志等.小波分析的理论、算法、进展和应用[M].北京：国防工业出版社,2007：304-310
[19]李振伟,何继善,刘兵全,廖云朋.小波图像压缩进展[J].微机发展,2004,14(6)：29-31
[20]隋波,于霖.小波变换在紫外光信号降噪处理中的应用[J].舰船电子工程,2009,29(4)：81-82
[21]邹国平,虞安军,黄铮.基于SVM和小波边缘检测的车辆图像识别[J].交通标准化,2007,11
[22]程正兴,杨守志等.小波分析的理论、算法、进展和应用[M].北京：国防工业出版社,2007：380-386
[23]葛哲学,沙威.小波分析理论与MATLAB R2007实现[M].北京：电子工业出版社,2007：375-381
[24]Condes E J,Donobo D L, Curvelets-a surprisingly effective nonadaptive representation for objects with edges[A].In:Cohen A,Rabut C,Schumaker L L editors.Curve and surface fitting[C].Saint-Malo:Vanderbilt University Press,1999:105-120
[25]E. J. Candes. Ridgelets:Theory and Application [D]. Ph. D. Thesis, Department of Statistics, Stanford University,1998.
[26]D. L. Donoho. Orthonormal ridgelets and linear singularities [R]. Tech. Report, Department of Statistics, Stanford University,1998.
[27]E. J. Candes., D. L. Donoho. Curvelets:a surprisingly effective nonadaptive representation for objects with edges. L. L. S. et al. Curves and Surfaces [M], Nashville:Vanderbilt University Press,1999.
[28]D. L. Donobo, M. R. Duncan. Digital curvelet transform:strategy, implementation and experiments [J]. Proc. Aerosense 2000, Wavelet Applications Ⅶ. SPIE,2000,4056, 12-29.
[29]M. N. Do, M. Vetterli. Framing pyramids [J]. IEEE Trans,2003, Signal Proc-51(9): 2329-2342
[30]M. N. Do, M. Vetterli. Contourlets. J. Stoeckler, G. V. Welland. Beyond Wavelets [M], Academic Press,2002.
[31]刘佳,韩鹏.浅谈人脸检测技术[J].科技论坛,2009：49.
[32]夏鹏.人脸识别关键技术的研究[D].浙江：浙江师范大学,2005.
[33]祝秀萍,吴学毅,刘文峰.人脸识别综述与展望[J].计算机与信息技术,2007：53-56
[34]O'Toole A J, Abdi H, Deffenbacher K A, etal. A low dimensional representation of faces in the higher dimensions of space [J]. Journal of the Optical Society of 2 America,1993, 10:405-411.
[35]张翠萍,苏光大.人脸识别技术综述[J].中国图像图形学报,2000,5(11)：885-894.
[36]A.Samal, P. A. Iyengar.Automatic recognition and analysis of human faces and facial expressions:a survey [J]. Pattern Recognition,1992,25(1):65-67.
[37]Turk M, Pentland A. Eigenfaces for recognition [J]. Journal of Cognitive Neuroscience, 1991,3(1):71-86.
[38]Bartlett M S, Movellan J R, Sejnowski TJ. Face Recognition by Independent Component Analysis [J]. IEEE Trans. On Neural Network,2002,13(6):1450-1464.
[39]Manjunath B S, Shekhar C and Chellappa R. A new approach to image feature detection with application [J]. Patt. Recog,1996,29(4):627-640.
[40]Cheng Y. Liu K, Yang J, etal. Human face recognition method based on the statistical model of small sample size [J]. SPIE Proc. Intell. Robots and Computer Vision Ⅹ: Algorithms and Technology,1991,1606:85-95
[41]Haddadnia J, Ahmadi M, Faez K A Hybrid Learning RBF Neural Network for Human Face Recognition with Pseudo Zernike Moment Invariant [A]. Proceedings of the 2002 International Joint Conference on Neural Networks [C].2002,1:11-16
[42]Adam D. Tibbalds. Three Dimensional Human Face Acquisitions for Recognition [D]. Phd. Thesis Cambridge, University of Cambridge,1998.
[43]Wenyi Zhao. Robust image based 3D face recognition [D]. PhD. Thesis. University of Maryland, College Park,1999.
[44]S. Mikat, G. Ratscht, J. Weston, B. Scholkopft, K. R. Mullers, "Fisher Discriminant Analysis with Kernels"[J], IEEE International Workshop on Neural Networks for Signal Processing,1999,6:41-48
[45]L ee T W, Girolami M., Bell A. J. A unifying information theoretic framework for independent component analysis [J]. Computers And Mathematics With Application, 2003,31(11):1221.
[46]李颖,张培珍,李灿苹.基于KL变换的人脸识别系统的设计与实现[J].学术论坛,2009,20：218-219
[47]Nastar C, Moghaddam B A.Flexible Images:Matching and Recognition Using Learned Deformations [J]. Computer Vision and Image Understanding,1997,65(2):179-191
[48]夏祥飞.人脸识别综述[J].重庆三峡学院学报,2009,25(117)：14-18
[49]Lades M, Vorbrueggen J C, Buhmann J. Distortion invariant object recognition in the dynamic link architecture [J]. IEEE Transactions on Computers,1993,42(3):300-311.
[50]祝磊.基于子空间分析的人脸识别研究[D].浙江：浙江大学,2007
[51]LI S Z, JAIN A K. Handbook of face recognition [M]. Springer-Verlag,2005.
[52]刘青山.人脸跟踪与识别的研究[J].中科院自动化所,2003
[53]SHAN S, YANG P, CHEN X, et al. Adaboost gabor fisher classifier for face recognition [C]. IEEE International Workshop on Analysis and Modeling of Faces and Gestures, 2005.
[54]ZHANG B, SHAN S, CHEN X, et al. Histogram of gabor phase patterns (HGPP):A novel object representation approach for face recognition [J]. IEEE Transactions on Image processing,2007,16(1):57-68.
[55]丁嵘,苏光大,林行刚.使用关键点信息改进弹性匹配人脸识别算法[J].电子学报,2002,30(9)：1292-1294.
[56]YAN S, ZHANG H, HU Y, et al. Diseriminant analysis on embedded manifold[C]. European Conference on Computer Vision,2004:121-132.
[57]JIN Z, LOU Z, YANG J, et al. Face detection using template matehing and skin-color information [J]. Neurocomputing,2007,70(4-6):794-800.
[58]SONG F, ZHANG D, YANG J. A novel dimensionality-reduetion approach for face recognition [J]. Neurocomputing,2006,69(13-15):1683-1657.
[59]ZHAO H, SUN S, JING Z, et al. Local strueture based supervised feature extraction [J]. Pattern Recognition,2006,39(8):1546-1550.
[60]TAN X, CHEN S, ZHOU Z-H, et al. Face recognition from a single image per person:A survey [J]. Pattern Recognition,2006,39(9):1725-1745.
[61]WU J, ZHOU Z H. Face recognition with one training image per person [J].Pattern Recognition Letters,2002,23(14):1711-1719.
[62]PAN G, WU Z H.3D face recognition from range data [J]. Intemational Journal of Image and Graphics,2005,5(3):573-593.
[63]PAN G, WANG Y M, QI Y P, et al. Finding symmetry plane of 3D face shape[C]. Intemational Conference on Pattem Recognition,2006,3:1143-1146.
[64]孙延奎.小波分析及其应用(第一版)[M].北京：机械工业出版社,2005.
[65]吴旋.基于小波分析与核方法的人脸识别研究[D].南昌：南昌大学,2007.
[66]焦李成,侯彪等.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,2008.7：7-8
[67]程正兴,杨守志等.小波分析的理论、算法、进展和应用[M].北京：国防工业出版社,2007：1-2.
[68]曹怀信,赵建伟.小波分析发展综述[J].咸阳师范学院学报,2002,17(6)：5-8
[69]M. Vetterli. Wavelets, Approximation and compression [J]. IEEE Signal Processing Magazine,2001,18(5):59-73.
[70]Stephane Mallat.信号处理的小波引导.杨力华,等,译.北京：机械工业出版社,2003.
[71]R. A. DeVore. Nonlinear approximation [M]. Acta Numerica, Cambridge University Press,1998.
[72]Rafael C. Gonzalez, Richard E. Woods etc数字图像处理[M].北京：电子工业出版社,2006：289-295.
[73]彭玉华.小波变换与工程应用[M].北京：科学出版社,2005：16-24.
[74]葛哲学,沙威.小波分析理论与MATLAB R2007实现[M].北京：电子工业出版社,2007：180-200
[75]程正兴,杨守志等.小波分析的理论、算法、进展和应用[M].北京：国防工业出版社,2007：79-80
[76]焦李成,侯彪等.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,2008.7：9-12
[77]E. J. Candes. Monoscale Ridgelets for the Representation of Images with Edges. Tech. Report, Department of Statistics, Stanford University,1999.
[78]D. L. Donoho. Sparse components of images and optimal atomic decompositions [J]. Constr. Approx.2001,17:353-382.
[79]David L. Donoho, Ana Georgina Flesia. Can Recent Innovations in Harmonic Analysis 'Explain' Key Findings in Natural Image Statistics?[J] Network:Computation in Neural Systems,2001,12(3):371-393
[80]D. L. Donoho. Orthonormal ridgelets and linear singularities [R]. Tech. Report, Department of Statistics, Stanford University,1998.
[81]E. L. Pennec, S. Mallat. Image compression with geometrical wavelets [J]. In Proc. of ICIP'2000, Vancouver, Canada, September 2000:661-664
[82]M. N. Do, M.Vetterli. Contourlets. Beyond Wavelets[M]. J. Stoecker and G.V. Welland eds. Academic Press,2002:1-27.
[83]林立宇,张友焱,孙涛等Contourlet变换-影像处理应用[M].北京：科学出版社,2008：28-58
[84]王蕊,尹忠科等.基于改进轮廓波变换的图像去噪算法[J].计算机工程,2009,35(6)：228-230
[85]Bamberger R H, Smith M J T. A filter bank for the directional decomposition of images: Theory and design [J]. IEEE Trans. Signal Proc.,1992,40(4):882-893
[86]林立宇,张友焱等Contourlet变换-影像处理应用[M].北京：科学出版社,2008：30-32
[87]焦李成,侯彪等.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,2008.7：281-284.
[88]张九龙,张志禹等.基于曲波与主分量分析的人脸识别[J].计算机应用,2008,28(5)：1255-1257.
[89]齐兴敏,刘冠梅.PCA在人脸识别方法中的比较研究[J].江西蓝天学院学报,2008,3(3)：28-31
[90]孔锐,张冰.基于核Fisher判别分析的高性能多类分类算法[J]计算机应用,2005,25(6)：1327-1329
[91]夏思宇,李久贤,袁晓辉,夏良正.一种基于Contourlet的人脸识别方法[J].信号处理,2008,24(4)：631-634
[92]Brailovsky V L. On Global, Local, Mixed and Neighborhood Kernels for Support Vector Machines [J]. Pattern Recognition Letters,1999,20(1):1183-1198.
[93]Sergios Theodoridis, Konstantinos Koutroumbas模式识别[M].北京：电子工业出版社,2008：30-32.
[2]束为,容刚,边肇祺,张大鹏.利用掌纹进行身份自动识别方法的研究[J].清华大学学报(自然科学报),1999,39(1)：95-99.
[3]王蕴红,朱勇,谭铁牛.基于虹膜识别的身份鉴别[J].自动化学报,2002,28(11)：1-10
[4]A.K.Jain, A.Ross, and S.Prabhaker. An Introduction to Biometric Recognition [J]. IEEE Trans. On CSVT, Special Issue on " Image-and Video-Based Biometrics",8,2003.
[5]孙冬梅,裘正定.生物特征识别技术综述[J].电子学报,2001,29(12A)：1744-1748
[6]Vladimir N.Vapnik, The Nature of Statistical Learning Theory [J]. Springer,1995.
[7]边肇祺,张学工.模式识别(第二版)[M].北京：清华大学出版社,1999.
[8]王建文,杨川.基于小波变换的人脸识别系统[J].安徽农业科学,2007,35(16)：5021-5022
[9]Cunjian.chen, Jiashu.zhang. Wavelet Energy Entropy as a New Feature Extractor for Face Recognition [J]. IEEE, Fourth International Conference on Image and Graphics,2007: 616-619.
[10]Bai-Ling Zhang, Haihong Zhang. Face Recognition by Applying Wavelet Subband Representation and Kernel Associative Memory [J]. IEEE, Trans on Neural Networks, vol.15, nol,2004:166-177.
[11]JIE LIN, JIAN-PING LI, MING JI. ROBUST FACE RECOGNITION BY WAVE-LET FEATURES AND MODEL ADAPTATION[C]. IEEE, Proceedings of the 2007 International Conference on Wavelet Analysis and Pattern Recognition, Beijing, China, 2-4 Nov.2007:1638-1643
[12]Rama Chellappa,Charles L.Wilson and Saad Sirohey,Human and machine recognition of faces:a survey,Proceedings of IEEE[J],May 1995, Vol.83,No.5.
[13]Ashok Samal and Prasana A.Iyengar,Automatic recognition and analysis of human faces and facial expression:a survey,Pattern Recognition[J],1992, Vol.25,No.l,pp.65-77.
[14]Dominique Valentin,Herve Abdi,Alice J.O'Toole and Garrison W.Cottrell,Connectionist models of face processing:a survey,Pattern Recognition[J],1994,Vol.27,No.9,pp.1209-1230.
[15]Jun Zhang,Yong Yan and Martin Lades,Face recognition:Eigenface,Elastic matching,and Neural nets, Proceedings of the IEEE[J],September 1997,Vol.85,No.9.
[16]陈绵书.计算机人脸识别方法研究[D].吉林：吉林大学,2003.
[17]林立宇,张友焱等Contourlet变换-影像处理应用[M].北京：科学出版社,2008：15-25
[18]程正兴,杨守志等.小波分析的理论、算法、进展和应用[M].北京：国防工业出版社,2007：304-310
[19]李振伟,何继善,刘兵全,廖云朋.小波图像压缩进展[J].微机发展,2004,14(6)：29-31
[20]隋波,于霖.小波变换在紫外光信号降噪处理中的应用[J].舰船电子工程,2009,29(4)：81-82
[21]邹国平,虞安军,黄铮.基于SVM和小波边缘检测的车辆图像识别[J].交通标准化,2007,11
[22]程正兴,杨守志等.小波分析的理论、算法、进展和应用[M].北京：国防工业出版社,2007：380-386
[23]葛哲学,沙威.小波分析理论与MATLAB R2007实现[M].北京：电子工业出版社,2007：375-381
[24]Condes E J,Donobo D L, Curvelets-a surprisingly effective nonadaptive representation for objects with edges[A].In:Cohen A,Rabut C,Schumaker L L editors.Curve and surface fitting[C].Saint-Malo:Vanderbilt University Press,1999:105-120
[25]E. J. Candes. Ridgelets:Theory and Application [D]. Ph. D. Thesis, Department of Statistics, Stanford University,1998.
[26]D. L. Donoho. Orthonormal ridgelets and linear singularities [R]. Tech. Report, Department of Statistics, Stanford University,1998.
[27]E. J. Candes., D. L. Donoho. Curvelets:a surprisingly effective nonadaptive representation for objects with edges. L. L. S. et al. Curves and Surfaces [M], Nashville:Vanderbilt University Press,1999.
[28]D. L. Donobo, M. R. Duncan. Digital curvelet transform:strategy, implementation and experiments [J]. Proc. Aerosense 2000, Wavelet Applications Ⅶ. SPIE,2000,4056, 12-29.
[29]M. N. Do, M. Vetterli. Framing pyramids [J]. IEEE Trans,2003, Signal Proc-51(9): 2329-2342
[30]M. N. Do, M. Vetterli. Contourlets. J. Stoeckler, G. V. Welland. Beyond Wavelets [M], Academic Press,2002.
[31]刘佳,韩鹏.浅谈人脸检测技术[J].科技论坛,2009：49.
[32]夏鹏.人脸识别关键技术的研究[D].浙江：浙江师范大学,2005.
[33]祝秀萍,吴学毅,刘文峰.人脸识别综述与展望[J].计算机与信息技术,2007：53-56
[34]O'Toole A J, Abdi H, Deffenbacher K A, etal. A low dimensional representation of faces in the higher dimensions of space [J]. Journal of the Optical Society of 2 America,1993, 10:405-411.
[35]张翠萍,苏光大.人脸识别技术综述[J].中国图像图形学报,2000,5(11)：885-894.
[36]A.Samal, P. A. Iyengar.Automatic recognition and analysis of human faces and facial expressions:a survey [J]. Pattern Recognition,1992,25(1):65-67.
[37]Turk M, Pentland A. Eigenfaces for recognition [J]. Journal of Cognitive Neuroscience, 1991,3(1):71-86.
[38]Bartlett M S, Movellan J R, Sejnowski TJ. Face Recognition by Independent Component Analysis [J]. IEEE Trans. On Neural Network,2002,13(6):1450-1464.
[39]Manjunath B S, Shekhar C and Chellappa R. A new approach to image feature detection with application [J]. Patt. Recog,1996,29(4):627-640.
[40]Cheng Y. Liu K, Yang J, etal. Human face recognition method based on the statistical model of small sample size [J]. SPIE Proc. Intell. Robots and Computer Vision Ⅹ: Algorithms and Technology,1991,1606:85-95
[41]Haddadnia J, Ahmadi M, Faez K A Hybrid Learning RBF Neural Network for Human Face Recognition with Pseudo Zernike Moment Invariant [A]. Proceedings of the 2002 International Joint Conference on Neural Networks [C].2002,1:11-16
[42]Adam D. Tibbalds. Three Dimensional Human Face Acquisitions for Recognition [D]. Phd. Thesis Cambridge, University of Cambridge,1998.
[43]Wenyi Zhao. Robust image based 3D face recognition [D]. PhD. Thesis. University of Maryland, College Park,1999.
[44]S. Mikat, G. Ratscht, J. Weston, B. Scholkopft, K. R. Mullers, "Fisher Discriminant Analysis with Kernels"[J], IEEE International Workshop on Neural Networks for Signal Processing,1999,6:41-48
[45]L ee T W, Girolami M., Bell A. J. A unifying information theoretic framework for independent component analysis [J]. Computers And Mathematics With Application, 2003,31(11):1221.
[46]李颖,张培珍,李灿苹.基于KL变换的人脸识别系统的设计与实现[J].学术论坛,2009,20：218-219
[47]Nastar C, Moghaddam B A.Flexible Images:Matching and Recognition Using Learned Deformations [J]. Computer Vision and Image Understanding,1997,65(2):179-191
[48]夏祥飞.人脸识别综述[J].重庆三峡学院学报,2009,25(117)：14-18
[49]Lades M, Vorbrueggen J C, Buhmann J. Distortion invariant object recognition in the dynamic link architecture [J]. IEEE Transactions on Computers,1993,42(3):300-311.
[50]祝磊.基于子空间分析的人脸识别研究[D].浙江：浙江大学,2007
[51]LI S Z, JAIN A K. Handbook of face recognition [M]. Springer-Verlag,2005.
[52]刘青山.人脸跟踪与识别的研究[J].中科院自动化所,2003
[53]SHAN S, YANG P, CHEN X, et al. Adaboost gabor fisher classifier for face recognition [C]. IEEE International Workshop on Analysis and Modeling of Faces and Gestures, 2005.
[54]ZHANG B, SHAN S, CHEN X, et al. Histogram of gabor phase patterns (HGPP):A novel object representation approach for face recognition [J]. IEEE Transactions on Image processing,2007,16(1):57-68.
[55]丁嵘,苏光大,林行刚.使用关键点信息改进弹性匹配人脸识别算法[J].电子学报,2002,30(9)：1292-1294.
[56]YAN S, ZHANG H, HU Y, et al. Diseriminant analysis on embedded manifold[C]. European Conference on Computer Vision,2004:121-132.
[57]JIN Z, LOU Z, YANG J, et al. Face detection using template matehing and skin-color information [J]. Neurocomputing,2007,70(4-6):794-800.
[58]SONG F, ZHANG D, YANG J. A novel dimensionality-reduetion approach for face recognition [J]. Neurocomputing,2006,69(13-15):1683-1657.
[59]ZHAO H, SUN S, JING Z, et al. Local strueture based supervised feature extraction [J]. Pattern Recognition,2006,39(8):1546-1550.
[60]TAN X, CHEN S, ZHOU Z-H, et al. Face recognition from a single image per person:A survey [J]. Pattern Recognition,2006,39(9):1725-1745.
[61]WU J, ZHOU Z H. Face recognition with one training image per person [J].Pattern Recognition Letters,2002,23(14):1711-1719.
[62]PAN G, WU Z H.3D face recognition from range data [J]. Intemational Journal of Image and Graphics,2005,5(3):573-593.
[63]PAN G, WANG Y M, QI Y P, et al. Finding symmetry plane of 3D face shape[C]. Intemational Conference on Pattem Recognition,2006,3:1143-1146.
[64]孙延奎.小波分析及其应用(第一版)[M].北京：机械工业出版社,2005.
[65]吴旋.基于小波分析与核方法的人脸识别研究[D].南昌：南昌大学,2007.
[66]焦李成,侯彪等.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,2008.7：7-8
[67]程正兴,杨守志等.小波分析的理论、算法、进展和应用[M].北京：国防工业出版社,2007：1-2.
[68]曹怀信,赵建伟.小波分析发展综述[J].咸阳师范学院学报,2002,17(6)：5-8
[69]M. Vetterli. Wavelets, Approximation and compression [J]. IEEE Signal Processing Magazine,2001,18(5):59-73.
[70]Stephane Mallat.信号处理的小波引导.杨力华,等,译.北京：机械工业出版社,2003.
[71]R. A. DeVore. Nonlinear approximation [M]. Acta Numerica, Cambridge University Press,1998.
[72]Rafael C. Gonzalez, Richard E. Woods etc数字图像处理[M].北京：电子工业出版社,2006：289-295.
[73]彭玉华.小波变换与工程应用[M].北京：科学出版社,2005：16-24.
[74]葛哲学,沙威.小波分析理论与MATLAB R2007实现[M].北京：电子工业出版社,2007：180-200
[75]程正兴,杨守志等.小波分析的理论、算法、进展和应用[M].北京：国防工业出版社,2007：79-80
[76]焦李成,侯彪等.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,2008.7：9-12
[77]E. J. Candes. Monoscale Ridgelets for the Representation of Images with Edges. Tech. Report, Department of Statistics, Stanford University,1999.
[78]D. L. Donoho. Sparse components of images and optimal atomic decompositions [J]. Constr. Approx.2001,17:353-382.
[79]David L. Donoho, Ana Georgina Flesia. Can Recent Innovations in Harmonic Analysis 'Explain' Key Findings in Natural Image Statistics?[J] Network:Computation in Neural Systems,2001,12(3):371-393
[80]D. L. Donoho. Orthonormal ridgelets and linear singularities [R]. Tech. Report, Department of Statistics, Stanford University,1998.
[81]E. L. Pennec, S. Mallat. Image compression with geometrical wavelets [J]. In Proc. of ICIP'2000, Vancouver, Canada, September 2000:661-664
[82]M. N. Do, M.Vetterli. Contourlets. Beyond Wavelets[M]. J. Stoecker and G.V. Welland eds. Academic Press,2002:1-27.
[83]林立宇,张友焱,孙涛等Contourlet变换-影像处理应用[M].北京：科学出版社,2008：28-58
[84]王蕊,尹忠科等.基于改进轮廓波变换的图像去噪算法[J].计算机工程,2009,35(6)：228-230
[85]Bamberger R H, Smith M J T. A filter bank for the directional decomposition of images: Theory and design [J]. IEEE Trans. Signal Proc.,1992,40(4):882-893
[86]林立宇,张友焱等Contourlet变换-影像处理应用[M].北京：科学出版社,2008：30-32
[87]焦李成,侯彪等.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,2008.7：281-284.
[88]张九龙,张志禹等.基于曲波与主分量分析的人脸识别[J].计算机应用,2008,28(5)：1255-1257.
[89]齐兴敏,刘冠梅.PCA在人脸识别方法中的比较研究[J].江西蓝天学院学报,2008,3(3)：28-31
[90]孔锐,张冰.基于核Fisher判别分析的高性能多类分类算法[J]计算机应用,2005,25(6)：1327-1329
[91]夏思宇,李久贤,袁晓辉,夏良正.一种基于Contourlet的人脸识别方法[J].信号处理,2008,24(4)：631-634
[92]Brailovsky V L. On Global, Local, Mixed and Neighborhood Kernels for Support Vector Machines [J]. Pattern Recognition Letters,1999,20(1):1183-1198.
[93]Sergios Theodoridis, Konstantinos Koutroumbas模式识别[M].北京：电子工业出版社,2008：30-32.