应用子空间方法的人脸识别研究
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摘要
自动人脸识别具有巨大的应用前景,已经成为模式识别、计算机视觉以及信息技术相关学科中活跃的研究领域。过去的几十年中,已经有多种人脸识别方法被提出。本文针对人脸识别中的特征提取和分类问题进行了研究,应用子空间方法,提出了新的人脸识别算法。
图像变换是重要的人脸特征提取方法。双树复小波变换可以提取多尺度,多方向的图像特征,同时具有平移不变特性。相对于Gabor小波,双树复小波变换可以有效地保持频域信息。本文提出了基于双树复小波变换和独立成分分析的人脸识别方法。人脸图像的双树复小波变换系数构成特征向量,通过独立成分分析进行子空间投影,采用基于概率推理模型的分类器进行分类。
双树复小波变换变换在每个尺度上提取6个固定方向的特征,其中不包括水平和竖直方向。人脸中的主要器官呈现水平和竖直方向特征,提供重要的分类信息。针对双树复小波变换不能直接提取水平和垂直两个方向特征的不足,本文提出了一种结合双树复小波特征和Gabor小波特征的人脸识别新方法。采用0和90的Gabor小波滤波器提取人脸图像水平和竖直方向的特征,与双树复小波特征共同构成特征向量。应用fisherfaces方法进行子空间投影,采用基于欧式距离的分类器实现分类。
贝叶斯人脸识别方法分别求取人脸图像的类内和类间差异,在主成分分析子空间中应用高斯概率分布对人脸差异进行建模,通过估计人脸图像差异的后验概率进行分类。由于人脸图像受到多种复杂因素的影响,高斯模型不能对人脸差异进行准确的描述。针对这一问题,本文提出了基于独立成分分析的贝叶斯人脸识别方法。采用独立成分分析计算人脸差异子空间,分别估计每一维度上的概率密度函数,各个维度相乘获得子空间中的高维概率密度函数。本文采用广义高斯模型对人脸差异在独立成分分析子空间中的投影进行建模,提高了概率密度函数估计的准确性和人脸识别方法的效果。
Automatic recognition of human faces has been an active research area in the communities of pattern recognition, computer vision and information technology due to its immense application potential. A large numbers of methods have been proposed for face recognition in the last several decades. Feature extraction and classification in face recognition are researched in this dissertation. Novel face recognition methods are proposed by using the subspace methods.
Image transform is one of the important face feature extraction methods. The multi-scales and multi-directions image features extracted by dual-tree complex wavelet transform (DT-CWT) are shift invariant. Compared with Gabor wavelet, DT-CWT features preserve more information in frequency domain. A new face recognition method is proposed by adopting the DT-CWT and independent component analysis (ICA). The face feature vectors are constructed by the DT-CWT coefficients of the face images. Subspace analysis is applied to feature vectors by using ICA. Feature vectors in ICA subspace is processed by probabilistic reasoning models for classification.
Features on horizontal and vertical directions are not included in the 6 fixed directions features which extracted by DT-CWT on each scale. The horizontal and vertical features provide important information for classification because that the key apparatus on human face are distributed on the two directions. Motivated by the deficiency of DT-CWT, a novel face recognition method is introduced by combining the DT-CWT features and the Gabor wavelet features. The face features on horizontal and vertical orientations are extracted by 0°and 90°Gabor wavelet filters. Face feature vectors are conducted by connecting the 0°and 90°Gabor wavelet features and the features extracted by DT-CWT. Subspace analysis is applied to feature vectors by fisherfaces method. Euclidean distance based classifier is exploited to classify the feature vectors in subspace.
Bayesian face recognition calculates the intrapersonal and interpersonal variations of the face images. The face variations are modeled by Gaussian probability distribution in the principal component analysis (PCA) subspace. The posteriori probability of the face variations is estimated for classification. However, Gaussian distribution can not describe the face variations accurately due to the complexity of the influence factors for face image. To overcome this deficiency, an ICA based Bayesian face recognition method is presented. Subspace analysis for face variations is applied to feature vectors by exploiting ICA. One dimension probability distributions are estimated separately in the ICA subspace. High dimension distribution is derived by the multiplication of the mutual independent one dimension distributions. The generalized Gaussian distribution is adopted to model the face variations in ICA subspace. The accuracy of the probability distribution estimation and the performance of the face recognition method are improved by the proposed method.
图像变换是重要的人脸特征提取方法。双树复小波变换可以提取多尺度,多方向的图像特征,同时具有平移不变特性。相对于Gabor小波,双树复小波变换可以有效地保持频域信息。本文提出了基于双树复小波变换和独立成分分析的人脸识别方法。人脸图像的双树复小波变换系数构成特征向量,通过独立成分分析进行子空间投影,采用基于概率推理模型的分类器进行分类。
双树复小波变换变换在每个尺度上提取6个固定方向的特征,其中不包括水平和竖直方向。人脸中的主要器官呈现水平和竖直方向特征,提供重要的分类信息。针对双树复小波变换不能直接提取水平和垂直两个方向特征的不足,本文提出了一种结合双树复小波特征和Gabor小波特征的人脸识别新方法。采用0和90的Gabor小波滤波器提取人脸图像水平和竖直方向的特征,与双树复小波特征共同构成特征向量。应用fisherfaces方法进行子空间投影,采用基于欧式距离的分类器实现分类。
贝叶斯人脸识别方法分别求取人脸图像的类内和类间差异,在主成分分析子空间中应用高斯概率分布对人脸差异进行建模,通过估计人脸图像差异的后验概率进行分类。由于人脸图像受到多种复杂因素的影响,高斯模型不能对人脸差异进行准确的描述。针对这一问题,本文提出了基于独立成分分析的贝叶斯人脸识别方法。采用独立成分分析计算人脸差异子空间,分别估计每一维度上的概率密度函数,各个维度相乘获得子空间中的高维概率密度函数。本文采用广义高斯模型对人脸差异在独立成分分析子空间中的投影进行建模,提高了概率密度函数估计的准确性和人脸识别方法的效果。
Automatic recognition of human faces has been an active research area in the communities of pattern recognition, computer vision and information technology due to its immense application potential. A large numbers of methods have been proposed for face recognition in the last several decades. Feature extraction and classification in face recognition are researched in this dissertation. Novel face recognition methods are proposed by using the subspace methods.
Image transform is one of the important face feature extraction methods. The multi-scales and multi-directions image features extracted by dual-tree complex wavelet transform (DT-CWT) are shift invariant. Compared with Gabor wavelet, DT-CWT features preserve more information in frequency domain. A new face recognition method is proposed by adopting the DT-CWT and independent component analysis (ICA). The face feature vectors are constructed by the DT-CWT coefficients of the face images. Subspace analysis is applied to feature vectors by using ICA. Feature vectors in ICA subspace is processed by probabilistic reasoning models for classification.
Features on horizontal and vertical directions are not included in the 6 fixed directions features which extracted by DT-CWT on each scale. The horizontal and vertical features provide important information for classification because that the key apparatus on human face are distributed on the two directions. Motivated by the deficiency of DT-CWT, a novel face recognition method is introduced by combining the DT-CWT features and the Gabor wavelet features. The face features on horizontal and vertical orientations are extracted by 0°and 90°Gabor wavelet filters. Face feature vectors are conducted by connecting the 0°and 90°Gabor wavelet features and the features extracted by DT-CWT. Subspace analysis is applied to feature vectors by fisherfaces method. Euclidean distance based classifier is exploited to classify the feature vectors in subspace.
Bayesian face recognition calculates the intrapersonal and interpersonal variations of the face images. The face variations are modeled by Gaussian probability distribution in the principal component analysis (PCA) subspace. The posteriori probability of the face variations is estimated for classification. However, Gaussian distribution can not describe the face variations accurately due to the complexity of the influence factors for face image. To overcome this deficiency, an ICA based Bayesian face recognition method is presented. Subspace analysis for face variations is applied to feature vectors by exploiting ICA. One dimension probability distributions are estimated separately in the ICA subspace. High dimension distribution is derived by the multiplication of the mutual independent one dimension distributions. The generalized Gaussian distribution is adopted to model the face variations in ICA subspace. The accuracy of the probability distribution estimation and the performance of the face recognition method are improved by the proposed method.
引文
[1]Jain A. K., Ross A., Prabhakar S., An introduction to biometric recognition, IEEE Transactions on Circuits and Systems for Video Technology, 2004, 14(1): 4~20
[2]Jain A. K., Lin H., Prabhakar S., Biometric identification, Communications of the ACM, 2000, 43(2): 90~98
[3]Zhao W., Chellappa R., Rosenfeld A., et al, Face Recognition: A Literature Survey, ACM Computing Surveys, 2003, 35(4): 399~458
[4]Daugman J., New methods in iris recognition, IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, 2007, 37(5): 1167~1175
[5]刘小华,人脸识别技术及其应用研究:[博士学位论文],吉林;吉林大学,2005
[6]Pankanti S., Prabhakar S., Jain A. K., On the individuality of fingerprints, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24(8): 1010~1025
[7] Shneiderman B., The limits of speech recognition, Communications of the ACM, 2000, 43(9): 63~65
[8] Faundez-Zanuy M., Signature recognition state-of-the-art, IEEE Aerospace and Electronic Systems Magazine, 2005, 20(7): 28~32
[9]Boulgouris N. V., Hatzinakos D., Plataniotis K. N., Gait recognition: a challenging signal processing technology for biometric identification, IEEE Signal Processing Magazine, 2005, 22(6): 78~90
[10]杜春华,人脸特征点定位及识别的研究:[博士学位论文],上海;上海交通大学,2008
[11]Yang M. H., Kriegman D. J., Ahuja N., Detecting Faces in Images: A Survey, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24(1): 34~58
[12]Moghaddam B., Yang M. H., Learning Gender with Support Faces, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24(5): 707~711
[13]Guo G., Fu Y., Dyer C. R., et al, Image-based human age estimation by manifold learning and locally adjusted robust regression, IEEE Transactions on Image Processing, 2008, 17(7): 1178~1188
[14]Fasel B., Luettin J., Automatic facial expression analysis: a survey, Pattern Recognition, 2003, 36(1): 259~275
[15]McKenna S. J., Gong S., Real-time face pose estimation, Real-Time Imaging,1998, 4(5): 333~347
[16]Beveridge J. R., Bolme D., Draper B. A., et al, The CSU Face Identification Evaluation System, Machine Vision and Applications, 2005, 16(2): 128~138
[17]Sirohey S. A., Rosenfeld A., Eye detection in a face image using linear and nonlinear filters, Pattern Recognition, 2001, 34(7): 1367~1391
[18]卢湖川,人脸识别中几个关键算法研究:[博士学位论文],辽宁;大连理工大学,2008
[19]Yang Q., Tang X., Recent Advances in Subspace Analysis for Face Recognition, Proceedings of Chinese Conference on Biometric Recognition, 2004, 1: 275~287
[20]Turk M. A., Pentland A. P., Eigenfaces for recognition. Journal of Cognitive Neuroscience, 1991, 3(1): 71~86.
[21]Moghaddama B., Jebarab T., Pentland A., Bayesian Face Recognition, Pattern Recognition, 2000, 33(11): 1771~1782
[22]Belhumeur P. N., Hespanha J. P., Kriegman D. J., Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997, 19(7): 711~720
[23]Bartlett M. S., Movellan J. R., Sejnowski T. J., Face recognition by independent component analysis, IEEE Transactions on Neural Networks, 2002, 13(6): 1450~1464
[24]Tenenbaum J. B., Silva V., Langford J. C., A Global Geometric Framework for Nonlinear Dimensionality Reduction, Science, 2000, 290(5500): 2319~2323
[25]Roweis S. T., Saul L. K., Nonlinear Dimensionality Reduction by Locally Linear Embedding, Science, 2000, 290(5500): 2323~2326
[26]Belkin M., Niyogi P., Laplacian Eigenmaps for Dimensionality Reduction and Data Representation, Neural Computation, 2003, 15(6): 1373~1396
[27]He X., Yan S., Hu Y., et al, Face Recognition Using Laplacianfaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(3): 328~340
[28]Wang Y., Jia Y., Hu C., et al, Non-negative matrix factorization framework for face recognition, International Journal of Pattern Recognition and Artificial Intelligence, 2005, 19 (4): 495~511
[29]Cover T. M., Hart P. E., Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 1967, 13(1): 21~27
[30]Muller K. R., Mika S., Ratsch G., et al. An introduction to kernel-based learning algorithms, IEEE Transactions on Neural Networks, 2001, 12(2): 181~201
[31]Guo G. D., Li S. Z., Chan K. L., Support vector machines for face recognition, Image and Vision Computing, 2001, 19 (9-10): 631~638
[32]Scholkopf B., Smola A., Muller K. R., Nonlinear Component Analysis as a Kernel Eigenvalue Problem, Neural Computation, 1998, 10(5): 1299~1319
[33]Mika S., Ratsch G., Weston J., et al, Fisher discriminant analysis with kernels, Proceedings of IEEE Workshop on Neural Networks for Signal Processing, 1999, 4: 41~48
[34]Baudat G., Anouar F., Generalized Discriminant Analysis Using a Kernel Approach, Neural Computation, 2000, 12(10): 2385~2404
[35]Bach F. R., Jordan M. I., Kernel Independent Component Analysis, Journal of Machine Learning Research, 2002, 3(1): l~48
[36]Brunelli R., Poggio T., Face recognition: Features versus Templates, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993, 15(10): 1042~1052
[37] Heisele B., Ho P., Wu J., et al, Face recognition: component-based versus global approaches, Computer Vision and Image Understanding, 2003, 91(1-2): 6~21
[38]Wiskott L., Fellous J. M., Kruger N., et al, Face Recognition by Elastic Bunch Graph Matching, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997, 19(7): 775~779
[39]Wana K. W., Lama K. M., Ng K. C., An accurate active shape model for facial feature extraction, Pattern Recognition Letters, 2005, 26(15): 2409~2423
[40]Edwards G. J., Cootes T. F., Taylor C. J., Face Recognition Using Active Appearance Models, Proceedings of European Conference on Computer Vision, 1998, 2: 581~595
[41]Bicego M., Lagorio A., Grosso E., et al, On the use of SIFT features for face authentication, Proceedings of Conference on Computer Vision and Pattern Recognition Workshop, 2006, 1: 17~22
[42]Cartoux J. Y, Lapreste J. T., Richetin M., Face authentication or recognition by profile extraction from range images. Proceedings of Workshop on Interpretation of 3D Scenes, 1989, 1: 194~199
[43]Achermann B., Bunke H., Classifying range images of human faces with Hausdorff distance, Proceedings of International Conference on Pattern Recognition, 2000, 2: 809~813
[44]Medioni G., Waupotitsch R., Face recognition and modeling in 3D, Proceedings of IEEE International Workshop on Analysis and Modeling of Faces and Gestures, 2003, 1: 232~233
[45]Beumier C., Acheroy M., Automatic 3D face authentication, Image and Vision Computing, 2000, 18(4): 315-321
[46]Samaria F. S., Harter A. C., Parameterisation of a Stochastic Model for Human Face Identification, Proceedings of IEEE Workshop on Applications of Computer Vision, 1994, 1: 138~142
[47]Belhumeur P., Hespanha J., Kriegman D., Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection, Proceedings of European Conference on Computer Vision, 1996, 1: 45~58
[48]Martinez A.M., Benavente R., The AR Face Database. CVC Technical Report No.24, Purdue University, 1998
[49]胡元奎,可变光照和可变姿态条件下的人脸图像识别研究:[博士学位论文],安徽;中国科学技术大学,2006
[50]Strang G., The Discrete Cosine Transform, SIAM Review, 1999, 41(1): 135~147
[51]Hafed Z. M., Levine M. D., Face Recognition Using the Discrete Cosine Transform, International Journal of Computer Vision, 2001, 43(3): 167~188
[52]Ramasubramanian D., Venkatesh Y.V., Encoding and recognition of faces based on the human visual model and DCT, Pattern Recognition, 2001, 34(12): 2447~2458
[53]Jing Y. X., Zhang D., A face and palmprint recognition approach based on discriminant DCT feature extraction, IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, 2004, 34(6): 2405~2415
[54]Er M. J., Chen W., Wu S., High-speed face recognition based on discrete cosine transform and RBF neural networks, IEEE Transactions on Neural Networks, 2005, 16(3): 679~691
[55]Choi J., Chung Y. S., Kim K. H., et al, Face Recognition using Energy Probability in DCT Domain, Proceedings of IEEE International Conference on Multimedia and Expo, 2006, 1: 1549~1552
[56]Chen W., Er M. J., Wu S., Illumination compensation and normalization for robust face recognition using discrete cosine transform in logarithm domain, IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, 2006, 36(2): 458~466
[57]Schwerin B., Paliwal K., Local-DCT features for facial recognition, Proceedings of International Conference on Signal Processing and Communication Systems, 2008, 1: 1~6
[58]Aroussi E. M., Amine A., Ghouzali S., et al, Combining DCT and LBP Feature Sets For Efficient Face Recognition, Proceedings of International Conference on Information and Communication Technologies: From Theory to Applications, 2008, 1: 1~6
[59]Dabbaghchiana S., Ghaemmaghamib M. P., Aghagolzadeh A., Feature extraction using discrete cosine transform and discrimination power analysis with a face recognition technology, Pattern Recognition, 2010, 43(4): 1431~1440
[60]Rioul O., Vetterli M., Wavelets and signal processing, IEEE SignalProcessing Magazine, 1991, 8(4): 14~38
[61]Bai L., Liu Y., When eigenfaces are combined with wavelets, Knowledge-Based Systems, 2002, 15(5-6): 343~347
[62]Ma Y., Li S., Face recognition by combining eigenface method with different wavelet subbands, Optoelectronics Letters, 2006, 2(5): 383-385
[63]Neo H. F., Teoh A., Ngo. D. L., Face Recognition Using Wavelet Transform and Non-negative Matrix Factorization, Proceedings of Australian Joint Conference on Artificial Intelligence, 2004, 1: 192~202
[64]Hazim Kemal Ekenel, Bulent Sankur, Multiresolution face recognition, Image and Vision Computing, 2005, 23(5): 469~477
[65]Li B., Yin H., Face Recognition Based on Support Vector Machine Fusion and Wavelet Transform, Proceedings of International Conference on Computational Intelligence and Security, 2005, 2: 764~771
[66]Vinod Pathangay, Sukhendu Das, Selection of Wavelet Subbands Using Genetic Algorithm for Face Recognition, Proceedings of Indian Conference Computer Vision, Graphics and Image Processing, 2006, 1: 585~596
[67]Selesnick I. W., Baraniuk R. G., Kingsbury N. G., The Dual-Tree Complex Wavelet Transform, IEEE Signal Processing Magazine, 2005, 22(6): 123~151
[68]Celik T., Ozkaramanh H., Demirela H., Facial feature extraction using complex dual-tree wavelet transform, Computer Vision and Image Understanding, 2008, 111(2): 229~246
[69]Liu C. C., Dai D. Q., Face recognition using dual-tree complex wavelet features, IEEE Transactions on Image Processing, 2009, 18(11): 2593~2599
[70]Zhang G.Y., Peng S. Y., Li H. M., Combination of dual-tree complex wavelet and SVM for face recognition, Proceedings of International Conference on Machine Learning and Cybernetics, 2008, 5: 2815~2819
[71]Peng Y., Xie X., Xu W., et al, Face recognition using anisotropic dual-tree complex wavelet packets, Proceedings of International Conference on Pattern Recognition, 2008, 1: 1~4
[72]Lee T. S., Image representation using 2D Gabor wavelets, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1996, 18(10): 959~971
[73]A. Serrano, I. Diego, Conde C., et al, Recent advances in face biometrics with Gabor wavelets: A review, Pattern Recognition Letters, 2010, 31(5): 372~381
[74]Buhmann J., Lange J., Malsburg C., Distortion invariant object recognition by matching hierarchically labeled graphs, Proccedings of International Joint Conference on Neural Networks, 1989, 1: 155~159
[75]Lades M., Vorbruggen J. C., Buhmann J., et al, Distortion invariant object recognition in the dynamic link architecture, IEEE Transactions on Computers, 1993,42(3): 300~311
[76]Chung K. C.,Kee S. C.,Kim S. R., Face recognition using principal component analysis of Gabor filter responses, Proceedings of International Workshop on Recognition, Analysis, and Tracking of Faces and Gestures in Real-Time Systems, 1999, 1: 53~57
[77]Liu C., Wechsler H., Gabor Feature Based Classification Using the Enhanced Fisher Linear Discriminant Model for Face Recognition, IEEE Transactions on Image Processing, 2002, 11(4): 467~476
[78]Liu C., Wechsler H. Independent component analysis of Gabor features for face recognition, IEEE Transactions on Neural Networks, 2003. 14(4): 919~928
[79]Liu C., Gabor-based kernel PCA with fractional power polynomial models for face recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, 26(5): 572~581
[80]Shan S., Yang P., Chen X., et al, AdaBoost Gabor Fisher Classifier for Face Recognition, Proceedings of International Workshop on Analysis and Modelling of Faces and Gestures, 2005, 1: 279~292
[81]Zhang W., Shan S., Gao W., et al, Local Gabor binary pattern histogram sequence (LGBPHS): a novel non-statistical model for face representation and recognition, Proceedings of International Conference on Computer Vision, 2005, 1: 786~791
[82]Nanni L., Maio D., Weighted Sub-Gabor for face recognition, Pattern Recognition Letters, 2007, 28(4): 487~492
[83]Zheng Z., Yang F., Tan W., et al, Gabor feature-based face recognition using supervised locality preserving projection, Signal Processing, 2007, 87(10): 2473~2483
[84]Pang Y., Yuan Y., Li X., Gabor based region covariance matrices for face recognition, IEEE Transactions on Circuits and Systems for Video Technology, 2008, 18(7): 989~993
[85]Beylkin G., Discrete Radon transform, IEEE Transactions on Acoustics, Speech and Signal Processing, 35(2): 162~172
[86]Karsili L., Acan A., A Radon Transform and PCA Hybrid for High Performance Face Recognition, Proceedings of IEEE International Symposium on Signal Processing and Information Technology, 2007, 1: 246~251
[87]Zhang Y.; Wang X., Study of Finite Radon Transform in Face Recognition, Proceedings of International Conference on Computer Modeling and Simulation, 2010, 4: 29~32
[88] Matus F., Flusser J., Image Representation via a Finite Radon Transform, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993, 15(10):996~1006
[89]Candes E., Demanet L., Donoho D., et al, Fast Discrete Curvelet Transforms, Multiscale Modeling and Simulation, 2006, 5(3): 861~899
[90]Mandal T., Majumdar A., Wu Q. M., Face Recognition by Curvelet Based Feature Extraction, Proceedings of International Conference on Image Analysis and Recognition, 2007, 1: 806~817
[91]Aroussi M. E., Hassouni, M. E., Ghouzali S., et al, Block based curvelet feature extraction for face recognition, Proceedings of International Conference on Multimedia Computing and Systems, 2009, 1: 299~303
[92]Mandal T., Wu Q. M., Yuan Y., Curvelet based face recognition via dimension reduction, Signal Processing, 2009, 89(12): 2345~2353
[93]Do M. N., Vetterli M., The Contourlet Transform: An Efficient Directional Multiresolution Image Representation, IEEE Transactions on Image Processing, 2005, 14(12): 2091~2106
[94]Boukabou W. R., Bouridane A., Contourlet-Based Feature Extraction with PCA for Face Recognition, Proceedings of NASA/ESA Conference on Adaptive Hardware and Systems, 2008, 1: 482~486
[95]Xu X., Zhang D., Zhang X., An efficient method for human face recognition using nonsubsampled contourlet transform and support vector machine, Optica Applicata, 2009, 39(3): 601-615
[96]Chougdali K., Jedra M., Zahid N., Contourlet feature based kernel relevance weighted discriminant analysis for face recognition, Proceedings of International Conference on Multimedia Computing and Systems, 2009, 1: 268~272
[97]Abouzar P., Yousefi S., Setarehdan S. K., Hybrid WT Based-DCT Based Face Recognition, Proceedings of IEEE International Conference on Signal Processing and Communications, 2007, 1: 963~966
[98]Jadhav D. V., Holambe R. S., Radon and discrete cosine transforms based feature extraction and dimensionality reduction approach for face recognition, Signal Processing, 2008, 88(10): 2604~2609
[99]Jadhav D. V., Holambe R. S., Feature extraction using Radon and wavelet transforms with application to face recognition, Neurocomputing, 2009, 72(7-9): 1951~1959
[100]Gabor D., Theory of communication, Journal of Institute for Electrical Engineering, 1946, 93(26): 429~457
[101]Daugman J. G., Uncertainty relation for resolution in space, spatial frequency and orientation optimized by two-dimensional visual cortical filters. Journal of the Optical Society of America A, 1985, 2(7): 1160~1169
[102]Marcelja S., Mathematical description of the responses of simple corticalcells, Journal of Optical Society ofAmerica, 1980, 70(11): 1297~1300
[103]Pollen D., Ronner S., Phase relationships between adjacent simple cells in the visual cortex, Science, 1981, 212(4501): 1409~1411
[104]Daugman J. G., Complete discrete 2-D Gabor transform by neural networks for image analysis and compression. IEEE Transactions on Acoustics, Speech and Signal Processing, 1988, 36(7): 1169~1179
[105]Porat M., Zeevi Y. Y., The generalized Gabor scheme of image representation in biological and machine vision. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1988, 10(4): 452~468
[106]山世光,人脸识别中若干关键问题的研究:[博士学位论文],北京;中国科学院计算技术研究所,2004
[107]Vetterli M., Wavelets, approximation, and compression, IEEE Signal Processing Magazine, 2001, 18(5): 59~73
[108]Mallat S., A theory for multiresolution signal decomposition: The wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989, 11(7): 674~693
[109]Choi H., Romberg J., Baraniuk R.G., et al, Hidden Markov tree modeling of complex wavelet transforms, Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, 2000, 1: 133~136
[110]Dragotti P. L., Vetterli M., Wavelet footprints: Theory, algorithms, and applications, IEEE Transactions on Signal Processing, 2003, 51(5) 1306~1323
[111]Kingsbury N.G., The dual-tree complex wavelet transform: A new efficient tool for image restoration and enhancement, Proceedings of European Signal Processing Conference, 1998, 1: 319~322
[112]Selesnick I. W., The design of approximate Hilbert transform pairs of wavelet bases. IEEE Transactions on Signal Processing, 2002, 50(5): 1144~1152
[113]Kingsbury N. G., Shift invariant properties of the Dual-Tree Complex Wavelet Transform, Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, 1999, 3: 1221~1224
[114]Kingsbury N. G., Complex wavelets for shift invariant analysis and filtering of signals, Applied and Computational Harmonic Analysis, 2001, 10(3): 234~253
[115]Pearson K., On lines and planes of closest fit to systems of points in space, Philosophical Magazine, 1901, 2(11): 559~572
[116]Hotelling H., Analysis of a complex of statistical variables into principal components, Journal of Educational Psychology, 1933, 24(6): 417~441
[117]Jutten C., Herault J., Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture, Signal Processing, 1991, 24(1): 1~10
[118]Tong L., Liu R. W., Soon V. C., et al, Indeterminacy and identifiability of blind identification, IEEE Transactions on Circuits and Systems, 1991, 38(5): 499~509
[119]Hyvarinen A., Oja E., Independent component analysis: algroithms and applications. Neural Networks, 2000, 13(4): 411~430
[120]Comon P., Independent component analysis: A new concept?, Signal Processing, 1994, 36(3): 287~313
[121]Cardoso J. F., Souloumiac A., Blind beamforming for non-Gaussian signals, IEE Proceedings F: Radar and Signal Processing, 1993, 140(6): 362~370
[122]Oja E., The nonlinear PCA learning rule in independent component analysis, Neurocomputing, 1997, 17(1): 25~45
[123]karhunen J., Loutsensalo J., Representation and separation of signals using nonlinear PCA type learning, Neural Networks, 1994, 7(1): 113~127
[124]Gaeta M., Lacoume J. L., Source separation without prior knowledge: The maximum likelihood solution, Proceedings of European Signal Processing Conference, 1990, 1: 621~624
[125]Pham, D. T., Garat P., Blind separation of mixture of independent sources through a quasi-maximum likelihood approach, IEEE Transactions on Signal Processing. 1997, 45(7): 1712~1725
[126]Pearlmutter B. and Parra L., A context-sensitive generalization of ICA, Proceedings of International Conference on Neural Information Processing, 1996, 1: 151~157
[127]Bell A.J., Sejnowski T.J., An information-maximization approach to blind separation and blind deconvolution, Neural Computation, 1995, 7(6): 1129~1159
[128]Lee T.W., Girolami M., Sejnowski T.J., Independent component analysis using an extended infomax algorithm for mixed sub-gaussian and super-gaussian sources, Neural Computation, 1999, 11(2): 417~441
[129]Amari S., Cichocki A., Adaptive blind signal processing-neural network approaches. Proceedings of the IEEE, 1998, 86(10): 2026~2048
[130]Hyvarinen A., Oja E., A fast fixed-point algorithm for independent component analysis, Neural Computation, 1997, 9(7): 1483~1492
[131]Hyvarinen A., Fast and robust fixed-point algorithms for independent component analysis, IEEE Transactions on Neural Networks, 1999, 10(3): 626~634
[132]Cardoso J. F., Infomax and maximum likelihood for blind separation, IEEE Signal Processing Letters, 1997, 4(4): 112~113
[133]Karhunen J., Pajunen P., Oja E., The nonlinear PCA criterion in blind source separation: Relations with other approaches, Neurocomputing, 1998, 22(1-3):
[134]Hyvarinen A., Gaussian moments for noisy independent component analysis, IEEE Signal Processing Letters, 1999, 6(6): 145~147
[135]Lewicki M. S., Sejnowslci T. J., Learning overcomplete representations, Neural Computation, 2000, 12(2): 337~365
[136]Hyvarinen A., Pajunen P., Nonlinear independent component analysis: Existence and uniqueness results. Neural Networks, 1999, 12(3): 429~439
[137]Liu C., Wechsler H., Robust Coding Schemes for Indexing and Retrieval from Large Face Databases, IEEE Transactions on Image Processing, 2000, 9(1): 132~137
[138]Fisher R. A., The Use of Multiple Measures in Taxonomic Problems, Annals of Eugenics, 1936, 7(1): 179~188
[139]Martinez A. M., Kak A. C., PCA versus LDA, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(2): 228~233
[140]边肇祺,张学工,模式识别(第二版),北京:清华大学出版社,2000,9~16
[141]Moghaddam B., Pentland A., Probabilistic Visual Learning for Object Representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997, 19(7): 696~710
[142]Mardia K. V., Kent J. T., Bibby J. M., Multivariate Analysis, Academic Press, Duluth, London, 1979, 103~104
[143]Tipping M.E., Bishop C.M., Probabilistic Principal Component Analysis, Journal of the Royal Statistical Society Series B (Statistical Methodology), 1999, 61(3): 611~622
[144]Wang X. G., Tang X. O., An improved Bayesian face recognition algorithm in PCA subspace, Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003, 3:129~132
[145]Moghaddam B., Nastar C., Pentland A., Bayesian Face Recognition with Deformable Image Models, Proceedings of International Conference on Image Analysis and Processing, 2001, 1:26~35
[146]Wang X. G., Tang X. O., Bayesian face recognition using Gabor features, Proceedings of ACM SIGMM workshop on Biometrics methods and applications, 2003, 1: 70~73
[147]Niu L., Zheng Y., Dou Y., et al, Combined Face Recognition Using Wavelet Transform and Bayesian, Proceedings of International Conference on Information and Computing Science, 2009, 2: 337~340
[148]Wang L.W., Wang X., Feng J. F., Intrapersonal subspace analysis with application to adaptive Bayesian face recognition, Pattern Recognition, 2005, 38(4): 617~621
[149]Wang L.W., Wang X., Feng J. F., Subspace distance analysis with application to adaptive Bayesian algorithm for face recognition, Pattern Recognition, 2006, 39(3): 456~464
[150]Zhang D.Q., Two-Dimensional Bayesian Subspace Analysis for Face Recognition, Proceedings of International Symposium on Neural Networks, 2007, 2: 778~784
[151]Yang J., Zhang D., Frangi A. F., et al, Two-dimensional PCA: a new approach to appearance-based face representation and recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, 26(1): 131~137
[152]Niu L., Zheng Y., Li X., et al, Bayesian Face Recognition Using 2DPCA, Proceedings of International Forum on Information Technology and Applications, 2009, 2: 567~570
[153]Wang X. G., Tang X. O., Bayesian Face Recognition Based on Gaussian Mixture Models, Proceedings of International Conference on Pattern Recognition, 2004, 4: 142~145
[154]Wang X. G., Tang X. O., Subspace Analysis Using Random Mixture Models, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005, 1:574~580
[155]Jiang X. D., Mandal B., Kot A., Enhanced maximum likelihood face recognition, Electronics Letters, 2006, 42(19): 1089~1090
[156]Li Z. F., Tang X. O., Using Support Vector Machines to Enhance the Performance of Bayesian Face Recognition, IEEE Transactions on Information Forensics and Security, 2007, 2(2): 174~180
[157]唐杰,基于贝叶斯策略的人脸识别研究:[硕士学位论文],北京;中国科学院计算技术研究所,2006
[158]李伟红,龚卫国,陈伟民,等,基于中国人人脸区域特征的贝叶斯分类法研究,仪器仪表学报,2004,25(4):461~464
[159]朱学毅,王崇骏,周新民,等,一种改进的贝叶斯人脸识别算法,计算机科学,2006,33(9):204~206
[160]Kokkinakis K., Nandi A. K., Exponent parameter estimation for generalized Gaussian probability density functions with application to speech modeling, Signal Processing, 2005, 85(9): 1852~1858
[161]Vlassis N., Likas A., A Greedy EM Algorithm for Gaussian Mixture Learning, Neural Processing Letters, 2002, 15(1): 77~87
[162]Fan S. K., Lin Y., A fast estimation method for the generalized Gaussian mixture distribution on complex images, Computer Vision and Image Understanding, 2009, 113(7): 839~853
[163]Bozdogan H., Akaike's Information Criterion and Recent Developments inInformation Complexity, Journal of Mathematical Psychology, 2000, 44(1): 62~91
[164]Konishi S., Ando T., Imoto S., Bayesian information criteria and smoothing parameter selection in radial basis function networks, Biometrika, 2004 91(1): 27~43
[165]Barron A., Rissanen J., Yu B., The minimum description length principle in coding and modeling, IEEE Transactions on Information Theory, 1998, 44(6): 2743~2760
[166]Bouguila N., Ziou D., Unsupervised selection of a finite Dirichlet mixture model: an MML-based approach, IEEE Transactions on Knowledge and Data Engineering, 2006, 18(8): 993~1009
[167]Dempster A. P., Laird N. M., Rubin D. B., Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society: Series B, 1977, 39(1): 1~38
[168]Bazi Y., Bruzzone L., Melgani F., Image thresholding based on the EM algorithm and the generalized Gaussian distribution, Pattern Recognition, 2007, 40(2): 619~634
[169]Ahonen T., Hadid A., Pietikainen M., Face Description with Local Binary Patterns: Application to Face Recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006, 28(12): 2037~2041
[170]Choi S., Cichocki A., Amari S., Flexible independent component analysis, Journal of VLSI Signal Processing, 2000, 26(1): 25~38
[171]Aiazzi B., Alparone L., Baronti S., Estimation based on entropy matching for generalized Gaussian PDF modeling, IEEE Signal Processing Letters, 1999, 6(6): 138~140
[172]Do M. N., Vetterli M., Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance, IEEE Transactions on Image Processing, 2002, 11(2): 146~158
[173]Doucet A., Wang X., Monte Carlo methods for signal processing: a review in the statistical signal processing context, IEEE Signal Processing Magazine, 2005, 22(6): 152~170
[174]Do M. N., Fast Approximation of Kullback-Leibler Distance for Dependence Trees and Hidden Markov Models, IEEE Signal Processing Letters, 2003, 10(4): 115~118
[2]Jain A. K., Lin H., Prabhakar S., Biometric identification, Communications of the ACM, 2000, 43(2): 90~98
[3]Zhao W., Chellappa R., Rosenfeld A., et al, Face Recognition: A Literature Survey, ACM Computing Surveys, 2003, 35(4): 399~458
[4]Daugman J., New methods in iris recognition, IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, 2007, 37(5): 1167~1175
[5]刘小华,人脸识别技术及其应用研究:[博士学位论文],吉林;吉林大学,2005
[6]Pankanti S., Prabhakar S., Jain A. K., On the individuality of fingerprints, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24(8): 1010~1025
[7] Shneiderman B., The limits of speech recognition, Communications of the ACM, 2000, 43(9): 63~65
[8] Faundez-Zanuy M., Signature recognition state-of-the-art, IEEE Aerospace and Electronic Systems Magazine, 2005, 20(7): 28~32
[9]Boulgouris N. V., Hatzinakos D., Plataniotis K. N., Gait recognition: a challenging signal processing technology for biometric identification, IEEE Signal Processing Magazine, 2005, 22(6): 78~90
[10]杜春华,人脸特征点定位及识别的研究:[博士学位论文],上海;上海交通大学,2008
[11]Yang M. H., Kriegman D. J., Ahuja N., Detecting Faces in Images: A Survey, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24(1): 34~58
[12]Moghaddam B., Yang M. H., Learning Gender with Support Faces, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24(5): 707~711
[13]Guo G., Fu Y., Dyer C. R., et al, Image-based human age estimation by manifold learning and locally adjusted robust regression, IEEE Transactions on Image Processing, 2008, 17(7): 1178~1188
[14]Fasel B., Luettin J., Automatic facial expression analysis: a survey, Pattern Recognition, 2003, 36(1): 259~275
[15]McKenna S. J., Gong S., Real-time face pose estimation, Real-Time Imaging,1998, 4(5): 333~347
[16]Beveridge J. R., Bolme D., Draper B. A., et al, The CSU Face Identification Evaluation System, Machine Vision and Applications, 2005, 16(2): 128~138
[17]Sirohey S. A., Rosenfeld A., Eye detection in a face image using linear and nonlinear filters, Pattern Recognition, 2001, 34(7): 1367~1391
[18]卢湖川,人脸识别中几个关键算法研究:[博士学位论文],辽宁;大连理工大学,2008
[19]Yang Q., Tang X., Recent Advances in Subspace Analysis for Face Recognition, Proceedings of Chinese Conference on Biometric Recognition, 2004, 1: 275~287
[20]Turk M. A., Pentland A. P., Eigenfaces for recognition. Journal of Cognitive Neuroscience, 1991, 3(1): 71~86.
[21]Moghaddama B., Jebarab T., Pentland A., Bayesian Face Recognition, Pattern Recognition, 2000, 33(11): 1771~1782
[22]Belhumeur P. N., Hespanha J. P., Kriegman D. J., Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997, 19(7): 711~720
[23]Bartlett M. S., Movellan J. R., Sejnowski T. J., Face recognition by independent component analysis, IEEE Transactions on Neural Networks, 2002, 13(6): 1450~1464
[24]Tenenbaum J. B., Silva V., Langford J. C., A Global Geometric Framework for Nonlinear Dimensionality Reduction, Science, 2000, 290(5500): 2319~2323
[25]Roweis S. T., Saul L. K., Nonlinear Dimensionality Reduction by Locally Linear Embedding, Science, 2000, 290(5500): 2323~2326
[26]Belkin M., Niyogi P., Laplacian Eigenmaps for Dimensionality Reduction and Data Representation, Neural Computation, 2003, 15(6): 1373~1396
[27]He X., Yan S., Hu Y., et al, Face Recognition Using Laplacianfaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(3): 328~340
[28]Wang Y., Jia Y., Hu C., et al, Non-negative matrix factorization framework for face recognition, International Journal of Pattern Recognition and Artificial Intelligence, 2005, 19 (4): 495~511
[29]Cover T. M., Hart P. E., Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 1967, 13(1): 21~27
[30]Muller K. R., Mika S., Ratsch G., et al. An introduction to kernel-based learning algorithms, IEEE Transactions on Neural Networks, 2001, 12(2): 181~201
[31]Guo G. D., Li S. Z., Chan K. L., Support vector machines for face recognition, Image and Vision Computing, 2001, 19 (9-10): 631~638
[32]Scholkopf B., Smola A., Muller K. R., Nonlinear Component Analysis as a Kernel Eigenvalue Problem, Neural Computation, 1998, 10(5): 1299~1319
[33]Mika S., Ratsch G., Weston J., et al, Fisher discriminant analysis with kernels, Proceedings of IEEE Workshop on Neural Networks for Signal Processing, 1999, 4: 41~48
[34]Baudat G., Anouar F., Generalized Discriminant Analysis Using a Kernel Approach, Neural Computation, 2000, 12(10): 2385~2404
[35]Bach F. R., Jordan M. I., Kernel Independent Component Analysis, Journal of Machine Learning Research, 2002, 3(1): l~48
[36]Brunelli R., Poggio T., Face recognition: Features versus Templates, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993, 15(10): 1042~1052
[37] Heisele B., Ho P., Wu J., et al, Face recognition: component-based versus global approaches, Computer Vision and Image Understanding, 2003, 91(1-2): 6~21
[38]Wiskott L., Fellous J. M., Kruger N., et al, Face Recognition by Elastic Bunch Graph Matching, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997, 19(7): 775~779
[39]Wana K. W., Lama K. M., Ng K. C., An accurate active shape model for facial feature extraction, Pattern Recognition Letters, 2005, 26(15): 2409~2423
[40]Edwards G. J., Cootes T. F., Taylor C. J., Face Recognition Using Active Appearance Models, Proceedings of European Conference on Computer Vision, 1998, 2: 581~595
[41]Bicego M., Lagorio A., Grosso E., et al, On the use of SIFT features for face authentication, Proceedings of Conference on Computer Vision and Pattern Recognition Workshop, 2006, 1: 17~22
[42]Cartoux J. Y, Lapreste J. T., Richetin M., Face authentication or recognition by profile extraction from range images. Proceedings of Workshop on Interpretation of 3D Scenes, 1989, 1: 194~199
[43]Achermann B., Bunke H., Classifying range images of human faces with Hausdorff distance, Proceedings of International Conference on Pattern Recognition, 2000, 2: 809~813
[44]Medioni G., Waupotitsch R., Face recognition and modeling in 3D, Proceedings of IEEE International Workshop on Analysis and Modeling of Faces and Gestures, 2003, 1: 232~233
[45]Beumier C., Acheroy M., Automatic 3D face authentication, Image and Vision Computing, 2000, 18(4): 315-321
[46]Samaria F. S., Harter A. C., Parameterisation of a Stochastic Model for Human Face Identification, Proceedings of IEEE Workshop on Applications of Computer Vision, 1994, 1: 138~142
[47]Belhumeur P., Hespanha J., Kriegman D., Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection, Proceedings of European Conference on Computer Vision, 1996, 1: 45~58
[48]Martinez A.M., Benavente R., The AR Face Database. CVC Technical Report No.24, Purdue University, 1998
[49]胡元奎,可变光照和可变姿态条件下的人脸图像识别研究:[博士学位论文],安徽;中国科学技术大学,2006
[50]Strang G., The Discrete Cosine Transform, SIAM Review, 1999, 41(1): 135~147
[51]Hafed Z. M., Levine M. D., Face Recognition Using the Discrete Cosine Transform, International Journal of Computer Vision, 2001, 43(3): 167~188
[52]Ramasubramanian D., Venkatesh Y.V., Encoding and recognition of faces based on the human visual model and DCT, Pattern Recognition, 2001, 34(12): 2447~2458
[53]Jing Y. X., Zhang D., A face and palmprint recognition approach based on discriminant DCT feature extraction, IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, 2004, 34(6): 2405~2415
[54]Er M. J., Chen W., Wu S., High-speed face recognition based on discrete cosine transform and RBF neural networks, IEEE Transactions on Neural Networks, 2005, 16(3): 679~691
[55]Choi J., Chung Y. S., Kim K. H., et al, Face Recognition using Energy Probability in DCT Domain, Proceedings of IEEE International Conference on Multimedia and Expo, 2006, 1: 1549~1552
[56]Chen W., Er M. J., Wu S., Illumination compensation and normalization for robust face recognition using discrete cosine transform in logarithm domain, IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, 2006, 36(2): 458~466
[57]Schwerin B., Paliwal K., Local-DCT features for facial recognition, Proceedings of International Conference on Signal Processing and Communication Systems, 2008, 1: 1~6
[58]Aroussi E. M., Amine A., Ghouzali S., et al, Combining DCT and LBP Feature Sets For Efficient Face Recognition, Proceedings of International Conference on Information and Communication Technologies: From Theory to Applications, 2008, 1: 1~6
[59]Dabbaghchiana S., Ghaemmaghamib M. P., Aghagolzadeh A., Feature extraction using discrete cosine transform and discrimination power analysis with a face recognition technology, Pattern Recognition, 2010, 43(4): 1431~1440
[60]Rioul O., Vetterli M., Wavelets and signal processing, IEEE SignalProcessing Magazine, 1991, 8(4): 14~38
[61]Bai L., Liu Y., When eigenfaces are combined with wavelets, Knowledge-Based Systems, 2002, 15(5-6): 343~347
[62]Ma Y., Li S., Face recognition by combining eigenface method with different wavelet subbands, Optoelectronics Letters, 2006, 2(5): 383-385
[63]Neo H. F., Teoh A., Ngo. D. L., Face Recognition Using Wavelet Transform and Non-negative Matrix Factorization, Proceedings of Australian Joint Conference on Artificial Intelligence, 2004, 1: 192~202
[64]Hazim Kemal Ekenel, Bulent Sankur, Multiresolution face recognition, Image and Vision Computing, 2005, 23(5): 469~477
[65]Li B., Yin H., Face Recognition Based on Support Vector Machine Fusion and Wavelet Transform, Proceedings of International Conference on Computational Intelligence and Security, 2005, 2: 764~771
[66]Vinod Pathangay, Sukhendu Das, Selection of Wavelet Subbands Using Genetic Algorithm for Face Recognition, Proceedings of Indian Conference Computer Vision, Graphics and Image Processing, 2006, 1: 585~596
[67]Selesnick I. W., Baraniuk R. G., Kingsbury N. G., The Dual-Tree Complex Wavelet Transform, IEEE Signal Processing Magazine, 2005, 22(6): 123~151
[68]Celik T., Ozkaramanh H., Demirela H., Facial feature extraction using complex dual-tree wavelet transform, Computer Vision and Image Understanding, 2008, 111(2): 229~246
[69]Liu C. C., Dai D. Q., Face recognition using dual-tree complex wavelet features, IEEE Transactions on Image Processing, 2009, 18(11): 2593~2599
[70]Zhang G.Y., Peng S. Y., Li H. M., Combination of dual-tree complex wavelet and SVM for face recognition, Proceedings of International Conference on Machine Learning and Cybernetics, 2008, 5: 2815~2819
[71]Peng Y., Xie X., Xu W., et al, Face recognition using anisotropic dual-tree complex wavelet packets, Proceedings of International Conference on Pattern Recognition, 2008, 1: 1~4
[72]Lee T. S., Image representation using 2D Gabor wavelets, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1996, 18(10): 959~971
[73]A. Serrano, I. Diego, Conde C., et al, Recent advances in face biometrics with Gabor wavelets: A review, Pattern Recognition Letters, 2010, 31(5): 372~381
[74]Buhmann J., Lange J., Malsburg C., Distortion invariant object recognition by matching hierarchically labeled graphs, Proccedings of International Joint Conference on Neural Networks, 1989, 1: 155~159
[75]Lades M., Vorbruggen J. C., Buhmann J., et al, Distortion invariant object recognition in the dynamic link architecture, IEEE Transactions on Computers, 1993,42(3): 300~311
[76]Chung K. C.,Kee S. C.,Kim S. R., Face recognition using principal component analysis of Gabor filter responses, Proceedings of International Workshop on Recognition, Analysis, and Tracking of Faces and Gestures in Real-Time Systems, 1999, 1: 53~57
[77]Liu C., Wechsler H., Gabor Feature Based Classification Using the Enhanced Fisher Linear Discriminant Model for Face Recognition, IEEE Transactions on Image Processing, 2002, 11(4): 467~476
[78]Liu C., Wechsler H. Independent component analysis of Gabor features for face recognition, IEEE Transactions on Neural Networks, 2003. 14(4): 919~928
[79]Liu C., Gabor-based kernel PCA with fractional power polynomial models for face recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, 26(5): 572~581
[80]Shan S., Yang P., Chen X., et al, AdaBoost Gabor Fisher Classifier for Face Recognition, Proceedings of International Workshop on Analysis and Modelling of Faces and Gestures, 2005, 1: 279~292
[81]Zhang W., Shan S., Gao W., et al, Local Gabor binary pattern histogram sequence (LGBPHS): a novel non-statistical model for face representation and recognition, Proceedings of International Conference on Computer Vision, 2005, 1: 786~791
[82]Nanni L., Maio D., Weighted Sub-Gabor for face recognition, Pattern Recognition Letters, 2007, 28(4): 487~492
[83]Zheng Z., Yang F., Tan W., et al, Gabor feature-based face recognition using supervised locality preserving projection, Signal Processing, 2007, 87(10): 2473~2483
[84]Pang Y., Yuan Y., Li X., Gabor based region covariance matrices for face recognition, IEEE Transactions on Circuits and Systems for Video Technology, 2008, 18(7): 989~993
[85]Beylkin G., Discrete Radon transform, IEEE Transactions on Acoustics, Speech and Signal Processing, 35(2): 162~172
[86]Karsili L., Acan A., A Radon Transform and PCA Hybrid for High Performance Face Recognition, Proceedings of IEEE International Symposium on Signal Processing and Information Technology, 2007, 1: 246~251
[87]Zhang Y.; Wang X., Study of Finite Radon Transform in Face Recognition, Proceedings of International Conference on Computer Modeling and Simulation, 2010, 4: 29~32
[88] Matus F., Flusser J., Image Representation via a Finite Radon Transform, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993, 15(10):996~1006
[89]Candes E., Demanet L., Donoho D., et al, Fast Discrete Curvelet Transforms, Multiscale Modeling and Simulation, 2006, 5(3): 861~899
[90]Mandal T., Majumdar A., Wu Q. M., Face Recognition by Curvelet Based Feature Extraction, Proceedings of International Conference on Image Analysis and Recognition, 2007, 1: 806~817
[91]Aroussi M. E., Hassouni, M. E., Ghouzali S., et al, Block based curvelet feature extraction for face recognition, Proceedings of International Conference on Multimedia Computing and Systems, 2009, 1: 299~303
[92]Mandal T., Wu Q. M., Yuan Y., Curvelet based face recognition via dimension reduction, Signal Processing, 2009, 89(12): 2345~2353
[93]Do M. N., Vetterli M., The Contourlet Transform: An Efficient Directional Multiresolution Image Representation, IEEE Transactions on Image Processing, 2005, 14(12): 2091~2106
[94]Boukabou W. R., Bouridane A., Contourlet-Based Feature Extraction with PCA for Face Recognition, Proceedings of NASA/ESA Conference on Adaptive Hardware and Systems, 2008, 1: 482~486
[95]Xu X., Zhang D., Zhang X., An efficient method for human face recognition using nonsubsampled contourlet transform and support vector machine, Optica Applicata, 2009, 39(3): 601-615
[96]Chougdali K., Jedra M., Zahid N., Contourlet feature based kernel relevance weighted discriminant analysis for face recognition, Proceedings of International Conference on Multimedia Computing and Systems, 2009, 1: 268~272
[97]Abouzar P., Yousefi S., Setarehdan S. K., Hybrid WT Based-DCT Based Face Recognition, Proceedings of IEEE International Conference on Signal Processing and Communications, 2007, 1: 963~966
[98]Jadhav D. V., Holambe R. S., Radon and discrete cosine transforms based feature extraction and dimensionality reduction approach for face recognition, Signal Processing, 2008, 88(10): 2604~2609
[99]Jadhav D. V., Holambe R. S., Feature extraction using Radon and wavelet transforms with application to face recognition, Neurocomputing, 2009, 72(7-9): 1951~1959
[100]Gabor D., Theory of communication, Journal of Institute for Electrical Engineering, 1946, 93(26): 429~457
[101]Daugman J. G., Uncertainty relation for resolution in space, spatial frequency and orientation optimized by two-dimensional visual cortical filters. Journal of the Optical Society of America A, 1985, 2(7): 1160~1169
[102]Marcelja S., Mathematical description of the responses of simple corticalcells, Journal of Optical Society ofAmerica, 1980, 70(11): 1297~1300
[103]Pollen D., Ronner S., Phase relationships between adjacent simple cells in the visual cortex, Science, 1981, 212(4501): 1409~1411
[104]Daugman J. G., Complete discrete 2-D Gabor transform by neural networks for image analysis and compression. IEEE Transactions on Acoustics, Speech and Signal Processing, 1988, 36(7): 1169~1179
[105]Porat M., Zeevi Y. Y., The generalized Gabor scheme of image representation in biological and machine vision. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1988, 10(4): 452~468
[106]山世光,人脸识别中若干关键问题的研究:[博士学位论文],北京;中国科学院计算技术研究所,2004
[107]Vetterli M., Wavelets, approximation, and compression, IEEE Signal Processing Magazine, 2001, 18(5): 59~73
[108]Mallat S., A theory for multiresolution signal decomposition: The wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989, 11(7): 674~693
[109]Choi H., Romberg J., Baraniuk R.G., et al, Hidden Markov tree modeling of complex wavelet transforms, Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, 2000, 1: 133~136
[110]Dragotti P. L., Vetterli M., Wavelet footprints: Theory, algorithms, and applications, IEEE Transactions on Signal Processing, 2003, 51(5) 1306~1323
[111]Kingsbury N.G., The dual-tree complex wavelet transform: A new efficient tool for image restoration and enhancement, Proceedings of European Signal Processing Conference, 1998, 1: 319~322
[112]Selesnick I. W., The design of approximate Hilbert transform pairs of wavelet bases. IEEE Transactions on Signal Processing, 2002, 50(5): 1144~1152
[113]Kingsbury N. G., Shift invariant properties of the Dual-Tree Complex Wavelet Transform, Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, 1999, 3: 1221~1224
[114]Kingsbury N. G., Complex wavelets for shift invariant analysis and filtering of signals, Applied and Computational Harmonic Analysis, 2001, 10(3): 234~253
[115]Pearson K., On lines and planes of closest fit to systems of points in space, Philosophical Magazine, 1901, 2(11): 559~572
[116]Hotelling H., Analysis of a complex of statistical variables into principal components, Journal of Educational Psychology, 1933, 24(6): 417~441
[117]Jutten C., Herault J., Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture, Signal Processing, 1991, 24(1): 1~10
[118]Tong L., Liu R. W., Soon V. C., et al, Indeterminacy and identifiability of blind identification, IEEE Transactions on Circuits and Systems, 1991, 38(5): 499~509
[119]Hyvarinen A., Oja E., Independent component analysis: algroithms and applications. Neural Networks, 2000, 13(4): 411~430
[120]Comon P., Independent component analysis: A new concept?, Signal Processing, 1994, 36(3): 287~313
[121]Cardoso J. F., Souloumiac A., Blind beamforming for non-Gaussian signals, IEE Proceedings F: Radar and Signal Processing, 1993, 140(6): 362~370
[122]Oja E., The nonlinear PCA learning rule in independent component analysis, Neurocomputing, 1997, 17(1): 25~45
[123]karhunen J., Loutsensalo J., Representation and separation of signals using nonlinear PCA type learning, Neural Networks, 1994, 7(1): 113~127
[124]Gaeta M., Lacoume J. L., Source separation without prior knowledge: The maximum likelihood solution, Proceedings of European Signal Processing Conference, 1990, 1: 621~624
[125]Pham, D. T., Garat P., Blind separation of mixture of independent sources through a quasi-maximum likelihood approach, IEEE Transactions on Signal Processing. 1997, 45(7): 1712~1725
[126]Pearlmutter B. and Parra L., A context-sensitive generalization of ICA, Proceedings of International Conference on Neural Information Processing, 1996, 1: 151~157
[127]Bell A.J., Sejnowski T.J., An information-maximization approach to blind separation and blind deconvolution, Neural Computation, 1995, 7(6): 1129~1159
[128]Lee T.W., Girolami M., Sejnowski T.J., Independent component analysis using an extended infomax algorithm for mixed sub-gaussian and super-gaussian sources, Neural Computation, 1999, 11(2): 417~441
[129]Amari S., Cichocki A., Adaptive blind signal processing-neural network approaches. Proceedings of the IEEE, 1998, 86(10): 2026~2048
[130]Hyvarinen A., Oja E., A fast fixed-point algorithm for independent component analysis, Neural Computation, 1997, 9(7): 1483~1492
[131]Hyvarinen A., Fast and robust fixed-point algorithms for independent component analysis, IEEE Transactions on Neural Networks, 1999, 10(3): 626~634
[132]Cardoso J. F., Infomax and maximum likelihood for blind separation, IEEE Signal Processing Letters, 1997, 4(4): 112~113
[133]Karhunen J., Pajunen P., Oja E., The nonlinear PCA criterion in blind source separation: Relations with other approaches, Neurocomputing, 1998, 22(1-3):
[134]Hyvarinen A., Gaussian moments for noisy independent component analysis, IEEE Signal Processing Letters, 1999, 6(6): 145~147
[135]Lewicki M. S., Sejnowslci T. J., Learning overcomplete representations, Neural Computation, 2000, 12(2): 337~365
[136]Hyvarinen A., Pajunen P., Nonlinear independent component analysis: Existence and uniqueness results. Neural Networks, 1999, 12(3): 429~439
[137]Liu C., Wechsler H., Robust Coding Schemes for Indexing and Retrieval from Large Face Databases, IEEE Transactions on Image Processing, 2000, 9(1): 132~137
[138]Fisher R. A., The Use of Multiple Measures in Taxonomic Problems, Annals of Eugenics, 1936, 7(1): 179~188
[139]Martinez A. M., Kak A. C., PCA versus LDA, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(2): 228~233
[140]边肇祺,张学工,模式识别(第二版),北京:清华大学出版社,2000,9~16
[141]Moghaddam B., Pentland A., Probabilistic Visual Learning for Object Representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997, 19(7): 696~710
[142]Mardia K. V., Kent J. T., Bibby J. M., Multivariate Analysis, Academic Press, Duluth, London, 1979, 103~104
[143]Tipping M.E., Bishop C.M., Probabilistic Principal Component Analysis, Journal of the Royal Statistical Society Series B (Statistical Methodology), 1999, 61(3): 611~622
[144]Wang X. G., Tang X. O., An improved Bayesian face recognition algorithm in PCA subspace, Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003, 3:129~132
[145]Moghaddam B., Nastar C., Pentland A., Bayesian Face Recognition with Deformable Image Models, Proceedings of International Conference on Image Analysis and Processing, 2001, 1:26~35
[146]Wang X. G., Tang X. O., Bayesian face recognition using Gabor features, Proceedings of ACM SIGMM workshop on Biometrics methods and applications, 2003, 1: 70~73
[147]Niu L., Zheng Y., Dou Y., et al, Combined Face Recognition Using Wavelet Transform and Bayesian, Proceedings of International Conference on Information and Computing Science, 2009, 2: 337~340
[148]Wang L.W., Wang X., Feng J. F., Intrapersonal subspace analysis with application to adaptive Bayesian face recognition, Pattern Recognition, 2005, 38(4): 617~621
[149]Wang L.W., Wang X., Feng J. F., Subspace distance analysis with application to adaptive Bayesian algorithm for face recognition, Pattern Recognition, 2006, 39(3): 456~464
[150]Zhang D.Q., Two-Dimensional Bayesian Subspace Analysis for Face Recognition, Proceedings of International Symposium on Neural Networks, 2007, 2: 778~784
[151]Yang J., Zhang D., Frangi A. F., et al, Two-dimensional PCA: a new approach to appearance-based face representation and recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, 26(1): 131~137
[152]Niu L., Zheng Y., Li X., et al, Bayesian Face Recognition Using 2DPCA, Proceedings of International Forum on Information Technology and Applications, 2009, 2: 567~570
[153]Wang X. G., Tang X. O., Bayesian Face Recognition Based on Gaussian Mixture Models, Proceedings of International Conference on Pattern Recognition, 2004, 4: 142~145
[154]Wang X. G., Tang X. O., Subspace Analysis Using Random Mixture Models, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005, 1:574~580
[155]Jiang X. D., Mandal B., Kot A., Enhanced maximum likelihood face recognition, Electronics Letters, 2006, 42(19): 1089~1090
[156]Li Z. F., Tang X. O., Using Support Vector Machines to Enhance the Performance of Bayesian Face Recognition, IEEE Transactions on Information Forensics and Security, 2007, 2(2): 174~180
[157]唐杰,基于贝叶斯策略的人脸识别研究:[硕士学位论文],北京;中国科学院计算技术研究所,2006
[158]李伟红,龚卫国,陈伟民,等,基于中国人人脸区域特征的贝叶斯分类法研究,仪器仪表学报,2004,25(4):461~464
[159]朱学毅,王崇骏,周新民,等,一种改进的贝叶斯人脸识别算法,计算机科学,2006,33(9):204~206
[160]Kokkinakis K., Nandi A. K., Exponent parameter estimation for generalized Gaussian probability density functions with application to speech modeling, Signal Processing, 2005, 85(9): 1852~1858
[161]Vlassis N., Likas A., A Greedy EM Algorithm for Gaussian Mixture Learning, Neural Processing Letters, 2002, 15(1): 77~87
[162]Fan S. K., Lin Y., A fast estimation method for the generalized Gaussian mixture distribution on complex images, Computer Vision and Image Understanding, 2009, 113(7): 839~853
[163]Bozdogan H., Akaike's Information Criterion and Recent Developments inInformation Complexity, Journal of Mathematical Psychology, 2000, 44(1): 62~91
[164]Konishi S., Ando T., Imoto S., Bayesian information criteria and smoothing parameter selection in radial basis function networks, Biometrika, 2004 91(1): 27~43
[165]Barron A., Rissanen J., Yu B., The minimum description length principle in coding and modeling, IEEE Transactions on Information Theory, 1998, 44(6): 2743~2760
[166]Bouguila N., Ziou D., Unsupervised selection of a finite Dirichlet mixture model: an MML-based approach, IEEE Transactions on Knowledge and Data Engineering, 2006, 18(8): 993~1009
[167]Dempster A. P., Laird N. M., Rubin D. B., Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society: Series B, 1977, 39(1): 1~38
[168]Bazi Y., Bruzzone L., Melgani F., Image thresholding based on the EM algorithm and the generalized Gaussian distribution, Pattern Recognition, 2007, 40(2): 619~634
[169]Ahonen T., Hadid A., Pietikainen M., Face Description with Local Binary Patterns: Application to Face Recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006, 28(12): 2037~2041
[170]Choi S., Cichocki A., Amari S., Flexible independent component analysis, Journal of VLSI Signal Processing, 2000, 26(1): 25~38
[171]Aiazzi B., Alparone L., Baronti S., Estimation based on entropy matching for generalized Gaussian PDF modeling, IEEE Signal Processing Letters, 1999, 6(6): 138~140
[172]Do M. N., Vetterli M., Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance, IEEE Transactions on Image Processing, 2002, 11(2): 146~158
[173]Doucet A., Wang X., Monte Carlo methods for signal processing: a review in the statistical signal processing context, IEEE Signal Processing Magazine, 2005, 22(6): 152~170
[174]Do M. N., Fast Approximation of Kullback-Leibler Distance for Dependence Trees and Hidden Markov Models, IEEE Signal Processing Letters, 2003, 10(4): 115~118