基于LDA的人脸识别
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摘要
人脸识别是模式识别和机器视觉领域最富挑战性的研究课题之一,它在人机交互,安全监视,身份认证等方面有着非常广阔的应用前景。在目前的特征提取算法中,基于Fisher准则的线性判别分析(LDA)算法是一种较成功的特征提取算法。
但是LDA用于人脸识别时,遇到三个问题：(1)小样本问题；(2)LDA利用同一个准则函数把所有样本投影到同一个特征空间,忽略了不同类的样本分布的特征差异；(3)LDA对于复合模型分类能力较低。本文针对问题一,利用最大散度差线性鉴别分析来解决；对问题二,利用类依赖线性判别分析方法,对每一类样本根据一定的准则函数,建立一个反应本身类别特性的投影矩阵；对问题三,利用增强LDA,通过两个不同的加权矩阵对类间离散度矩阵和类内离散度矩阵进行重新定义,改进的Fisher准则可以在降维后的子空间中保存局部信息,使距离较近的类别投影后不会混在一起。
最后本文在这些方法的基础上提出了一种改进方法,类依赖增强LDA,充分发挥了增强LDA和类依赖的优点,最后在ORL和YaleB人脸库上进行实验,实验结果表明了该方法的有效性。
Face recognition is one of the most challenging problems in the fields of pattern recognition and machine vision. It has a wide range of promising application, such as human-computer interaction, security surveillance, identity authentication, and so on. Linear Discriminate Analysis algorithm (LDA) based on the Fisher criterion is a successful algorithm among the feature extraction algorithms.
However, there are three problems with LDA for face recognition. First one is the small training sample size(SSS) problem, we introduce the maximum margin criterion(MMC) to solve this problem;The second one is LDA projects samples from all classes to one single subspace obtained by the same criterion function. It ignores the fact that a class has its own optimal feature vector discriminating itself from the other classes; we introduce the class-dependent LDA (CDLDA).In the scheme of CDLDA, a class has its own optimal feature vector to discriminate itself from the other classes. The third one is it would collapse the samples from different classes into one single cluster when the class distributions are multimodal. An enhanced LDA method is proposed. The between-class and the within-class scatter are reformulated by introducing two different weighted matrices in respective, which can preserve the local structure of different class in the reduced subspace. Then it can avoid collapsing samples of different classes into one single cluster.
In the end an improved method based on these above methods is presented, called class-dependent and enhanced LDA (CD-ELDA).Experiments show encouraging performance of the proposed algorithm.
但是LDA用于人脸识别时,遇到三个问题：(1)小样本问题；(2)LDA利用同一个准则函数把所有样本投影到同一个特征空间,忽略了不同类的样本分布的特征差异；(3)LDA对于复合模型分类能力较低。本文针对问题一,利用最大散度差线性鉴别分析来解决；对问题二,利用类依赖线性判别分析方法,对每一类样本根据一定的准则函数,建立一个反应本身类别特性的投影矩阵；对问题三,利用增强LDA,通过两个不同的加权矩阵对类间离散度矩阵和类内离散度矩阵进行重新定义,改进的Fisher准则可以在降维后的子空间中保存局部信息,使距离较近的类别投影后不会混在一起。
最后本文在这些方法的基础上提出了一种改进方法,类依赖增强LDA,充分发挥了增强LDA和类依赖的优点,最后在ORL和YaleB人脸库上进行实验,实验结果表明了该方法的有效性。
Face recognition is one of the most challenging problems in the fields of pattern recognition and machine vision. It has a wide range of promising application, such as human-computer interaction, security surveillance, identity authentication, and so on. Linear Discriminate Analysis algorithm (LDA) based on the Fisher criterion is a successful algorithm among the feature extraction algorithms.
However, there are three problems with LDA for face recognition. First one is the small training sample size(SSS) problem, we introduce the maximum margin criterion(MMC) to solve this problem;The second one is LDA projects samples from all classes to one single subspace obtained by the same criterion function. It ignores the fact that a class has its own optimal feature vector discriminating itself from the other classes; we introduce the class-dependent LDA (CDLDA).In the scheme of CDLDA, a class has its own optimal feature vector to discriminate itself from the other classes. The third one is it would collapse the samples from different classes into one single cluster when the class distributions are multimodal. An enhanced LDA method is proposed. The between-class and the within-class scatter are reformulated by introducing two different weighted matrices in respective, which can preserve the local structure of different class in the reduced subspace. Then it can avoid collapsing samples of different classes into one single cluster.
In the end an improved method based on these above methods is presented, called class-dependent and enhanced LDA (CD-ELDA).Experiments show encouraging performance of the proposed algorithm.
引文
[1]T. Kanade. Picture processing system by computer and recognition of human faces. Ph. D Dissertation, Kyoto university.1973
[2]R. Brunelli,T. Poggio. Face recognition:features vs. templates. IEEE Transactions on Pattern Analysis and Machine Intelligence.1993,vol.15,no.10,pp.1042-1052
[3]Huang C L, Chen C W. Human facial feature extraction for face interpretation and recognition[J]. Pattern Recognition,1992,vol.25,no.l2,pp.1435-1444
[4]M. Ldes,J.C. Vorbruggen, J. Buhmann. Distortion invariant object recognition in the dynamic link architecture. IEEE Transactions on Computers.1993,vol.42,no.3,pp. 300-310
[5]L.Wishott,J.M. Fellous,N. Kruger. Face Recognition by Elastic Bunch Graph Matching. IEEE Transactions on Pattern Analysis and Machine Intelligence.1997, vol.19, pp.775-779
[6]Turk M and Pentland A. Eigenfaces for recognition. J.Cognitive Neuroscience,1991, vol.3,no.1,pp.71-86
[7]Peter N.Belhumeur,et al,Egienfaces vs Fisherfaces:Recognition using class specific linear projection. IEEE Trans.Pattern Anal Machine Intell.vol.l9,no.7,pp 711-720
[8]Chen Li-Fen, Liao H-Y Mark, Ko M-T,et al. A new LDA-based face recognition system which can solve the small sample size problem [J]. Pattern Recognition,2000, vol.33,no.10,pp.1713-1726
[9]H. Yu, J. Yang, A direct LDA algorithm for high-dimensional data-with application to face recognition. Pattern Recognition 34 (2001) pp.2067-2070
[10]Xiaogang Wang, Xiaoou Tang, Dual-Space Linear Discriminant Analysis for Face Recognition. IEEE Computer Society Conference on Computer Vision and Pattern Recognition(CVPR'04),1063-6919/04,2004.
[11]K.FUKUNAGA, Nonparametric Discriminant Analysis, IEEE Computer Society vol. PAMI-5,no.6, NOVEMBER 1983.
[12]BAUDAT G, ANOUAR F. Generalized discriminant analysis using a kernel approach [J]. Neural Computation,2000, vol.12,no.10,pp2385-2404
[13]Yu Bing. Lin Lian. fu, chen Ping. A new LDA-based method for face recognition[c]. Proceedings of 16th International Conference on Pattern Recognition,2002,ppl68-171.
[14]陈晓红,陈松灿,类依赖的线性判别分析,Journal of Chinese Computer Systems, vol.29, no.5,2008. pp894-897.
[15]M.S.Bartlett,H.M.Lades,T.J.Sejnowski, Independent component representations for face recognition.SPIE Proc.2399,1998
[16]Cevikalp H, Neamtu M, Wilkes M. Discriminative common vectors for face recognition. IEEE Transactionson Pattern Analysis and Machine Intelligence,2005, vol.27,no.1,4/13
[17]He Y H, Zhao L, Zou C R. Face recognition using common faces method. Pattern Recognition,2006, vol.39,no.11,pp2218-2222
[18]Belkin M, Niyogi P. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation,2003,vol.15,no.6,pp1373-1396.
[19]He XF, Yan S, Hu Y, Niyogi P, Zhang HJ. Face recognition using Laplacianfaces. IEEE Trans. on Pattern Analysis and Machine Intelligence, 2005,vol.27,no.3,pp328-340.
[20]Yu WW, Teng XL, Liu CQ. Face recognition using discriminant locality preserving projections. Image and Vision Computing,2006,24:pp239-248.
[21]Lu K, Zhao JD, Wu Y, He XF. Relevance feedbacks algorithm based on locality preserving projections. Journal of Computer-Aided Design & Computer Graphics, 2007,vol.19,no.1,pp20-24 (in Chinese with English abstract).
[22]Li JB, Pan JS, Chu SC. Kernel class-wise locality preserving projection. Information Sciences,2008,178,pp1825-1835.
[23]Yang LP, Gong WG, Gu XH, Li WH, Liang YX. Null space discriminant locality preserving projections for face recognition.Neurocomputing, 2008,71,pp3644-3649.
[24]Kohonen T.Self-organization and associative memory[M].Berlin:Springer,1988
[25]Lawrence S, Giles C L, Tsoi A C, etal. Face reeognition:a convolutional neural-network approaeh[J]. IEEETrans. Neural Network,1997,vol.8,no.l,pp98-113
[26]Lin S H, Kung SY, Lin L J. Face recognition and deteetion by probabilistic decision-based neural network[J].IEEE Trans.on Neural Networks,1997, vol.8,no.1,pp114-132
[27]Lee D and Seung H. Cognition. The manifold ways of perception. Science,2000,2 90 (5500) pp2268-2269
[28]Tenenbaum, J., De Silva, V., Langford, J., A global geometric framework for nonlinear dimension reduction. Science,2000,290:pp2319-2323
[29]Roweis, S., Saul, L., Nonlinear dimensionality reduction by locally linear embedding. Science,2000,290:pp2323-2326
[30]Face Recognition Homepage.http://www.face-rec.org
[31]赵宏伟,基于PCA针对表情变化的人脸识别技术研究。西安电子科技大学,2009.
[32]Peter N.Belhumeur,et al.Eigenfaces vs.Fisherfaces:Recognition using class specific linear projection.IEEE Trans.Pattern Anal. Machine Intell.19(7)(1997),pp711-720.
[33]Liu K,Yang J.-Y.et al.An efficient algorithm for Foley-Sammon optimal set of discriminant vectors by algebraic method.International Journal of Pattern Recognition and Artificial Intelligence 1992,vol.6,no.5,pp817-829.
[34]R. Duda and P. Hart.Pattern Classification and Scene Analysis. Wiley, New York, 1973
[35]Chen Li-Fen, Liao H-Y Mark, Ko M-T, et al.A new LDA-based face recognition system which can solve the small sample size problem [J]. Pattern Recognition 2000, vol.33,no.l0,pp1713-1726.
[36]Huang R, LIU Q S, LU H Q, et al. Solving the small sample size problem of LDA [C]. Proceedings of International Conference on Pattern Recognition, Canada, Quebec,2002
[37]H. Yu, J. Yang.A direct LDA algorithm for high-dimensional data—with application to face recognition. Pattern Recognition 34 (2001) pp2067-2070
[38]杨利平,龚卫国,辜小花,完备鉴别保局投影人脸识别算法,Journal of Software, vol.21, no.6, June 2010, pp.1277-1286
[39]刘永俊,扬州大学,小样本问题下人脸图像的鉴别特征抽取方法研究,硕士学位论文
[40]程云鹏,矩阵论,西北工业大学出版社,1989,pp294-302
[41]Paul M B.Class-specific feature sets in classification.[J].IEEE Transactionm on Signal processing,1999, vol.47,no.10,pp3428-3432.
[42]PuaI M B, Niemann H. A theoretically optiml probabilistic classifier using class-specific features[c]. Proceedings of the 15th International Conference on Pattern Recognition. Barcelona. Spanish,IEEE Computer Society Press-2000,pp763-769.
[43]Paul M B. The class-specific classfier avoiding the curse of dimensionaIity[J]. Aerospace and Electronic Systems Magazine 2004.vol.19,no.1,pp37-52.
[44]Caputo B, Niemann H. To each according to its need:kernel class-specific classifiers[c]. Proceedings of the 16th International Conference on Pattern Recognition. Quebec. Canada:IEEE Press,2002,pp94-97.
[45]A. Mahalanobis, B. V. K. Vijaya Kumar, and D. Casasent.Minimum average correlation energy filters.Appl. Opt., vol.26,pp.3630-3633,1987.
[46]何润,方驰,丁晓青,用于人脸识别的一种新的类依赖特征抽取方法,电视技术2007年第31卷第8期,pp137-139
[47]Yan Yan, Yu-Jin Zhang, 1D correlation filter based class-dependence feature analysis for face recognition. Pattern Recognition 41 (2008) pp3834-3841
[48]Yan YAN, Yu-Jin ZHANG. Effective Discriminant Feature Extraction Framework for Face Recognition.Proceedings of the 4th International Symposium on ommunications,Control and Signal Processing. ISCCSP 2010, Limassol, cyprus, 3-5,March,2010
[49]H.Hul, P.Zhang, F.De la Torre.Face recognition using enhanced linear discriminant analysis.IET Comput.Vis.2010,vol4,Iss.3,ppl95-208.
[50]FUKUNAGA K. Introduction to statistical pattern recognition.Academic Press, 1990,2nd edn.
[51]HE X.,YAN S.,HU Y. Face recognition using Laplacian faces.IEEE Trans. Pattern Anal. Mach.Intell.,2005, vol.27,no.3, pp328-340
[52]MANLI Z.,MARTINEZ A.Subclass discriminant analysis.IEEE Trans. Pattern Anal. Mach. Intell.,2006, vol.28,no.8,pp.1274-1286
[53]KIM T.,KITTLER J.Locally linear discriminant analysis for multimodally distributed classes for face recognition with a single model image.IEEE Trans. Pattern Anal. Mach. Intell.,2005, vol.27,no.3,pp318-327
[54]HARANDI M., NILI AHMADABADI M., ARAABI B.Optimal local basis:a reinforcement learning approach for face recognition.Int. J. Comput. Vis., 2009,vol.81,no.2,pp191-204
[55]RODRIGUEZ Y., MARCEL S.Face authentication using adapted local binary pattern PDFs.Proc. Ninth European Conf. Computer Vision (ECCV), Graz, Austria, 2006,pp321-332
[56]FRIEDMAN J.H.Regularized discriminant analysis.J. Am.Stat. Assoc.,1989,84, pp165-175
[2]R. Brunelli,T. Poggio. Face recognition:features vs. templates. IEEE Transactions on Pattern Analysis and Machine Intelligence.1993,vol.15,no.10,pp.1042-1052
[3]Huang C L, Chen C W. Human facial feature extraction for face interpretation and recognition[J]. Pattern Recognition,1992,vol.25,no.l2,pp.1435-1444
[4]M. Ldes,J.C. Vorbruggen, J. Buhmann. Distortion invariant object recognition in the dynamic link architecture. IEEE Transactions on Computers.1993,vol.42,no.3,pp. 300-310
[5]L.Wishott,J.M. Fellous,N. Kruger. Face Recognition by Elastic Bunch Graph Matching. IEEE Transactions on Pattern Analysis and Machine Intelligence.1997, vol.19, pp.775-779
[6]Turk M and Pentland A. Eigenfaces for recognition. J.Cognitive Neuroscience,1991, vol.3,no.1,pp.71-86
[7]Peter N.Belhumeur,et al,Egienfaces vs Fisherfaces:Recognition using class specific linear projection. IEEE Trans.Pattern Anal Machine Intell.vol.l9,no.7,pp 711-720
[8]Chen Li-Fen, Liao H-Y Mark, Ko M-T,et al. A new LDA-based face recognition system which can solve the small sample size problem [J]. Pattern Recognition,2000, vol.33,no.10,pp.1713-1726
[9]H. Yu, J. Yang, A direct LDA algorithm for high-dimensional data-with application to face recognition. Pattern Recognition 34 (2001) pp.2067-2070
[10]Xiaogang Wang, Xiaoou Tang, Dual-Space Linear Discriminant Analysis for Face Recognition. IEEE Computer Society Conference on Computer Vision and Pattern Recognition(CVPR'04),1063-6919/04,2004.
[11]K.FUKUNAGA, Nonparametric Discriminant Analysis, IEEE Computer Society vol. PAMI-5,no.6, NOVEMBER 1983.
[12]BAUDAT G, ANOUAR F. Generalized discriminant analysis using a kernel approach [J]. Neural Computation,2000, vol.12,no.10,pp2385-2404
[13]Yu Bing. Lin Lian. fu, chen Ping. A new LDA-based method for face recognition[c]. Proceedings of 16th International Conference on Pattern Recognition,2002,ppl68-171.
[14]陈晓红,陈松灿,类依赖的线性判别分析,Journal of Chinese Computer Systems, vol.29, no.5,2008. pp894-897.
[15]M.S.Bartlett,H.M.Lades,T.J.Sejnowski, Independent component representations for face recognition.SPIE Proc.2399,1998
[16]Cevikalp H, Neamtu M, Wilkes M. Discriminative common vectors for face recognition. IEEE Transactionson Pattern Analysis and Machine Intelligence,2005, vol.27,no.1,4/13
[17]He Y H, Zhao L, Zou C R. Face recognition using common faces method. Pattern Recognition,2006, vol.39,no.11,pp2218-2222
[18]Belkin M, Niyogi P. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation,2003,vol.15,no.6,pp1373-1396.
[19]He XF, Yan S, Hu Y, Niyogi P, Zhang HJ. Face recognition using Laplacianfaces. IEEE Trans. on Pattern Analysis and Machine Intelligence, 2005,vol.27,no.3,pp328-340.
[20]Yu WW, Teng XL, Liu CQ. Face recognition using discriminant locality preserving projections. Image and Vision Computing,2006,24:pp239-248.
[21]Lu K, Zhao JD, Wu Y, He XF. Relevance feedbacks algorithm based on locality preserving projections. Journal of Computer-Aided Design & Computer Graphics, 2007,vol.19,no.1,pp20-24 (in Chinese with English abstract).
[22]Li JB, Pan JS, Chu SC. Kernel class-wise locality preserving projection. Information Sciences,2008,178,pp1825-1835.
[23]Yang LP, Gong WG, Gu XH, Li WH, Liang YX. Null space discriminant locality preserving projections for face recognition.Neurocomputing, 2008,71,pp3644-3649.
[24]Kohonen T.Self-organization and associative memory[M].Berlin:Springer,1988
[25]Lawrence S, Giles C L, Tsoi A C, etal. Face reeognition:a convolutional neural-network approaeh[J]. IEEETrans. Neural Network,1997,vol.8,no.l,pp98-113
[26]Lin S H, Kung SY, Lin L J. Face recognition and deteetion by probabilistic decision-based neural network[J].IEEE Trans.on Neural Networks,1997, vol.8,no.1,pp114-132
[27]Lee D and Seung H. Cognition. The manifold ways of perception. Science,2000,2 90 (5500) pp2268-2269
[28]Tenenbaum, J., De Silva, V., Langford, J., A global geometric framework for nonlinear dimension reduction. Science,2000,290:pp2319-2323
[29]Roweis, S., Saul, L., Nonlinear dimensionality reduction by locally linear embedding. Science,2000,290:pp2323-2326
[30]Face Recognition Homepage.http://www.face-rec.org
[31]赵宏伟,基于PCA针对表情变化的人脸识别技术研究。西安电子科技大学,2009.
[32]Peter N.Belhumeur,et al.Eigenfaces vs.Fisherfaces:Recognition using class specific linear projection.IEEE Trans.Pattern Anal. Machine Intell.19(7)(1997),pp711-720.
[33]Liu K,Yang J.-Y.et al.An efficient algorithm for Foley-Sammon optimal set of discriminant vectors by algebraic method.International Journal of Pattern Recognition and Artificial Intelligence 1992,vol.6,no.5,pp817-829.
[34]R. Duda and P. Hart.Pattern Classification and Scene Analysis. Wiley, New York, 1973
[35]Chen Li-Fen, Liao H-Y Mark, Ko M-T, et al.A new LDA-based face recognition system which can solve the small sample size problem [J]. Pattern Recognition 2000, vol.33,no.l0,pp1713-1726.
[36]Huang R, LIU Q S, LU H Q, et al. Solving the small sample size problem of LDA [C]. Proceedings of International Conference on Pattern Recognition, Canada, Quebec,2002
[37]H. Yu, J. Yang.A direct LDA algorithm for high-dimensional data—with application to face recognition. Pattern Recognition 34 (2001) pp2067-2070
[38]杨利平,龚卫国,辜小花,完备鉴别保局投影人脸识别算法,Journal of Software, vol.21, no.6, June 2010, pp.1277-1286
[39]刘永俊,扬州大学,小样本问题下人脸图像的鉴别特征抽取方法研究,硕士学位论文
[40]程云鹏,矩阵论,西北工业大学出版社,1989,pp294-302
[41]Paul M B.Class-specific feature sets in classification.[J].IEEE Transactionm on Signal processing,1999, vol.47,no.10,pp3428-3432.
[42]PuaI M B, Niemann H. A theoretically optiml probabilistic classifier using class-specific features[c]. Proceedings of the 15th International Conference on Pattern Recognition. Barcelona. Spanish,IEEE Computer Society Press-2000,pp763-769.
[43]Paul M B. The class-specific classfier avoiding the curse of dimensionaIity[J]. Aerospace and Electronic Systems Magazine 2004.vol.19,no.1,pp37-52.
[44]Caputo B, Niemann H. To each according to its need:kernel class-specific classifiers[c]. Proceedings of the 16th International Conference on Pattern Recognition. Quebec. Canada:IEEE Press,2002,pp94-97.
[45]A. Mahalanobis, B. V. K. Vijaya Kumar, and D. Casasent.Minimum average correlation energy filters.Appl. Opt., vol.26,pp.3630-3633,1987.
[46]何润,方驰,丁晓青,用于人脸识别的一种新的类依赖特征抽取方法,电视技术2007年第31卷第8期,pp137-139
[47]Yan Yan, Yu-Jin Zhang, 1D correlation filter based class-dependence feature analysis for face recognition. Pattern Recognition 41 (2008) pp3834-3841
[48]Yan YAN, Yu-Jin ZHANG. Effective Discriminant Feature Extraction Framework for Face Recognition.Proceedings of the 4th International Symposium on ommunications,Control and Signal Processing. ISCCSP 2010, Limassol, cyprus, 3-5,March,2010
[49]H.Hul, P.Zhang, F.De la Torre.Face recognition using enhanced linear discriminant analysis.IET Comput.Vis.2010,vol4,Iss.3,ppl95-208.
[50]FUKUNAGA K. Introduction to statistical pattern recognition.Academic Press, 1990,2nd edn.
[51]HE X.,YAN S.,HU Y. Face recognition using Laplacian faces.IEEE Trans. Pattern Anal. Mach.Intell.,2005, vol.27,no.3, pp328-340
[52]MANLI Z.,MARTINEZ A.Subclass discriminant analysis.IEEE Trans. Pattern Anal. Mach. Intell.,2006, vol.28,no.8,pp.1274-1286
[53]KIM T.,KITTLER J.Locally linear discriminant analysis for multimodally distributed classes for face recognition with a single model image.IEEE Trans. Pattern Anal. Mach. Intell.,2005, vol.27,no.3,pp318-327
[54]HARANDI M., NILI AHMADABADI M., ARAABI B.Optimal local basis:a reinforcement learning approach for face recognition.Int. J. Comput. Vis., 2009,vol.81,no.2,pp191-204
[55]RODRIGUEZ Y., MARCEL S.Face authentication using adapted local binary pattern PDFs.Proc. Ninth European Conf. Computer Vision (ECCV), Graz, Austria, 2006,pp321-332
[56]FRIEDMAN J.H.Regularized discriminant analysis.J. Am.Stat. Assoc.,1989,84, pp165-175