基于小波包变换和二维四元数主成分分析的人脸识别方法
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摘要
人脸识别是模式识别和人工智能领域的研究热点之一,在近些年受到了人们越来越多的重视。主成分分析算法(PCA)作为一种经典的人脸识别方法,识别过程简单直接,但识别效果受光照、表情等因素的影响较大;四元数主成分分析算法(QPCA)对图像像素之间的结构信息利用充分,但对图像的预处理要求较高,且大多用于彩色人脸图像识别。鉴于目前大部分人脸数据库收集的是灰度图像,本文以人脸灰度图像作为研究对象,综合考虑识别算法性能和计算复杂度两方面的因素,在特征提取和识别方面进行了对主成分分析算法的改进工作。
首先,研究了小波包变换和四元代数的相关理论,提出了人脸特征的表示方法。利用小波包变换的正交多尺度特性,对人脸图像这一非平稳信号进行小波包变换,分解得到的各分量构造成四元数人脸模型。这样既保留了图像的全局信息,又获得了图像的细节信息,增强了各分量之间的相关性。
然后,针对四元数主成分分析算法计算量大的问题,提出了二维四元数主成分分析方法(2D-QPCA),对四元数人脸模型进行降维并构造特征空间;在识别时,将特征空间划分为若干子块,对每个子块根据最近邻算法进行分类并对分类结果投票,根据投票结果实现最终的人脸识别。
最后,在ORL、Yale、YaleB和Indian人脸数据库上进行实验仿真,研究了本文方法中参数与识别率之间的关系,并与PCA等算法进行了比较。实验表明本文方法改善了光照、表情变化的鲁棒性,具有识别精度高、计算复杂度低的特点。
As one of hotspots in the field of pattern recognition and artificial intelligence, the research of face recognition has been drawn more and more attention in recent years. Principal component analysis (PCA) is a classical algorithm in face recognition with the character of that the process of recognition is simple and direct, but affected easily by illumination, facial expression and other factors; Quaternion principal component analysis (QPCA) is another face recognition algorithm, which can make full use of the structural information among pixels, but need high image preprocessing and often is referred to color face image recognition. Now a fact is that pictures collected in most people face databases are gray images. Considering two factors of recognition performance and computational complexity, this paper makes the improvements in feature extraction and recognition based on the PCA.
Firstly, according to studying the theory of wavelet packet transform and quaternion, a new method of facial feature representation is proposed. Face images are decomposed by wavelet packet transform, which can provide multi-scale decomposition for a non-stationary signal. Each decomposition component is used to construct quaternion matrix, which can contain the global and detailed information of images, but also enhance the relationship between each component.
Secondly, for quaternion principal component analysis has heavy work in calculation, two dimensional quaternion principal component analysis (2D-QPCA) is proposed to reduce dimensions and construct feature space. The space is divided into several sub-blocks, and each sub-block is classified based on nearest neighbor classification. The ultimate face recognition is completed according to classification results.
Simulation experiments are carried on the face databases of ORL, Yale, YaleB and Indian to research the relationship of different parameters and recognition accuracy in the proposed method. Compared with PCA and other algorithms, experiment results show that the proposed face recognition method improves the robustness to illumination and expression changes, and is possessed the characteristics of high accuracy and low computational complexity.
首先,研究了小波包变换和四元代数的相关理论,提出了人脸特征的表示方法。利用小波包变换的正交多尺度特性,对人脸图像这一非平稳信号进行小波包变换,分解得到的各分量构造成四元数人脸模型。这样既保留了图像的全局信息,又获得了图像的细节信息,增强了各分量之间的相关性。
然后,针对四元数主成分分析算法计算量大的问题,提出了二维四元数主成分分析方法(2D-QPCA),对四元数人脸模型进行降维并构造特征空间;在识别时,将特征空间划分为若干子块,对每个子块根据最近邻算法进行分类并对分类结果投票,根据投票结果实现最终的人脸识别。
最后,在ORL、Yale、YaleB和Indian人脸数据库上进行实验仿真,研究了本文方法中参数与识别率之间的关系,并与PCA等算法进行了比较。实验表明本文方法改善了光照、表情变化的鲁棒性,具有识别精度高、计算复杂度低的特点。
As one of hotspots in the field of pattern recognition and artificial intelligence, the research of face recognition has been drawn more and more attention in recent years. Principal component analysis (PCA) is a classical algorithm in face recognition with the character of that the process of recognition is simple and direct, but affected easily by illumination, facial expression and other factors; Quaternion principal component analysis (QPCA) is another face recognition algorithm, which can make full use of the structural information among pixels, but need high image preprocessing and often is referred to color face image recognition. Now a fact is that pictures collected in most people face databases are gray images. Considering two factors of recognition performance and computational complexity, this paper makes the improvements in feature extraction and recognition based on the PCA.
Firstly, according to studying the theory of wavelet packet transform and quaternion, a new method of facial feature representation is proposed. Face images are decomposed by wavelet packet transform, which can provide multi-scale decomposition for a non-stationary signal. Each decomposition component is used to construct quaternion matrix, which can contain the global and detailed information of images, but also enhance the relationship between each component.
Secondly, for quaternion principal component analysis has heavy work in calculation, two dimensional quaternion principal component analysis (2D-QPCA) is proposed to reduce dimensions and construct feature space. The space is divided into several sub-blocks, and each sub-block is classified based on nearest neighbor classification. The ultimate face recognition is completed according to classification results.
Simulation experiments are carried on the face databases of ORL, Yale, YaleB and Indian to research the relationship of different parameters and recognition accuracy in the proposed method. Compared with PCA and other algorithms, experiment results show that the proposed face recognition method improves the robustness to illumination and expression changes, and is possessed the characteristics of high accuracy and low computational complexity.
引文
1王伟,张佑生,方芳.人脸检测与识别技术综述.合肥工业大学学报(自然科学版), 2006, 29(2):158-163
2 R. Chellappa, C. L.Wilson, S. Sirohey. Human and machine recognition of faces: a survey. Proc. IEEE, 1995, 83(5):705-740
3周杰,卢春雨,张长水.人脸自动识别方法综述.电子学报, 2000, 28(4):102-106
4 Andrea F. Abate, Michele Nappi, Daniel Riccio, Gabriele Sabatino. 2D and 3D face recognition: a survey. Pattern Recognition Letters, 2007, 28(14-15):1885-1906
5李武军,王崇骏,张炜,等.人脸识别研究综述.模式识别与人工智能, 2006, 19(1):58-66
6 D. Zhang. Biometric security research& development.北京:生物特征识别技术高级研讨班, 2003
7段锦.人脸自动机器识别.北京:科学出版社, 2008
8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
9周激流,张晔.人脸识别理论研究进展.中国计算机辅助设计与图形学学报, 1999, 11(2):180-184
10 L. Sirovitch, M. Kirby. Low-dimensional procedure for the characterization of human face. Journal of the Optical Society of America, 1987, 4(3):519-524
11 P. N. Belhumeur, J. P. Hespanha, D. J. Kriegman. Eigenfaces vs Fisherface: recognition using class specific linear projection. IEEE Trans on Pattern Analysis and Machine Intelligence, 1997, 19(7):711-720
12 M. S. Bartlett, T. J. Sejnowski. Independent of face images: a representation for face recognition. IEEE Trans. Neural Networks, 1999, 10(3):626-634
13 T. Kohonen. Self-organization and associative memory. New York: Springer, 1989
14 K. Lee. SVM-based face verification with feature set of small size. Electronics Letters, 2002, 38(15):787-789
15 F. Samaria, S. Young. HMM based architecture for face identification. Image and Vision Computer, 1994, (12):537-583
16 B. Li, Y. H. Liu. When eigenfaces are combined with wavelets. Knowledge-based Systems, 2002, 15:343-347
17 L. Wiskott, J. M. Fellous, N. Kruger, et al. Face recognition by elastic bunch graph matching. IEEE Trans on Pattern Analysis and Machine Intelligence, 1997, 19(7):775-779
18 B. Moghaddam, T. Jebara, A. Pentland. Bayesian face recognition. Pattern Recognition, 2000, 33(11):1771-1782
19苏剑波,徐波,等.应用模式识别技术导论:人脸识别与语音识别.上海:上海交通大学出版社, 2001
20吴巾一,周德龙.人脸识别方法综述.计算机应用研究, 2009, 26(9):3205-3209
21中国公共安全. 2010, http://www.isvision.com/cn/index/window.asp?OID=460
22 Su Yu, Shan Shiguang, Chen Xilin, et al. Hierarchical ensemble of global and local classifiers for face recognition. IEEE Transactions on Image Processing, 2009, 18(8):1885-1896
23 Yu Weiwei, Teng Xiaolong, Liu Chongqing. Feature fusing in face recognition. Journal of Southeast University, 2005, 21(4):427-431
24 Lang Fangnian, Zhou Jiliu, Yan Bin, et al. Obtain method of quaternion matrix orthogonal eigenvector set and its application in color face recognition. Acta Automatica Sinica, 2008, 34(2):121-129
25 Ding Lijun, Feng Hao. Quaternion K-L transform and biomimetic pattern recognition approaches for color-face recognition. Proc of IEEE International Conference on Intelligent Computing and Intelligent Systems, 2009, 1:165-169
26 C. Xie, M. Savvides, B. V. K. Vijaya Kumar. Quaternion correlation filters for face recognition in wavelet domain. Proc of IEEE International Conference on Acoustics, Speech and Signal Processing, Philadelphia, 2005:85-88
27庞彦伟,愈能海,等.基于核邻域保持投影的人脸识别.电子学报, 2006, 34(8):1542-1544
28 Neerja, Walia, Ekta. Face recognition using improved fast PCA algorithm. 1st International Congress on Image and Signal Processing, 2008, (1):554-558
29谢晓华,赖剑煌,郑伟诗.基于二次多项式模式的人脸光照归一化.电子学报, 2010, 38(8):1791-1797
30程勇,赵春霞,王欢,等.基于NSCT和SQI的光照不变量及人脸识别.南京理工大学学报, 2010, 34(4):425-430
31 Holappa Jukka, Ahonen Timo, et al. An optimized illumination normalization method for face recognition. BTAS 2008 - IEEE 2nd International Conference on Biometrics: Theory, Applications and Systems, 2008
32 Li Jianke, Zhao Baojun, et al. Face recognition system using SVM classifier and feature extraction by PCA and LDA combination. Proceedings - 2009 International Conference on Computational Intelligence and Software Engineering, 2009
33 Mao Xia, Chen Lijiang, Fu Liqin. Multi-level speech emotion recognition based on HMM and ANN. 2009 WRI World Congress on Computer Science and Information Engineering, CSIE 2009 (7):225-229
34 Shen Linlin, Bai Li. Mutual boost learning for selecting Gabor features for face recognition. Pattern Recognition Letters, 2006, 27(15):1758-1767
35尹洪涛,付平,沙学年.基于DCT和线性判别分析的人脸识别.电子学报, 2009, 37(10):2211-2214
36何立民,万跃华.基于隐马尔可夫链和支持向量机人脸识别混合模型的视频节目聚类标注.上海交通大学学报, 2003, 37:176-183
37 Javier Ruiz-del-Solar, Julio Quinteros. Illumination compensation and normalization in eigenspace based face recognition: A comparative study of different pre-processing approaches. Pattern Recognition Letters, 2008, 29:1966-1979
38 R. L. Hsu, A. K. Jain. Face model for recognition. Proc. IEEE ICIP, 2001, 2(10):693-696
39 Wang Yueming, Pan Gang, Wu Zhaohui. Survey of 3D face recognition. Journal of Computer-Aided Design and Computer Graphics, 2008, 20(7):819-829
40柳杨.三维人脸识别算法综述.系统仿真学报, 2006, 18(1):400-403
41 A. Boggess, F. J. Narcowich. A first course in wavelets with Fourier analysis. Upper Saddle River: Prentice Hall, 2001
42张国华,张文娟,薛鹏翔.小波分析与应用基础.西安:西北工业大学出版社, 2006
43 S. Mallat. A theory for multi-resolution signal decomposition: the wavelet representation. IEEE Trans. on PAMI, 1999,11(7):674-693
44 S. Mallat. A wavelet tour of signal processing. 2nd ed. Beijing: China Machine Press, 2003
45 Z. Xiong, K. Ramchandran, M. T. Orchard. Wavelet packet image coding using space- frequency quantization. IEEE Trans on Image Processing, 1998, 7(6):892-898
46唐晓初.小波分析及其应用.重庆:重庆大学出版社, 2006
47边肇祺,张学工.模式识别(第二版).北京:清华大学出版社, 2000
48 M. Turk, A. Pentland. Eigenfaces for recognition. Journal of Cognitive Neuroscience, 1991, 3(1):71-86
49 N. L. Bihan, J. Mars. Singular value decomposition of quaternion matrices: a new tool for vector-sensor signal processing. Signal Processing, 2004, 84(7):1177-1199
50 J. Yang, Zhang David, J. Y. Yang. Two-dimensional PCA: a new approach to appearance-based face representation and recognition. IEEE Trans on Pattern Analysis and Machine Intelligence, 2004, 26(1):131-137
51李文亮.四元数矩阵.长沙:国防科技大学出版社, 2002,1-5,34,76
52 Soo-Chang Pei, Ching-Min Cheng. Quaternion matrix singular value decomposition and its application for color image processing. IEEE International Symposium on Circuits and Systems, 1996:684-687
53黎云汉,朱善安,祝磊.基于四元数主成分分析的人脸识别算法.信号处理, 2007, 23(2):214-216
54郎方年,周激流,闫斌,等.四元数矩阵正交特征向量系的求解方法及其在彩色人脸识别中的应用.自动化学报, 2008,34(2):121-129
55 Oliver research laboratory. http://www.uk.research.att.Com/pub/data/att_faces.zip. Cambridge, UK
56 P. N. Belhumeur. Yale face database. http://cvc.yale.edu/projects/yalefaces/yalefaces.h- tml, 2002
57 A. S. Georgihiades, P. N. Belhumeur, D .J. Kriegman. From few to many: illumination cone models for face recognition under variable lighting and pose. IEEE Trans on Pattern Analysis and Machine Intelligence, 2001, 23(6):643-660
58 K. C. Lee. J. Ho. D. Kriegman. Acquiring linear subspaces for face recognition under variable lighting. IEEE Trans on Pattern Analysis and Machine Intelligence, 2005, 27(5):684-698
59董长虹,高志,余啸海. MATLAB小波分析工具箱原理与应用.北京:国防工业出版社, 2004
60张德丰,等. MATLAB数字图像处理.北京:机械工业出版社, 2009
61毕迎春,王相海.小波基和图像分解层数对不同类型图像EZW算法的性能的影响.计算机科学, 2006, 33(6):232-235, 246
2 R. Chellappa, C. L.Wilson, S. Sirohey. Human and machine recognition of faces: a survey. Proc. IEEE, 1995, 83(5):705-740
3周杰,卢春雨,张长水.人脸自动识别方法综述.电子学报, 2000, 28(4):102-106
4 Andrea F. Abate, Michele Nappi, Daniel Riccio, Gabriele Sabatino. 2D and 3D face recognition: a survey. Pattern Recognition Letters, 2007, 28(14-15):1885-1906
5李武军,王崇骏,张炜,等.人脸识别研究综述.模式识别与人工智能, 2006, 19(1):58-66
6 D. Zhang. Biometric security research& development.北京:生物特征识别技术高级研讨班, 2003
7段锦.人脸自动机器识别.北京:科学出版社, 2008
8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
9周激流,张晔.人脸识别理论研究进展.中国计算机辅助设计与图形学学报, 1999, 11(2):180-184
10 L. Sirovitch, M. Kirby. Low-dimensional procedure for the characterization of human face. Journal of the Optical Society of America, 1987, 4(3):519-524
11 P. N. Belhumeur, J. P. Hespanha, D. J. Kriegman. Eigenfaces vs Fisherface: recognition using class specific linear projection. IEEE Trans on Pattern Analysis and Machine Intelligence, 1997, 19(7):711-720
12 M. S. Bartlett, T. J. Sejnowski. Independent of face images: a representation for face recognition. IEEE Trans. Neural Networks, 1999, 10(3):626-634
13 T. Kohonen. Self-organization and associative memory. New York: Springer, 1989
14 K. Lee. SVM-based face verification with feature set of small size. Electronics Letters, 2002, 38(15):787-789
15 F. Samaria, S. Young. HMM based architecture for face identification. Image and Vision Computer, 1994, (12):537-583
16 B. Li, Y. H. Liu. When eigenfaces are combined with wavelets. Knowledge-based Systems, 2002, 15:343-347
17 L. Wiskott, J. M. Fellous, N. Kruger, et al. Face recognition by elastic bunch graph matching. IEEE Trans on Pattern Analysis and Machine Intelligence, 1997, 19(7):775-779
18 B. Moghaddam, T. Jebara, A. Pentland. Bayesian face recognition. Pattern Recognition, 2000, 33(11):1771-1782
19苏剑波,徐波,等.应用模式识别技术导论:人脸识别与语音识别.上海:上海交通大学出版社, 2001
20吴巾一,周德龙.人脸识别方法综述.计算机应用研究, 2009, 26(9):3205-3209
21中国公共安全. 2010, http://www.isvision.com/cn/index/window.asp?OID=460
22 Su Yu, Shan Shiguang, Chen Xilin, et al. Hierarchical ensemble of global and local classifiers for face recognition. IEEE Transactions on Image Processing, 2009, 18(8):1885-1896
23 Yu Weiwei, Teng Xiaolong, Liu Chongqing. Feature fusing in face recognition. Journal of Southeast University, 2005, 21(4):427-431
24 Lang Fangnian, Zhou Jiliu, Yan Bin, et al. Obtain method of quaternion matrix orthogonal eigenvector set and its application in color face recognition. Acta Automatica Sinica, 2008, 34(2):121-129
25 Ding Lijun, Feng Hao. Quaternion K-L transform and biomimetic pattern recognition approaches for color-face recognition. Proc of IEEE International Conference on Intelligent Computing and Intelligent Systems, 2009, 1:165-169
26 C. Xie, M. Savvides, B. V. K. Vijaya Kumar. Quaternion correlation filters for face recognition in wavelet domain. Proc of IEEE International Conference on Acoustics, Speech and Signal Processing, Philadelphia, 2005:85-88
27庞彦伟,愈能海,等.基于核邻域保持投影的人脸识别.电子学报, 2006, 34(8):1542-1544
28 Neerja, Walia, Ekta. Face recognition using improved fast PCA algorithm. 1st International Congress on Image and Signal Processing, 2008, (1):554-558
29谢晓华,赖剑煌,郑伟诗.基于二次多项式模式的人脸光照归一化.电子学报, 2010, 38(8):1791-1797
30程勇,赵春霞,王欢,等.基于NSCT和SQI的光照不变量及人脸识别.南京理工大学学报, 2010, 34(4):425-430
31 Holappa Jukka, Ahonen Timo, et al. An optimized illumination normalization method for face recognition. BTAS 2008 - IEEE 2nd International Conference on Biometrics: Theory, Applications and Systems, 2008
32 Li Jianke, Zhao Baojun, et al. Face recognition system using SVM classifier and feature extraction by PCA and LDA combination. Proceedings - 2009 International Conference on Computational Intelligence and Software Engineering, 2009
33 Mao Xia, Chen Lijiang, Fu Liqin. Multi-level speech emotion recognition based on HMM and ANN. 2009 WRI World Congress on Computer Science and Information Engineering, CSIE 2009 (7):225-229
34 Shen Linlin, Bai Li. Mutual boost learning for selecting Gabor features for face recognition. Pattern Recognition Letters, 2006, 27(15):1758-1767
35尹洪涛,付平,沙学年.基于DCT和线性判别分析的人脸识别.电子学报, 2009, 37(10):2211-2214
36何立民,万跃华.基于隐马尔可夫链和支持向量机人脸识别混合模型的视频节目聚类标注.上海交通大学学报, 2003, 37:176-183
37 Javier Ruiz-del-Solar, Julio Quinteros. Illumination compensation and normalization in eigenspace based face recognition: A comparative study of different pre-processing approaches. Pattern Recognition Letters, 2008, 29:1966-1979
38 R. L. Hsu, A. K. Jain. Face model for recognition. Proc. IEEE ICIP, 2001, 2(10):693-696
39 Wang Yueming, Pan Gang, Wu Zhaohui. Survey of 3D face recognition. Journal of Computer-Aided Design and Computer Graphics, 2008, 20(7):819-829
40柳杨.三维人脸识别算法综述.系统仿真学报, 2006, 18(1):400-403
41 A. Boggess, F. J. Narcowich. A first course in wavelets with Fourier analysis. Upper Saddle River: Prentice Hall, 2001
42张国华,张文娟,薛鹏翔.小波分析与应用基础.西安:西北工业大学出版社, 2006
43 S. Mallat. A theory for multi-resolution signal decomposition: the wavelet representation. IEEE Trans. on PAMI, 1999,11(7):674-693
44 S. Mallat. A wavelet tour of signal processing. 2nd ed. Beijing: China Machine Press, 2003
45 Z. Xiong, K. Ramchandran, M. T. Orchard. Wavelet packet image coding using space- frequency quantization. IEEE Trans on Image Processing, 1998, 7(6):892-898
46唐晓初.小波分析及其应用.重庆:重庆大学出版社, 2006
47边肇祺,张学工.模式识别(第二版).北京:清华大学出版社, 2000
48 M. Turk, A. Pentland. Eigenfaces for recognition. Journal of Cognitive Neuroscience, 1991, 3(1):71-86
49 N. L. Bihan, J. Mars. Singular value decomposition of quaternion matrices: a new tool for vector-sensor signal processing. Signal Processing, 2004, 84(7):1177-1199
50 J. Yang, Zhang David, J. Y. Yang. Two-dimensional PCA: a new approach to appearance-based face representation and recognition. IEEE Trans on Pattern Analysis and Machine Intelligence, 2004, 26(1):131-137
51李文亮.四元数矩阵.长沙:国防科技大学出版社, 2002,1-5,34,76
52 Soo-Chang Pei, Ching-Min Cheng. Quaternion matrix singular value decomposition and its application for color image processing. IEEE International Symposium on Circuits and Systems, 1996:684-687
53黎云汉,朱善安,祝磊.基于四元数主成分分析的人脸识别算法.信号处理, 2007, 23(2):214-216
54郎方年,周激流,闫斌,等.四元数矩阵正交特征向量系的求解方法及其在彩色人脸识别中的应用.自动化学报, 2008,34(2):121-129
55 Oliver research laboratory. http://www.uk.research.att.Com/pub/data/att_faces.zip. Cambridge, UK
56 P. N. Belhumeur. Yale face database. http://cvc.yale.edu/projects/yalefaces/yalefaces.h- tml, 2002
57 A. S. Georgihiades, P. N. Belhumeur, D .J. Kriegman. From few to many: illumination cone models for face recognition under variable lighting and pose. IEEE Trans on Pattern Analysis and Machine Intelligence, 2001, 23(6):643-660
58 K. C. Lee. J. Ho. D. Kriegman. Acquiring linear subspaces for face recognition under variable lighting. IEEE Trans on Pattern Analysis and Machine Intelligence, 2005, 27(5):684-698
59董长虹,高志,余啸海. MATLAB小波分析工具箱原理与应用.北京:国防工业出版社, 2004
60张德丰,等. MATLAB数字图像处理.北京:机械工业出版社, 2009
61毕迎春,王相海.小波基和图像分解层数对不同类型图像EZW算法的性能的影响.计算机科学, 2006, 33(6):232-235, 246