人脸特征子空间方法研究
摘要
人脸识别和表情识别研究工作一般分为三个步骤：人脸检测、人脸特征提取以及分类与识别。而人脸特征的提取是整个过程中较为关键的环节。本文以模式识别中的特征子空间思想为主要研究方法，系统地研究了人脸特征提取技术。
人脸特征子空间方法的基本思想是找到能够表征人脸特征的子空间，不同的方法对于特征的提取，有不同的特点。PCA、ICA、NMF和LNMF这四种子空间方法中，相对而言，PCA主要提取的是人脸图像的整体信息，而其他三种方法能够提取出图像的局部信息，其中LNMF提取人脸图像局部信息的能力最强。因为每种方法的机器学习过程不尽相同，其得到的基图像和重构图像也各有不同的特征。同时每种方法对其本身的基向量的个数要求以及系数矩阵的约束条件不同，其收敛方式和收敛速度也有所差异。在实际应用中，四种方法都可以应用到人脸识别和表情识别中，识别率与其基向量的个数以及迭代的次数有关。其中，LNMF达到收敛所需要的基向量个数较少，并且用来重构图像所需的基向量的个数也较少。在基向量个数相同的情况下，LNMF的识别率也比较高。但是其达到收敛所需的迭代次数较多。
子空间提取出来的特征，通常是人脸的最佳描述特征，但并不一定是最适合于分类的特征。而判决分析可以总结为：找到一个能够返回某种度量值的函数，而且该度量值能够成为区分样本不同类别的依据。这些依据可以用来训练分类器，或者提取特征。因此，判决分析可以理解为一种监督学习或者特征提取方式。NKFDA就是这样一种基于零空间的核函数Fisher判决分析，这种方法结合了核函数与线性判决分析以及零空间思想，能够挑选出人脸特征子空间中有利于分类的特征，所以可以和子空间方法结合起来应用到人脸识别和表情识别等实际的分类问题。
通过对ORL图像库中的人脸图像进行人脸识别实验，以及对Cohn-Kanade图像库的表情图像进行的表情识别实验，表明了将子空间方法和NKFDA结合的有效性和合理性，针对上述的实验，都取得了比较好的实验结果，优于单纯的子空间方法。其中LNMF结合NKFDA的方法，识别效果最佳。同时，为了验证光照和分辨率等外界条件对其识别结果的影响，本文也进行了相应实验，结果表明该方法对于光照条件和图像分辨率具有较强的鲁棒性。
The research of face recognition and facial expression recognition can be divided into three steps: face detection, face feature extraction and classify and recognition. The extracting of face feature is the key tache of the whole course. Based on the subspace methods of the pattern recognition as the research field, this paper has studied the face feature extraction technology.
The main point of subspace method is to find a subspace which can show the features of face images. Different methods have different characters. Among the methods PCA ICA NMF and LNMF, comparatively, PCA extracts the whole information of the images, but the other three methods can extract the local information of the images, which LNMF has the best ability to get local information. In the practicality applications, all the four methods can be used into face recognition and facial expression recognition, and the recognition rates have relationship with the number of base vectors and iterance. LNMF needs the least number of base vectors to reach convergence and reconstruction. When the number of base vectors is the same, LNMF has the best recognition rate. But it needs more number of iterance than the other three methods.
The features extracted by subspace can usually show the information of face images, but are not always suitable for classify. The discriminant analysis can be summed-up as: find a function which can return a measurement value, and the value can distinguish different samples. It can train the classifier, as well as extracting features. Thereby, discriminant analysis can be considered as a supervise learning or a method of feature extracting. NKFDA is a Fisher discriminant analysis combined null-space and kernel function, it can select the features which are suitable for classify. So it can be combined with subspace methods.
It has been proved that subspace methods combined NKFDA has validity and rationality, based on the face recognition experiments on ORL database and facial expression recognition experiments on Cohn-Kanade database. This method has better results than using subspace methods only. And the method LNMF combined NKFDA has the best result of all the four methods. At the meanwhile, it is robust to illumination and resolution.
人脸特征子空间方法的基本思想是找到能够表征人脸特征的子空间，不同的方法对于特征的提取，有不同的特点。PCA、ICA、NMF和LNMF这四种子空间方法中，相对而言，PCA主要提取的是人脸图像的整体信息，而其他三种方法能够提取出图像的局部信息，其中LNMF提取人脸图像局部信息的能力最强。因为每种方法的机器学习过程不尽相同，其得到的基图像和重构图像也各有不同的特征。同时每种方法对其本身的基向量的个数要求以及系数矩阵的约束条件不同，其收敛方式和收敛速度也有所差异。在实际应用中，四种方法都可以应用到人脸识别和表情识别中，识别率与其基向量的个数以及迭代的次数有关。其中，LNMF达到收敛所需要的基向量个数较少，并且用来重构图像所需的基向量的个数也较少。在基向量个数相同的情况下，LNMF的识别率也比较高。但是其达到收敛所需的迭代次数较多。
子空间提取出来的特征，通常是人脸的最佳描述特征，但并不一定是最适合于分类的特征。而判决分析可以总结为：找到一个能够返回某种度量值的函数，而且该度量值能够成为区分样本不同类别的依据。这些依据可以用来训练分类器，或者提取特征。因此，判决分析可以理解为一种监督学习或者特征提取方式。NKFDA就是这样一种基于零空间的核函数Fisher判决分析，这种方法结合了核函数与线性判决分析以及零空间思想，能够挑选出人脸特征子空间中有利于分类的特征，所以可以和子空间方法结合起来应用到人脸识别和表情识别等实际的分类问题。
通过对ORL图像库中的人脸图像进行人脸识别实验，以及对Cohn-Kanade图像库的表情图像进行的表情识别实验，表明了将子空间方法和NKFDA结合的有效性和合理性，针对上述的实验，都取得了比较好的实验结果，优于单纯的子空间方法。其中LNMF结合NKFDA的方法，识别效果最佳。同时，为了验证光照和分辨率等外界条件对其识别结果的影响，本文也进行了相应实验，结果表明该方法对于光照条件和图像分辨率具有较强的鲁棒性。
The research of face recognition and facial expression recognition can be divided into three steps: face detection, face feature extraction and classify and recognition. The extracting of face feature is the key tache of the whole course. Based on the subspace methods of the pattern recognition as the research field, this paper has studied the face feature extraction technology.
The main point of subspace method is to find a subspace which can show the features of face images. Different methods have different characters. Among the methods PCA ICA NMF and LNMF, comparatively, PCA extracts the whole information of the images, but the other three methods can extract the local information of the images, which LNMF has the best ability to get local information. In the practicality applications, all the four methods can be used into face recognition and facial expression recognition, and the recognition rates have relationship with the number of base vectors and iterance. LNMF needs the least number of base vectors to reach convergence and reconstruction. When the number of base vectors is the same, LNMF has the best recognition rate. But it needs more number of iterance than the other three methods.
The features extracted by subspace can usually show the information of face images, but are not always suitable for classify. The discriminant analysis can be summed-up as: find a function which can return a measurement value, and the value can distinguish different samples. It can train the classifier, as well as extracting features. Thereby, discriminant analysis can be considered as a supervise learning or a method of feature extracting. NKFDA is a Fisher discriminant analysis combined null-space and kernel function, it can select the features which are suitable for classify. So it can be combined with subspace methods.
It has been proved that subspace methods combined NKFDA has validity and rationality, based on the face recognition experiments on ORL database and facial expression recognition experiments on Cohn-Kanade database. This method has better results than using subspace methods only. And the method LNMF combined NKFDA has the best result of all the four methods. At the meanwhile, it is robust to illumination and resolution.
引文
[1] Liu C J, Wechsler H. Learning the face space representation and recognition. 15th International Conference on Patern Recognition, ICPR'2000, Barcelona,Spain, September 3,2000.
[2] Chellappa R, Wilson C L, Sirohey S.Human and machine recognition of faces:a survey. Proc. IEEE, 1995,83:705-740.
[3] Hong J L, Pankanti S. Biometric identification. Communications of the ACM, 2000,43(2).
[4] 孙冬梅，裘正定．生物特征识别技术综述．电子学报 2001：29(12A)．
[5] 曹宇佳，郑文明等．基于差值模板特征的表情识别方法．北京：第十二届全国图像图像学学术会议，2005：263-267．
[6] 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．
[7] 周激流，张哗．人脸识别理论研究进展．计算机辅助设计与图形学学报，1999，11(2)：180-184．
[8] Samal A, Iyengar P A. Automatic recognition and analysis of human faces and facial expressions:a survey. Pattern Recognition, 1992,25:65-77.
[9] 王宇博，艾海舟，武勃等．人脸表情的实时分类．计算机辅助设计与图形图像学报，2005，17(6)：296-301．
[10] Brunelli R, Poggio T. Face recognition:features versus templates. IEEE Trans, PAMI, 1993,15(10):1042-1052.
[11] Valentin D, Abdi H,O'Toole J et al. Connectionist models of face processing:A survey. Pattern Recognition, 1994, 27 (9) :1209-1230.
[12] Allen A L. Personal Descriptions. London:Butterworth, 1950.
[13] Parke FI. Computer geberated animation of face. In:Proceeding ACM Conference, 1972,1:451-457.
[14] Goldstion R J, Harmon L D, Lesk A B. Man-machine interaction in human face identification. Bell Syst. Tech Journal, 1972, 51:399-472.
[15]vara Y, Kobayashi K.A basic study on human face recognition. S. Watanabe (Ed.),Frontiers of Pattern Recognition, Academic Press, New York, 1972:265-289.
[16] Beldeso W W. Man-machine facial recognition, Panoramic Res. Inc. Palo Alto, CA, Rep, PRI:22, Aug, 1966.
[17] Craw I, Ellis H, Lishman J R. Automatic extraction of face features. Pattern recognition Lett, 5(1987):183-187.
[18] Poggio T, Girosi F. Networks for approximation and learning. Proc, IEEE 78(1990):1481-1497.
[19] Brunelli R, Poggio T. Face recognition:feature versus templates. IEEE Trans, PAMI 15(1993):1042-1052.
[20] Jia X,Nixon M S.Extending the feature vector for automatic face recognition. IEEE Trans,PAMI 17(1995):1167-1176.
[21] Nicholas R,Li X B. Accuracy analysis for facial feature detection. Pattern Recogruhon:29(1996)1:143-157.
[22] Kirby M, Sirovich L. Application of the Karhunen-Loeve procedure for the characterization of human faces. IEEE Trans, PAMI 12(1990):103-108.
[23] Turk M A, Pentland A. Face recognition using eigenfaces. Proc, Inte. Conf. On PR,1991:586-591.
[24] Baron R J. Mechanisms of human facial recognition.Int. J. Man. Mach. Stud. 15(1981):137-178.
[25] Osamu N, Mathur S.Minami T. Identification of human faces based on isodensity maps. Pattern Recognition, 1991(24)3:263-272.
[26] Yuille A, Cohn D, Hallinen P. Feature extraction from faces using deformable temples. In:Proc. IEEE Computer Soc. Conf. on Computer Vision and Patt. Recog., 1989:104-109.
[27] Hallinan P W. Recognizing human eyes. SPIE Proc. :Geometric Methods m Computer Vision, 1991,1570:214-226.
[28] Sirovich L, Kirby M. Application of Karhunen-Loeve procedure for the characterization of human faces. IEEE Trans. PAMI, 1990, 3(1):71-79.
[29] Belhumeur P, Hespanha J, Kriegman D. Eigenfaces vs. fisherfaces:class-specific linear projection. IEEE Trans. PAMI. 1997, 19(7):711-720.
[30] Common P. Independent component analysis:A new concept. Signal Processing, 1994, 36(3):287-314.
[31] Kim T K, Kim H, Hwang W et al. Independent component analysis in a local residue space for face recognition. Pattern Recognition, 2004, 37(9) :1873-1885.
[32] Bartlett M S, Lades H M, Sejnowski T J. Independent component representations for face recognition. SPIE Proc.1998,2399:528-564.
[33] Liu C J, Wechsler H. Comparative assessment of independent component analysis (ICA) for face recognition. Proceedings of International Conference on Audio and Video Based Biometric Person Authentication, USA, Washington DC,1999.
[34] Back K, Draper B A, Beveridge J R. PCA vs. ICA:a comparison on the FERET data set. In:Proceedings of International Conference on Computer Vision, Pattern Recognition and Image Processing, North Carolina, Durham, 2002:824-827.
[35] 汪鹏．非负矩阵分解：数学的奇妙力量．计算机教育,2004,10：38—40．
[36] Sirovich L, Kirby M. Low-dimensional procedure for the characterization of human face. Journal of the Optical Society of America, 1987, 4(3).
[37] Turk M A, Pentland A P. Eigenfaces for recognition. Journal of Cognitive Neuroscience, 1991,3(1).
[38] Karhunen A, Joutsensalo J.A class of neural networks for independent component analysis. Neural Networks, 1997,8(3):486-504.
[39] Cichocki A, Unbehauen R, Rummert E. Robust learning algorithm for blind separation of signals. Electronics Letters 30,1994,6(3):2210-2215.
[40] Common P. Independent component analysis- a new conception. Signal Processing, 1994,36:287-314.
[41] Lee T W.A unifying information-theoretic framework for ICA. Computers and Mathematics with Applications, 2000,39:1-21.
[42] Bell, Sejnowski. Face recognition by independent component analysis. IEEE Transaction on Networks, 2002,13(6):1450-1464.
[43] Lee D D, Seung H S. Unsupervised learning by convex and conic coding. Advances in Neural Information Processing Systems, The MIT Press. 1997,9:515-521.
[44] Lee D, Seung H. Learning the parts of objects by non-negative matrix factorization. Nature, 1999,401:788-791.
[45] Lee D, Seung H S. Algorithms for non-negative matrix factorization. Advances in Neural Information Processing Systems 13,2001.
[46] Tag Feng, Stan Z. Li,Heung-Yeung Shum. Local non-negative matrix factorization as a visual representation. Proceedings of the 2nd International Conference on Development and Learning.
[47] 边肇祺，张学工．模式识别．北京：清华大学出版社，2000．
[48] Baudat G, Anour F. Generalized discriminant analysis using a kernel approach. Neural Computation, 2000,12:2385-2404.
[49] Liu W, Stan Z L, Tan T, Null space-based kernel fisher discriminant analysis for face recognition. Proceedings of the Sixth IEEE International Conference on Automatic Face and Gesture Recognition.
[2] Chellappa R, Wilson C L, Sirohey S.Human and machine recognition of faces:a survey. Proc. IEEE, 1995,83:705-740.
[3] Hong J L, Pankanti S. Biometric identification. Communications of the ACM, 2000,43(2).
[4] 孙冬梅，裘正定．生物特征识别技术综述．电子学报 2001：29(12A)．
[5] 曹宇佳，郑文明等．基于差值模板特征的表情识别方法．北京：第十二届全国图像图像学学术会议，2005：263-267．
[6] 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．
[7] 周激流，张哗．人脸识别理论研究进展．计算机辅助设计与图形学学报，1999，11(2)：180-184．
[8] Samal A, Iyengar P A. Automatic recognition and analysis of human faces and facial expressions:a survey. Pattern Recognition, 1992,25:65-77.
[9] 王宇博，艾海舟，武勃等．人脸表情的实时分类．计算机辅助设计与图形图像学报，2005，17(6)：296-301．
[10] Brunelli R, Poggio T. Face recognition:features versus templates. IEEE Trans, PAMI, 1993,15(10):1042-1052.
[11] Valentin D, Abdi H,O'Toole J et al. Connectionist models of face processing:A survey. Pattern Recognition, 1994, 27 (9) :1209-1230.
[12] Allen A L. Personal Descriptions. London:Butterworth, 1950.
[13] Parke FI. Computer geberated animation of face. In:Proceeding ACM Conference, 1972,1:451-457.
[14] Goldstion R J, Harmon L D, Lesk A B. Man-machine interaction in human face identification. Bell Syst. Tech Journal, 1972, 51:399-472.
[15]vara Y, Kobayashi K.A basic study on human face recognition. S. Watanabe (Ed.),Frontiers of Pattern Recognition, Academic Press, New York, 1972:265-289.
[16] Beldeso W W. Man-machine facial recognition, Panoramic Res. Inc. Palo Alto, CA, Rep, PRI:22, Aug, 1966.
[17] Craw I, Ellis H, Lishman J R. Automatic extraction of face features. Pattern recognition Lett, 5(1987):183-187.
[18] Poggio T, Girosi F. Networks for approximation and learning. Proc, IEEE 78(1990):1481-1497.
[19] Brunelli R, Poggio T. Face recognition:feature versus templates. IEEE Trans, PAMI 15(1993):1042-1052.
[20] Jia X,Nixon M S.Extending the feature vector for automatic face recognition. IEEE Trans,PAMI 17(1995):1167-1176.
[21] Nicholas R,Li X B. Accuracy analysis for facial feature detection. Pattern Recogruhon:29(1996)1:143-157.
[22] Kirby M, Sirovich L. Application of the Karhunen-Loeve procedure for the characterization of human faces. IEEE Trans, PAMI 12(1990):103-108.
[23] Turk M A, Pentland A. Face recognition using eigenfaces. Proc, Inte. Conf. On PR,1991:586-591.
[24] Baron R J. Mechanisms of human facial recognition.Int. J. Man. Mach. Stud. 15(1981):137-178.
[25] Osamu N, Mathur S.Minami T. Identification of human faces based on isodensity maps. Pattern Recognition, 1991(24)3:263-272.
[26] Yuille A, Cohn D, Hallinen P. Feature extraction from faces using deformable temples. In:Proc. IEEE Computer Soc. Conf. on Computer Vision and Patt. Recog., 1989:104-109.
[27] Hallinan P W. Recognizing human eyes. SPIE Proc. :Geometric Methods m Computer Vision, 1991,1570:214-226.
[28] Sirovich L, Kirby M. Application of Karhunen-Loeve procedure for the characterization of human faces. IEEE Trans. PAMI, 1990, 3(1):71-79.
[29] Belhumeur P, Hespanha J, Kriegman D. Eigenfaces vs. fisherfaces:class-specific linear projection. IEEE Trans. PAMI. 1997, 19(7):711-720.
[30] Common P. Independent component analysis:A new concept. Signal Processing, 1994, 36(3):287-314.
[31] Kim T K, Kim H, Hwang W et al. Independent component analysis in a local residue space for face recognition. Pattern Recognition, 2004, 37(9) :1873-1885.
[32] Bartlett M S, Lades H M, Sejnowski T J. Independent component representations for face recognition. SPIE Proc.1998,2399:528-564.
[33] Liu C J, Wechsler H. Comparative assessment of independent component analysis (ICA) for face recognition. Proceedings of International Conference on Audio and Video Based Biometric Person Authentication, USA, Washington DC,1999.
[34] Back K, Draper B A, Beveridge J R. PCA vs. ICA:a comparison on the FERET data set. In:Proceedings of International Conference on Computer Vision, Pattern Recognition and Image Processing, North Carolina, Durham, 2002:824-827.
[35] 汪鹏．非负矩阵分解：数学的奇妙力量．计算机教育,2004,10：38—40．
[36] Sirovich L, Kirby M. Low-dimensional procedure for the characterization of human face. Journal of the Optical Society of America, 1987, 4(3).
[37] Turk M A, Pentland A P. Eigenfaces for recognition. Journal of Cognitive Neuroscience, 1991,3(1).
[38] Karhunen A, Joutsensalo J.A class of neural networks for independent component analysis. Neural Networks, 1997,8(3):486-504.
[39] Cichocki A, Unbehauen R, Rummert E. Robust learning algorithm for blind separation of signals. Electronics Letters 30,1994,6(3):2210-2215.
[40] Common P. Independent component analysis- a new conception. Signal Processing, 1994,36:287-314.
[41] Lee T W.A unifying information-theoretic framework for ICA. Computers and Mathematics with Applications, 2000,39:1-21.
[42] Bell, Sejnowski. Face recognition by independent component analysis. IEEE Transaction on Networks, 2002,13(6):1450-1464.
[43] Lee D D, Seung H S. Unsupervised learning by convex and conic coding. Advances in Neural Information Processing Systems, The MIT Press. 1997,9:515-521.
[44] Lee D, Seung H. Learning the parts of objects by non-negative matrix factorization. Nature, 1999,401:788-791.
[45] Lee D, Seung H S. Algorithms for non-negative matrix factorization. Advances in Neural Information Processing Systems 13,2001.
[46] Tag Feng, Stan Z. Li,Heung-Yeung Shum. Local non-negative matrix factorization as a visual representation. Proceedings of the 2nd International Conference on Development and Learning.
[47] 边肇祺，张学工．模式识别．北京：清华大学出版社，2000．
[48] Baudat G, Anour F. Generalized discriminant analysis using a kernel approach. Neural Computation, 2000,12:2385-2404.
[49] Liu W, Stan Z L, Tan T, Null space-based kernel fisher discriminant analysis for face recognition. Proceedings of the Sixth IEEE International Conference on Automatic Face and Gesture Recognition.
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