基于子空间的人脸识别方法研究
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摘要
人脸识别是模式识别中的热点研究课题,人脸识别研究的关键是特征提取。子空间方法由于计算方便、提取特征稳定等在特征提取领域得到了广泛地应用。线性子空间分析方法的思想就是根据一定的性能目标来寻找一线性的空间变换,把原始数据样本投影到一个有利于分类的低维子空间,使子空间中的数据分布更为紧凑,降低计算复杂度。本文以人脸识别的鲁棒性为目标,主要以子空间方法作为研究手段,对人脸识别方法进行了更深入的研究。
本文主要围绕典型的子空间分析方法进行研究。首先研究实现了积分投影法和人脸识别的PCA方法以及SPCA方法,分析了方法的优缺点以及训练集和特征维数对识别率的影响。PCA方法是基于最小均方误差的原理,没有对样本的类内和类间进行区分；SPCA方法的实现验证了偶分量对人脸识别比较重要,奇分量容易受到外界光照条件的影响。
为了能更好对类内和类间样本进行区分,本文对LDA方法进行研究实现,分析了影响其识别率的因素主要有高维小样本问题、判别特征空间的正交性问题以及边缘值问题。针对高维小样本问题首先出现了两步降维法即传统的Fisherface方法。为了改善判别特征子空间正交性并提高识别率,本文对Fisherface方法提出了一种矩阵对称性的Fisherface方法,它的依据是PCA降维所得到的特征向量是相互正交的,而Fisher准则所求出的判别空间的基是非正交的,所以修正Fisher准则使所求的判别特征向量也相互正交,可以进一步消除统计相关。试验表明此方法在识别率上比传统方法表现出更好的鲁棒性。
为了改善边缘值对识别率的影响,本文还提出了一种边缘值替换的Fisherface算法,该算法首先利用PCA进行降维,消除类内离散度矩阵的奇异性,然后在降维的子空间内,以与同类样本间距离最小的样本作为参考对象,将同类的其它样本按一定权值向其靠拢,再用新的修正后的样本求取类均值,以新的类均值重新构造类内散布矩阵和类间散布矩阵。实验表明边缘值替换能够改善离群点偏离类中心的问题,并能提高识别率。
本文还研究了另外一种解决高维小样本问题的方法,即直接求解Fisher判别准则的方法,针对直接求解出现的两种投影方法进行实现研究,并探讨了加权值修正对其影响。
Face recognition is a hot topic in pattern recognition, the key of facerecognition is feature extraction.The subspace methods have been the mostpopular owing to their calculation convenient and good performance onexpression. The idea of the linear subspace analysis methods are based oncertain performance goals to find a linear space transformation which canreduce a high-dimensional original sample space to a low-dimensional spacethat is benefit to classfication. The distribution of the data is more compact inthe subspace.This dissertation focuses on the robustness of face recognitionbased on linear subspace methods.
This dissertation studies the typical linear subspace analysis methods. Toachieve integral projection for pretreatment and PCA method and SPCAmethod for face recognition.Analysis the advantages and disadvantages of themethod as well as the training set and the characteristic dimension impact onthe recognition rate. The PCA method is based on the principle of minimummean square error, which is no distinction the sample of within-class andbetween-class.The SPCA method validation even component is moreimportant for face recognition, while the odd component is vulnerable to theimpact of external conditions.
In order to distinguish between-class and within-class sample better, theLDA method is studied. The factors that affect this method including thehigh-dimension small sample, the edge values and discriminant feature spaceorthogonality problem. Research aimed at linear subspace analysis methods, aFisherface algorithm which has two-step dimensionality reduction was beenproposed.In order to improve the orthogonality of discriminant subspace inFisherface and increase the recognition rate, a new algorithm called matrix symmetry of Fisherface was proposed. Firstly, the PCA was used fordimensionality reduction to eliminate the small sample size problem. Secondly,the Fisher criterion was redefined by introducing a symmetric matrix. Finally,some examples were classified by the symmetric matrix. Experimental resultsindicate that the proposed method is more effective than the previous ones.
In order to improve the recognition rate of discriminant analysis algorithm,a new algorithm called outlier value substitution of Fisherface was proposed.Firstly, the PCA was used for dimensionality. The substitution or correction ofsample is accorded to the distance between the feature vector and others in thesame class. Secondly, the new class means are calculated using new samples.Finally, the within-class scatter matrix and between-class scatter matrix arerebuilt. Experimental results on ORL face image database indicate that theproposed method is more effective than the previous one and adaptivelyweighted Fisherface.
Studied another method to solve the problem of high-dimension and smallsample size, which is to directly solve the Fisher criterion. Studied andimplemented the two projection methods and discusses the impact of weightedvalue.
本文主要围绕典型的子空间分析方法进行研究。首先研究实现了积分投影法和人脸识别的PCA方法以及SPCA方法,分析了方法的优缺点以及训练集和特征维数对识别率的影响。PCA方法是基于最小均方误差的原理,没有对样本的类内和类间进行区分；SPCA方法的实现验证了偶分量对人脸识别比较重要,奇分量容易受到外界光照条件的影响。
为了能更好对类内和类间样本进行区分,本文对LDA方法进行研究实现,分析了影响其识别率的因素主要有高维小样本问题、判别特征空间的正交性问题以及边缘值问题。针对高维小样本问题首先出现了两步降维法即传统的Fisherface方法。为了改善判别特征子空间正交性并提高识别率,本文对Fisherface方法提出了一种矩阵对称性的Fisherface方法,它的依据是PCA降维所得到的特征向量是相互正交的,而Fisher准则所求出的判别空间的基是非正交的,所以修正Fisher准则使所求的判别特征向量也相互正交,可以进一步消除统计相关。试验表明此方法在识别率上比传统方法表现出更好的鲁棒性。
为了改善边缘值对识别率的影响,本文还提出了一种边缘值替换的Fisherface算法,该算法首先利用PCA进行降维,消除类内离散度矩阵的奇异性,然后在降维的子空间内,以与同类样本间距离最小的样本作为参考对象,将同类的其它样本按一定权值向其靠拢,再用新的修正后的样本求取类均值,以新的类均值重新构造类内散布矩阵和类间散布矩阵。实验表明边缘值替换能够改善离群点偏离类中心的问题,并能提高识别率。
本文还研究了另外一种解决高维小样本问题的方法,即直接求解Fisher判别准则的方法,针对直接求解出现的两种投影方法进行实现研究,并探讨了加权值修正对其影响。
Face recognition is a hot topic in pattern recognition, the key of facerecognition is feature extraction.The subspace methods have been the mostpopular owing to their calculation convenient and good performance onexpression. The idea of the linear subspace analysis methods are based oncertain performance goals to find a linear space transformation which canreduce a high-dimensional original sample space to a low-dimensional spacethat is benefit to classfication. The distribution of the data is more compact inthe subspace.This dissertation focuses on the robustness of face recognitionbased on linear subspace methods.
This dissertation studies the typical linear subspace analysis methods. Toachieve integral projection for pretreatment and PCA method and SPCAmethod for face recognition.Analysis the advantages and disadvantages of themethod as well as the training set and the characteristic dimension impact onthe recognition rate. The PCA method is based on the principle of minimummean square error, which is no distinction the sample of within-class andbetween-class.The SPCA method validation even component is moreimportant for face recognition, while the odd component is vulnerable to theimpact of external conditions.
In order to distinguish between-class and within-class sample better, theLDA method is studied. The factors that affect this method including thehigh-dimension small sample, the edge values and discriminant feature spaceorthogonality problem. Research aimed at linear subspace analysis methods, aFisherface algorithm which has two-step dimensionality reduction was beenproposed.In order to improve the orthogonality of discriminant subspace inFisherface and increase the recognition rate, a new algorithm called matrix symmetry of Fisherface was proposed. Firstly, the PCA was used fordimensionality reduction to eliminate the small sample size problem. Secondly,the Fisher criterion was redefined by introducing a symmetric matrix. Finally,some examples were classified by the symmetric matrix. Experimental resultsindicate that the proposed method is more effective than the previous ones.
In order to improve the recognition rate of discriminant analysis algorithm,a new algorithm called outlier value substitution of Fisherface was proposed.Firstly, the PCA was used for dimensionality. The substitution or correction ofsample is accorded to the distance between the feature vector and others in thesame class. Secondly, the new class means are calculated using new samples.Finally, the within-class scatter matrix and between-class scatter matrix arerebuilt. Experimental results on ORL face image database indicate that theproposed method is more effective than the previous one and adaptivelyweighted Fisherface.
Studied another method to solve the problem of high-dimension and smallsample size, which is to directly solve the Fisher criterion. Studied andimplemented the two projection methods and discusses the impact of weightedvalue.
引文
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[34]张龙翔.改进的模块2DPCA人脸识别方法[J].计算机工程与应用.2010,46(13)：147-150.
[35]杨健,杨静宇,叶晖Fisher线性鉴别分析的理论研究及其应用[J].自动化学报,2003,29(4)：481-493.
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[2]Samal A, Iyengar P A.Automatic recognition and analysis of human faces and facial expressions:a survey[J].Pattern Recognition,1992(25):65-77.
[3]Bledsoe W W., Man Machine Facial Recognition,Palo Alto,CA,TR:Rep PRI:22,1966
[4]周杰,卢春雨,张长水等.人脸自动识别方法综述[J].电子学报,2000,28(4)：102-106.
[5]周激流,张哗.人脸识别理论研究进展[J],计算机辅助设计与图形学学报,1999,11(2)：180-184.
[6]Bellman R.Adaptive Control Processes:A Guided Tour.New Jersey:Princeton University Press,1961.
[7]边肇棋,张学工等.模式识别(第二版)[M].北京：清华大学出版社,2000.
[8]段锦.人脸自动机器识别[M].北京：科学出版社,2009.
[9]山世光.人脸识别理论与应用研究[J].信息技术快报,2005.3(10).
[10]Harmon L D.The recognition of faces [J].Science of America,1973,(229):71-82.
[11]Kaya Y,Kobayashi K.A Basic Study on Human Recognition [M]. New York:Academic,1971,265-289.
[12]张翠平,苏光大.人脸识别技术综述[J].中国图像图形学报,2000,5(11)：855-894.
[13]刘小华.人脸识别技术及其应用研究[D].吉林：吉林大学,2005.
[14]周昌军.基于图像重构和特征融合的人脸识别方法研究[D].大连：大连理工大学,2008.
[15]孔万增.基于学习的人脸识别研究[D].浙江：浙江大学.2008.
[16]Brunelli R, Poggio T.Face recognition:Feature versus templates [J].IEEE Trans.on patter Analysis and Machine Intelligence,1993,15(10):1042-1052.
[17]Huang C L, Chen C W. Human facial feature extraction for face interpretation [J].Pattern Recognition,1992,25(12):1435-1444.
[18]山世光,高文,陈熙霖.基于而部纹理分布和变形模板的而部特征提取[J].软件学报,2001,12(4)：570-577.
[19]Pardas M,Losada M. Facial parameter extraction system based on active contours [C].Proceeding of the2001IEEE International Conference on Image Processing,2001,1058-1061.
[20]刘青山等.综述人脸识别中的子空间方法[J].自动化学报,2003,29(6)：900-911.
[21]Kirby M,L Sirovich. Application of the Karhunen-Loeve Procedure for the Charaterization of human faces[J].IEEE Trans. On Pattern Analysis and Machine Intelligence,1990,12(l):103-108.
[22]Turk M,Pentland A. Eigenfaces for recogniton [J]. Cognitive Neuroscience,1991,3(1):71-86.
[23]Swets D L and Weng J Y.Using Discriminant Eigenfeatures for Image Retrieval[J].IEEE Trans.on PAMI,1996,18(8):831-836.
[24]Belhumeur P N.Eigenfaces vs.Fisherfaces:Recognition using class specific linear projection [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1997,19(7):711-720.
[25]Bartlett M S, Movellan J R, Ejnowski T J.Face recognition by independent Component analysis[J]. IEEE Trans actions On Neural Networks,2002,13(6)1450-1464.
[26]Back K,Draper B A,Beveridge J R.PCA vs.ICA:A comparison on the FERET dataset[C]. International Conference on Computer Vision Pattern Recognition and Image.2002,524-827.
[27]Kohenen.Self-organization and assoeiative memory.SPringer-Verlag,1988.
[28]Lin S H,Kung S Y,Lin L J. Face recognition/detection by Probabilistic Decision-base neural network[J].IEEE Transactions on Neural Networks,1997,8(1):114-132.
[29]Lee S Y,Ham Y K,Park R H.Recognition of human front faces using knowledge-based feature extaction and neuro-fuzzy algorithm.Pattern Recogniton,1996,29(11):1863-1876.
[30]Bow S T.Pattern Recognition and Image Preprocessing [M].New York:Marcel Dekker Inc.,1992:203-274.
[31]Nastar C,Ayache N.Frequency-based nonrigid motion analysis:application to four dimensional medical images [J].IEEE Trans.PAMI,1996,18(11):1067-1079.
[32]黄丽坤.线性子空间人脸识别算法及姿态问题研究[D].成都：成都电子科技大学.2010.
[33]Jian Yang,David Zhang and etc.Two-Dimensional PCA:A New Approach to Appearance-Based Face Representation and Recognition[J].IEEE Trans.on Pattern Analysis and Machine Intelligence.2004,26(1):131-137.
[34]张龙翔.改进的模块2DPCA人脸识别方法[J].计算机工程与应用.2010,46(13)：147-150.
[35]杨健,杨静宇,叶晖Fisher线性鉴别分析的理论研究及其应用[J].自动化学报,2003,29(4)：481-493.
[36]石跃祥,蔡自兴,王学武等.基于改进的PCA算法和Fisher线性判别的人脸识别技术[J].小型微型计算机系统,2006,27(9)：1731-1736.
[37]赵宏伟.基于PCA针对表情变化的人脸识别技术研究[D].西安：西安电子科技大学.2009.
[38]于清澄.基于K-L变换的人脸识别算法研究[D].沈阳：沈阳工业大学.2007.
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