基于流形学习的人脸识别技术
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摘要
人脸识别作为生物特征识别的主流方向之一,因其在安全验证系统、信用卡验证、医学、档案管理、视频会议、人机交互、公安系统罪犯识别等方面的巨大应用前景而越来越成为当前模式识别和人工智能领域的一个研究热点。人脸识别是利用计算机对人脸图像进行处理、分析,并从中提取能表征人脸图像的鉴别信息,用于进行身份识别的一门技术。人脸识别与其它生物特征识别技术相比,具有直接、友好、方便的特点,易于被用户所接受。
但是,由于人脸结构的复杂性、人脸表情的多样性以及人脸成像过程的多变性等原因,人脸机器自动识别至今仍然被公认是一个具有挑战性的研究领域。一般认为,人脸从某种意义上来说是一种流形结构,人脸数据集是由某些内在变量控制形成的非线性流形,只要能从流形中寻找出光照、表情和姿态等控制变量,就能大幅度降低观测空间的维数。流形学习是近年来机器学习及模式识别等领域的一个研究热点,其主要目标是去发现高维观察数据空间的低维光滑流形。流形学习分为线性和非线性两种。线性流形学习目前已较成熟,主要方法有主成分分析(Principal Component Analysis, PCA)和线性鉴别分析(Linear Discriminant Analysis, LDA)等,这些算法具有较强的数学基础且易于实现。但是线性方法无法表现数据的内在结构。非线性流形学习主要有局部线性嵌入算法(Locally Linear Embedding, LLE)和监督局部线性嵌入算法(Supervised Locally Linear Embedding, SLLE)等,能够较有效地发现非线性高维数据的本质维数,利于进行维数约简和数据分析。
本文研究流表学习算法在人脸识别中的应用,对线性流形降维算法中的两种算法PCA、LDA和非线性流形降维算法中的两种算法LLE、SLLE分别进行仿真研究,并在此基础上实现了线性流形若干算法和非线性流形若干算法的融合研究。以下为本文主要的工作内容：
1)本文首先对原始PCA算法改进,使其具有灰度归一化操作能力,克服了光照对目标的影响。
2)研究并比较主成分分析(PCA)和线性鉴别分析(LDA)在人脸识别中的性能,并在分析LDA算法基础上提出了一种改进LDA算法。该方法主要解决传统LDA算法在投影空间出现边缘类样本重叠的问题。
3)基于PCA和LDA两种算法各自的优点,提出了一种融合算法。该方法融合了改进PCA算法与改进LDA算法。首先,用改进PCA算法对原样本降维,获得最优特征表示子空间；然后,在保证该子空间类内散度矩阵非奇异的基础上,作改进的线性判别分析。
4)介绍了非线性流形学习中的两种主流算法,主要分析局部线性嵌入算法(LLE),并针对LLE对样本无法分类的不足,引入了有监督的局部线性嵌入算法(SLLE)。对这两种算法仿真比较,得出SLLE方法有较好的分类能力。通过研究比较这两种算法,加深了对非线性流形学习算法的认识。
5)将线性降维算法(PCA)和非线性流形降维算法(LLE)进行比较,分析了两者的优缺点。针对线性算法PCA不能很好地保持人脸样本内在的拓扑结构、而非线性流形学习算法LLE能较好保持人脸样本内在拓扑结构的优点,提出了一种改进PCA和LLE相融合的算法。基于ORL人脸数据库的实验结果表明了所提出的算法应用于人脸识别的有效性。
Face recognition is a main orientation of biometrics, which is widely used in secure authentication system, credit card verification, medical, archive management, video conferencing, human-computer interaction, public security system and becomes a hotspot in the fields of current pattern recognition and artificial intelligence. Face recognition is an identification technique. The face images are processed and analyzed by computer and then the discriminant features are extracted. Compared with other biometric recognition techniques, face recognition is more direct, friendly, more convenient and easily accepted by customers.
However, due to the complexity of human face structure, the diversity of face expression and the change in the process of face image formation, computer face recognition technology is universally considered a challenging study topic. In a sense, it is commonly accepted that human face is a manifold structure. Face dataset is a nonlinear manifold formed by some inner variables, such as illumination condition, face pose and facial expression. If some controlled variables can be seek, space dimensionality could be reduced greatly. In recent years, manifold learning becomes a hot study topic in the fields of artificial intelligence and model recognition, and its aim is to seek low-dimensional smooth manifold in high-dimensional observation data space. The manifold learning can be divided into two classes:linear and nonlinear. At present, the linear manifold learning is mature, mainly contains Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA), etc. They have substantial mathematical foundation and can be implemented easily. However, it can not show the inner structure of the data in linear methods. Nonlinear methods, represented by Locally Linear Embedding (I.LE). and Supervised Locally Linear Embedding (SLLE), etc, can discover the intrinsic dimensions of nonlinear high dimensional data effectively, which can help researchers to reduce dimensionality and analyze data better.
The application of manifold learning in face recognition is studied in this paper. Two linear manifold learning algorithms PCA and LDA, and two nonlinear manifold learning algorithms LLE and SLLE are researched and simulated.
I) An improved PCA. in which the formula of PCA is modified, is presented first in this paper. This algorithm has the ability of gray normalization and can overcome the influence of light on the sample.
2) The performance of PCA and LDA in face recognition are researched respectively and compared. Then the traditional LDA is improved, mainly to solve the problem of the overlap of neighbor classes in the projection space.
3) According to the advantages of PCA and LDA, an improved algorithm, which combined the improved PCA and the improved LDA, is presented. The improved PCA is used to reduce the dimension first to get the optimal characteristic subspace of the original sample data set. In this process, the intra-class scatter matrix of the characteristic subspace should be ensured to be non-singular. On this basis, the improved LDA is carried out.
4) Two nonlinear manifold learning algorithms are introduced. LLE is mainly analyzed. Aimed at its disadvantage of unable to classify samples, SLLE is introduced. Through the simulation and comparison of LLE and SLLE, we can get that SLLE has stronger ability to classify the different samples.
5) The merits and demerits of PCA and LLE are analyzed respectively. Linear dimensionality reduction method PCA can not be good at keeping the intrinsic distribution of face sample data. while nonlinear algorithm LLE has the advantage of keeping the intrinsic distribution of face sample data. In this paper, an improved PCA is combined with LLE and used in face recognition, which has the ability of gray normalization and can overcome the influence of light on the sample. Experimental results on ORL (Olivetti Research Laboratory) database demonstrate the validity of the algorithm.
但是,由于人脸结构的复杂性、人脸表情的多样性以及人脸成像过程的多变性等原因,人脸机器自动识别至今仍然被公认是一个具有挑战性的研究领域。一般认为,人脸从某种意义上来说是一种流形结构,人脸数据集是由某些内在变量控制形成的非线性流形,只要能从流形中寻找出光照、表情和姿态等控制变量,就能大幅度降低观测空间的维数。流形学习是近年来机器学习及模式识别等领域的一个研究热点,其主要目标是去发现高维观察数据空间的低维光滑流形。流形学习分为线性和非线性两种。线性流形学习目前已较成熟,主要方法有主成分分析(Principal Component Analysis, PCA)和线性鉴别分析(Linear Discriminant Analysis, LDA)等,这些算法具有较强的数学基础且易于实现。但是线性方法无法表现数据的内在结构。非线性流形学习主要有局部线性嵌入算法(Locally Linear Embedding, LLE)和监督局部线性嵌入算法(Supervised Locally Linear Embedding, SLLE)等,能够较有效地发现非线性高维数据的本质维数,利于进行维数约简和数据分析。
本文研究流表学习算法在人脸识别中的应用,对线性流形降维算法中的两种算法PCA、LDA和非线性流形降维算法中的两种算法LLE、SLLE分别进行仿真研究,并在此基础上实现了线性流形若干算法和非线性流形若干算法的融合研究。以下为本文主要的工作内容：
1)本文首先对原始PCA算法改进,使其具有灰度归一化操作能力,克服了光照对目标的影响。
2)研究并比较主成分分析(PCA)和线性鉴别分析(LDA)在人脸识别中的性能,并在分析LDA算法基础上提出了一种改进LDA算法。该方法主要解决传统LDA算法在投影空间出现边缘类样本重叠的问题。
3)基于PCA和LDA两种算法各自的优点,提出了一种融合算法。该方法融合了改进PCA算法与改进LDA算法。首先,用改进PCA算法对原样本降维,获得最优特征表示子空间；然后,在保证该子空间类内散度矩阵非奇异的基础上,作改进的线性判别分析。
4)介绍了非线性流形学习中的两种主流算法,主要分析局部线性嵌入算法(LLE),并针对LLE对样本无法分类的不足,引入了有监督的局部线性嵌入算法(SLLE)。对这两种算法仿真比较,得出SLLE方法有较好的分类能力。通过研究比较这两种算法,加深了对非线性流形学习算法的认识。
5)将线性降维算法(PCA)和非线性流形降维算法(LLE)进行比较,分析了两者的优缺点。针对线性算法PCA不能很好地保持人脸样本内在的拓扑结构、而非线性流形学习算法LLE能较好保持人脸样本内在拓扑结构的优点,提出了一种改进PCA和LLE相融合的算法。基于ORL人脸数据库的实验结果表明了所提出的算法应用于人脸识别的有效性。
Face recognition is a main orientation of biometrics, which is widely used in secure authentication system, credit card verification, medical, archive management, video conferencing, human-computer interaction, public security system and becomes a hotspot in the fields of current pattern recognition and artificial intelligence. Face recognition is an identification technique. The face images are processed and analyzed by computer and then the discriminant features are extracted. Compared with other biometric recognition techniques, face recognition is more direct, friendly, more convenient and easily accepted by customers.
However, due to the complexity of human face structure, the diversity of face expression and the change in the process of face image formation, computer face recognition technology is universally considered a challenging study topic. In a sense, it is commonly accepted that human face is a manifold structure. Face dataset is a nonlinear manifold formed by some inner variables, such as illumination condition, face pose and facial expression. If some controlled variables can be seek, space dimensionality could be reduced greatly. In recent years, manifold learning becomes a hot study topic in the fields of artificial intelligence and model recognition, and its aim is to seek low-dimensional smooth manifold in high-dimensional observation data space. The manifold learning can be divided into two classes:linear and nonlinear. At present, the linear manifold learning is mature, mainly contains Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA), etc. They have substantial mathematical foundation and can be implemented easily. However, it can not show the inner structure of the data in linear methods. Nonlinear methods, represented by Locally Linear Embedding (I.LE). and Supervised Locally Linear Embedding (SLLE), etc, can discover the intrinsic dimensions of nonlinear high dimensional data effectively, which can help researchers to reduce dimensionality and analyze data better.
The application of manifold learning in face recognition is studied in this paper. Two linear manifold learning algorithms PCA and LDA, and two nonlinear manifold learning algorithms LLE and SLLE are researched and simulated.
I) An improved PCA. in which the formula of PCA is modified, is presented first in this paper. This algorithm has the ability of gray normalization and can overcome the influence of light on the sample.
2) The performance of PCA and LDA in face recognition are researched respectively and compared. Then the traditional LDA is improved, mainly to solve the problem of the overlap of neighbor classes in the projection space.
3) According to the advantages of PCA and LDA, an improved algorithm, which combined the improved PCA and the improved LDA, is presented. The improved PCA is used to reduce the dimension first to get the optimal characteristic subspace of the original sample data set. In this process, the intra-class scatter matrix of the characteristic subspace should be ensured to be non-singular. On this basis, the improved LDA is carried out.
4) Two nonlinear manifold learning algorithms are introduced. LLE is mainly analyzed. Aimed at its disadvantage of unable to classify samples, SLLE is introduced. Through the simulation and comparison of LLE and SLLE, we can get that SLLE has stronger ability to classify the different samples.
5) The merits and demerits of PCA and LLE are analyzed respectively. Linear dimensionality reduction method PCA can not be good at keeping the intrinsic distribution of face sample data. while nonlinear algorithm LLE has the advantage of keeping the intrinsic distribution of face sample data. In this paper, an improved PCA is combined with LLE and used in face recognition, which has the ability of gray normalization and can overcome the influence of light on the sample. Experimental results on ORL (Olivetti Research Laboratory) database demonstrate the validity of the algorithm.
引文
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