人脸识别方法的研究
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摘要
人脸识别作为计算机视觉以及模式识别研究的一个重要子领域,它具有重要的理论研究意义和实际应用价值。近年来,人脸识别系统已经可以较为准确地在某些限定的条件下对人脸图像进行识别,但在实际应用中还面临着很多困难,其采用的识别方法尚需进一步改进和完善。
鉴于此,本文对人脸识别技术中的三种主流方法(PCA方法、贝叶斯方法和LDA方法)进行了深入的研究,提出了相应的改进方法。本文的主要贡献如下：
(1)PCA是重要的降维方法之一,它能用空间的主成分来逼近原空间。通常,PCA需要将一幅图像转化为一个高维向量,这个高维向量生成一个高维的协方差矩阵,这个高维的协方差矩阵导致计算的复杂性增加和存储空间也增大。和经典的PCA相比,2DPCA直接利用二维图像计算协方差矩阵,这个协方差矩阵的维数较小,它减少了计算的复杂性和节约了存储空间。尽管2DPCA促进了人脸识别技术的发展和进步,但相对于PCA生成的高维的协方差矩阵而言,2DPCA生成的协方差矩阵空间结构小,丢失了一些信息,这些丢失的信息对人脸是识别非常重要。为了利用更多的鉴别信息,本文提出了一种人脸垂直对称的变形2DPCA算法(S2DPCA),该算法与PCA相比降低了计算复杂性,与2DPCA和PCA相比提高了人脸识别率。
(2)因为S2DPCA比2DPCA有更高的自由度,所以它对小样本问题非常敏感。为了进一步提高S2DPCA方法的性能,本文提出了一种加权变形2DPCA的人脸特征提取方法(WV2DPCA)。该方法首先将人脸图像分为三个子图像(眉毛以上的部分、眉毛和鼻尖之间的部分和鼻尖以下的部分),接着对各子图像进行特征提取,最后根据每个子图像在人脸分类中的权重,利用加权最近邻分方法进行分类。该方法有三个优点：能减轻小样本的影响,提高人脸识别率,减小计算的复杂性。
(3) WV2DPCA方法中的权值大小是根据样本粗略估计,不够准确。为了解决以上问题,本文提出一种自适应加权变形2DPCA方法(AWV2DPCA),该方法直接将人脸图像分割成若干个子图像集(相同位置的子图像形成一个集合),然后根据相似性原理自适应地计算每个子图像集在分类中的权重,最后根据加权最近邻方法计算测试样本的类别。该方法的优点是：权重的大小自适应样本的类别。
(4)传统贝叶斯空间的人脸识别算法一般是假设样本空间满足高斯分布,实际上样本空间是很复杂的,并不一定满足高斯分布。为了适应人脸复杂的空间变化,本文提出了一种基于二值数据的贝叶斯子空间的人脸识别算法,该算法将图像二值化；然后假设各样本的特征空间变量相互独立,计算类条件概率；最后根据贝叶斯公式求后验概率。它克服了传统贝叶斯方法难求类内和类间协方差矩阵的缺点,简单易用。
为了进一步提高识别效果,提出了最小风险贝叶斯决策的二值化人脸识别算法,该算法根据图像的相似性估计其损失函数,利用贝叶斯公式求最小风险,最后根据最小风险判断其所属类。该算法增大类间距离,提高人脸正确识别率。
(5)线性判别分析法(LDA)在进行高维的人脸识别时,经常会出现“小样本问题(SSS)”和边缘类重叠问题。鉴于此,本文提出了一种可调控参数的LDA人脸识别方法。该方法重新定义了类内离散度矩阵,利用参数平衡其特征值估计的偏差和方差,从而解决小样本问题；对类间离散度矩阵加权,使边缘类均匀分布来防止边缘类的重叠,从而提高人脸正确识别率；实验表明,该方法可以解决小样本问题,且其性能优于传统的Eigenfaces和Fisherface等方法。在此基础上本文还提出了一种人脸本征空间的特征提取算法,该算法将类内离散度矩阵的特征空间分解为二个子解空间(主成分子空间和零子空间),利用本征谱模型对二个子空间进行正则化,从而减轻了不稳定性、过拟合和推广能力差的问题。实验表明,该算法使用较少的特征维数就能达到其它方法相同的识别率。
Face recognition, an important sub-field of computer vision and pattern recognition, has been extensively studied mainly due to its theoretical and practical significance. Although the face recognition has gained great progress, it includes still a lot of unsolved difficult problems. Hence, face recognition requires a further study for practical applications. This paper simply discusses the current research focus such as PCA, LDA and Bayesian methods, and proposes some improved methods for face recognition.
(1) PCA is one of the most important algorithms for dimension reduction, in which the original space is approximated by several principal components of all features so that mean square error (MSE) is minimized. Usually, PCA methods require that an image matrix is arranged into a high dimensional vector that will produce a very high dimensional covariance matrix which leads to two limits, extremely high computational complexity and very large storage space. Compared with the classical PCA,2DPCA directly uses two-dimensional images matrix to calculate a smaller (lower) covariance matrix, which decreases the computation load and saves the storage space. Although 2DPCA promotes the development of face recognition, some information contained in the high dimensional covariance matrix, which can help to improve face recognition rate, is lost by lower dimensional covariance matrix. To exploit more discriminant information, we propose a vertically symmetrical variation 2DPCA (S2DPCA) algorithm for face recognition. The experiments on face databases show that S2DPCA reduces the computational complexity comparing with PCA, and improves the face recognition rate comparing with PCA and 2DPCA.
(2) However, because S2DPCA has higher degree of freedom than 2DPCA, it is more sensitive to small sample size. To further improve the performance of the S2DPCA, an efficient algorithm of face feature extraction is proposed on basis of the weighted variation of 2DPCA (WV2DPCA), in which the face space is elaborately divided into three parts:the part above the eyebrows, one between eyebrows and the nasal tip, and that below nasal tip. WV2DPCA extracts the features from each sub-image matrix. According to taking the different roles of three sub-images in face recognition, a common weight is assigned to each sub-image. Finally, the classification is performed by the weighted nearest neighbor method. The WV2DPCA has three advantages that include alleviating the bad effect of small sample size, increasing face recognition rate, and decreasing the computational complexity.
(3) The main drawback in WV2DPCA is the strategy how to assign appropriate weights to the sub-images. However, weights used in WV2DPCA are roughly estimated according to different samples, and may be inaccurate. To overcome this drawback, an adaptive weighted variation 2DPCA (AWV2DPCA) for face recognition is developed. In AWV2DPCA, each face image is divided into several sub-images, and all the sub-images of the same position are defined as a sub-image set. AWV2DPCA extracts the features associated with each of sub-image sets, and adaptively estimates the weight corresponding to each of sub-image sets according to the similarity of features, and performs the classification by the weighted nearest neighbor method.
(4) The traditional Bayesian algorithms for face recognition assume that the samples meet the Gaussian distribution. In fact, the distributions of samples are very complicated. To adapt to the complicated distributions of samples, a face recognition algorithm based on the binary image is proposed in the light of the Bayesian principle. In this algorithm, the images binarization is firstly performed, and the class conditional probability is calculated under the assumption that the sample feature variables are mutually independent each other, and finally posterior probability is calculated by Bayesian formula. The above simple method decreases the computational complexity.
To further enhance the face recognition rate, a face recognition algorithm of binary image is proposed by the smallest Bayesian risk method, which estimates the loss function according to the similarity of the samples, then evaluates the smallest risk by Bayesian formula, and finally determines that they belong to which class. This algorithm increases the gaps between classes and improves face recognition rate.
(5) It is well-known that the line discriminant analysis (LDA) applied to high-dimensional face recognition often suffers from two problems, small sample size (SSS) and close-to-class overlap. To overcome these problems, a LDA-based face recognition algorithm with regularization parameters is proposed, which resolves the SSS problem by regularization parameters and redefined within-class scatter matrices, and prevents from the overlap of edge classes through weighting between-class scatter matrices. Extensive experimental results show the proposed LDA algorithm can solve the above two problems and outperforms traditional methods such as eigenfaces and Fisherfaces by controlling the regularization parameters. On the basis of the above method, an algorithm of feature extraction in face image space is proposed. This algorithm decomposes the eigenfeature space into two subspaces, principal component subspace and null subspace, and regularizes two subspaces with the eigen-feature spectrum model to alleviate the instability, overfitting or poor generalization. The experiments on ORL face database show that our method, which uses fewer features, can achieve higher recognition rate than other approaches, such as FLDA, BML, and DSL.
鉴于此,本文对人脸识别技术中的三种主流方法(PCA方法、贝叶斯方法和LDA方法)进行了深入的研究,提出了相应的改进方法。本文的主要贡献如下：
(1)PCA是重要的降维方法之一,它能用空间的主成分来逼近原空间。通常,PCA需要将一幅图像转化为一个高维向量,这个高维向量生成一个高维的协方差矩阵,这个高维的协方差矩阵导致计算的复杂性增加和存储空间也增大。和经典的PCA相比,2DPCA直接利用二维图像计算协方差矩阵,这个协方差矩阵的维数较小,它减少了计算的复杂性和节约了存储空间。尽管2DPCA促进了人脸识别技术的发展和进步,但相对于PCA生成的高维的协方差矩阵而言,2DPCA生成的协方差矩阵空间结构小,丢失了一些信息,这些丢失的信息对人脸是识别非常重要。为了利用更多的鉴别信息,本文提出了一种人脸垂直对称的变形2DPCA算法(S2DPCA),该算法与PCA相比降低了计算复杂性,与2DPCA和PCA相比提高了人脸识别率。
(2)因为S2DPCA比2DPCA有更高的自由度,所以它对小样本问题非常敏感。为了进一步提高S2DPCA方法的性能,本文提出了一种加权变形2DPCA的人脸特征提取方法(WV2DPCA)。该方法首先将人脸图像分为三个子图像(眉毛以上的部分、眉毛和鼻尖之间的部分和鼻尖以下的部分),接着对各子图像进行特征提取,最后根据每个子图像在人脸分类中的权重,利用加权最近邻分方法进行分类。该方法有三个优点：能减轻小样本的影响,提高人脸识别率,减小计算的复杂性。
(3) WV2DPCA方法中的权值大小是根据样本粗略估计,不够准确。为了解决以上问题,本文提出一种自适应加权变形2DPCA方法(AWV2DPCA),该方法直接将人脸图像分割成若干个子图像集(相同位置的子图像形成一个集合),然后根据相似性原理自适应地计算每个子图像集在分类中的权重,最后根据加权最近邻方法计算测试样本的类别。该方法的优点是：权重的大小自适应样本的类别。
(4)传统贝叶斯空间的人脸识别算法一般是假设样本空间满足高斯分布,实际上样本空间是很复杂的,并不一定满足高斯分布。为了适应人脸复杂的空间变化,本文提出了一种基于二值数据的贝叶斯子空间的人脸识别算法,该算法将图像二值化；然后假设各样本的特征空间变量相互独立,计算类条件概率；最后根据贝叶斯公式求后验概率。它克服了传统贝叶斯方法难求类内和类间协方差矩阵的缺点,简单易用。
为了进一步提高识别效果,提出了最小风险贝叶斯决策的二值化人脸识别算法,该算法根据图像的相似性估计其损失函数,利用贝叶斯公式求最小风险,最后根据最小风险判断其所属类。该算法增大类间距离,提高人脸正确识别率。
(5)线性判别分析法(LDA)在进行高维的人脸识别时,经常会出现“小样本问题(SSS)”和边缘类重叠问题。鉴于此,本文提出了一种可调控参数的LDA人脸识别方法。该方法重新定义了类内离散度矩阵,利用参数平衡其特征值估计的偏差和方差,从而解决小样本问题；对类间离散度矩阵加权,使边缘类均匀分布来防止边缘类的重叠,从而提高人脸正确识别率；实验表明,该方法可以解决小样本问题,且其性能优于传统的Eigenfaces和Fisherface等方法。在此基础上本文还提出了一种人脸本征空间的特征提取算法,该算法将类内离散度矩阵的特征空间分解为二个子解空间(主成分子空间和零子空间),利用本征谱模型对二个子空间进行正则化,从而减轻了不稳定性、过拟合和推广能力差的问题。实验表明,该算法使用较少的特征维数就能达到其它方法相同的识别率。
Face recognition, an important sub-field of computer vision and pattern recognition, has been extensively studied mainly due to its theoretical and practical significance. Although the face recognition has gained great progress, it includes still a lot of unsolved difficult problems. Hence, face recognition requires a further study for practical applications. This paper simply discusses the current research focus such as PCA, LDA and Bayesian methods, and proposes some improved methods for face recognition.
(1) PCA is one of the most important algorithms for dimension reduction, in which the original space is approximated by several principal components of all features so that mean square error (MSE) is minimized. Usually, PCA methods require that an image matrix is arranged into a high dimensional vector that will produce a very high dimensional covariance matrix which leads to two limits, extremely high computational complexity and very large storage space. Compared with the classical PCA,2DPCA directly uses two-dimensional images matrix to calculate a smaller (lower) covariance matrix, which decreases the computation load and saves the storage space. Although 2DPCA promotes the development of face recognition, some information contained in the high dimensional covariance matrix, which can help to improve face recognition rate, is lost by lower dimensional covariance matrix. To exploit more discriminant information, we propose a vertically symmetrical variation 2DPCA (S2DPCA) algorithm for face recognition. The experiments on face databases show that S2DPCA reduces the computational complexity comparing with PCA, and improves the face recognition rate comparing with PCA and 2DPCA.
(2) However, because S2DPCA has higher degree of freedom than 2DPCA, it is more sensitive to small sample size. To further improve the performance of the S2DPCA, an efficient algorithm of face feature extraction is proposed on basis of the weighted variation of 2DPCA (WV2DPCA), in which the face space is elaborately divided into three parts:the part above the eyebrows, one between eyebrows and the nasal tip, and that below nasal tip. WV2DPCA extracts the features from each sub-image matrix. According to taking the different roles of three sub-images in face recognition, a common weight is assigned to each sub-image. Finally, the classification is performed by the weighted nearest neighbor method. The WV2DPCA has three advantages that include alleviating the bad effect of small sample size, increasing face recognition rate, and decreasing the computational complexity.
(3) The main drawback in WV2DPCA is the strategy how to assign appropriate weights to the sub-images. However, weights used in WV2DPCA are roughly estimated according to different samples, and may be inaccurate. To overcome this drawback, an adaptive weighted variation 2DPCA (AWV2DPCA) for face recognition is developed. In AWV2DPCA, each face image is divided into several sub-images, and all the sub-images of the same position are defined as a sub-image set. AWV2DPCA extracts the features associated with each of sub-image sets, and adaptively estimates the weight corresponding to each of sub-image sets according to the similarity of features, and performs the classification by the weighted nearest neighbor method.
(4) The traditional Bayesian algorithms for face recognition assume that the samples meet the Gaussian distribution. In fact, the distributions of samples are very complicated. To adapt to the complicated distributions of samples, a face recognition algorithm based on the binary image is proposed in the light of the Bayesian principle. In this algorithm, the images binarization is firstly performed, and the class conditional probability is calculated under the assumption that the sample feature variables are mutually independent each other, and finally posterior probability is calculated by Bayesian formula. The above simple method decreases the computational complexity.
To further enhance the face recognition rate, a face recognition algorithm of binary image is proposed by the smallest Bayesian risk method, which estimates the loss function according to the similarity of the samples, then evaluates the smallest risk by Bayesian formula, and finally determines that they belong to which class. This algorithm increases the gaps between classes and improves face recognition rate.
(5) It is well-known that the line discriminant analysis (LDA) applied to high-dimensional face recognition often suffers from two problems, small sample size (SSS) and close-to-class overlap. To overcome these problems, a LDA-based face recognition algorithm with regularization parameters is proposed, which resolves the SSS problem by regularization parameters and redefined within-class scatter matrices, and prevents from the overlap of edge classes through weighting between-class scatter matrices. Extensive experimental results show the proposed LDA algorithm can solve the above two problems and outperforms traditional methods such as eigenfaces and Fisherfaces by controlling the regularization parameters. On the basis of the above method, an algorithm of feature extraction in face image space is proposed. This algorithm decomposes the eigenfeature space into two subspaces, principal component subspace and null subspace, and regularizes two subspaces with the eigen-feature spectrum model to alleviate the instability, overfitting or poor generalization. The experiments on ORL face database show that our method, which uses fewer features, can achieve higher recognition rate than other approaches, such as FLDA, BML, and DSL.
引文
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