特征提取方法研究及其在人脸识别中的应用
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摘要
人脸识别是一项极具发展潜力的生物特征识别技术,在信息安全,公共安全,金融等领域具有广阔的应用前景。在人脸识别研究领域中,特征提取是解决该问题的一个关键技术。在过去几十年中,学者们提出了许多相关的特征提取方法,如线性鉴别分析、主成分分析和保局投影等线性特征提取方法,以及在支持向量机的基础上演变而来的基于核函数的非线性特征提取方法等等。因此,本论文以特征提取方法为研究目标,以人脸识别为应用背景,对线性特征提取方法和非线性特征提取方法进行了深入的研究,所提出的改进方法不但提高了计算效率和识别性能,而且能够有效地解决小样本问题。具体的研究内容包括：
(1)不相关鉴别分析方法是一种有效的特征提取方法,但是将其应用到人脸识别中将遇到所谓的小样本问题,而且由于采用迭代求解方式,算法运算速度缓慢。基于图像矩阵模型的特征提取方法可有效地解决小样本问题,故此提出了一种基于图像矩阵模型的二维不相关鉴别矢量集方法,该方法由于采用了图像矩阵模型,避免了小样本问题,通过对类内散布矩阵的白化变换,可以非迭代的求得二维不相关鉴别矢量集,不但求解速度快且数值解稳定；
(2)对基于图像向量模型的不相关鉴别分析方法进行了深入的研究,以不相关空间方法为理论基础,提出了一种改进的不相关空间方法,其思想是将原始数据空间降到一个低维的子空间,从而避免了总体散布矩阵奇异；另外根据散布矩阵的对称性,引入了一种快速的矩阵分解方法,进一步提高了求解不相关鉴别矢量集的速度。该方法不但在理论上有效地解决了小样本问题,同时具有较快的计算速度；
(3)基于核映射的方法是一种广泛使用的非线性方法。已有的实验结果表明：基于核映射的特征提取方法可有效提高原线性方法的识别性能。正交鉴别保局投影、鉴别通用矢量集和不相关空间方法是三种具有较好识别性能的特征提取方法,但它们都是线性方法,故此针对三种线性方法进行了研究,分别提出了其相应的非线性方法,即核正交鉴别保局投影、核鉴别通用矢量集和核不相关空间方法。三种核特征提取方法通过巧妙的变换,使其在实现过程中转化成样本的内积形式,然后用核函数替换内积计算即可完成非线性特征的提取,不但降低了算法的计算复杂性,同时也提高了原相应线性特征提取方法的识别性能；
(4)针对核特征提取方法解决高维小样本问题存在的缺点,提出了一种基于压缩变换的核特征提取优化模型。该模型的求解思想是首先对高维的训练样本根据Fisher准则进行降维处理,然后再将降维后的训练样本按核特征提取方法进行非线性特征提取。优化后的方法在保证原方法的识别性能的同时,将有效地节省算法的计算量与存储开销,增强算法的实用性。
Face recognition is a biological recognition technology with great developable potential, which is believed to have a great deal of potential applications in information security, public security and financial security. In face recognition, feature extraction is one of the key steps. In the passed decade years, many correlated algorithms have been proposed to solve this problem. Linear feature extraction methods, such as Linear Discriminant Analysis (LDA), Principal Component Analysis (PCA) and Locality Preserving Projections (LPP), are developed to solve linear problem, and nonlinear feature extraction methods, such as kernel function methods based on support vector machine (SVM), are proposed to solve nonlinear problem. In this paper, linear and nonlinear methods on feature extraction field are both deeply analyzed. Not only are effectiveness and performance considered in our proposed methods, but the propsed methods can effectively overcome small size samples problem. The researchs of the dissertation are:
(1) The uncorrelated discriminant analysis is a effective method for feature extraction, but it may encounter the small size sample problem when this method is applied in face recognition task. This algorithm, which is solved by recursive method, has low speed of computation. Feature extraction methods based on image matrix model can effectively solve the small sample size problem, so a new algorithm based on image matrix model is proposed, which is called two-dimensional uncorrelated discriminant vectors. Being based on image matrix model, the new algorithm avoids small sample sizes problem. Through whitening transform of within-class scatter matrix, uncorrelated discriminant vectors can be obtained non-recursively.The new method computes faster while maintaining numerical stability.
(2) The uncorrelated discriminant analysis based on image vector model is deeply analyzed. An improved uncorrelated space method is proposed. The main idea of the proposed algorithm is to map the original space into a low dimensional subspace, and then the singularity of the total-scatter matrix can be avoided in this low dimensional subspace. In addition, according to the symmetry of scatter matrix, a fast method is introduced in order to further improve speed of computing uncorrelated discriminant vectors. The new method not only effectively solves the small size sample problem but also computes faster.
(3) Kernel method as a non-linear dimension reduction method is widely used. The existed results show that the feature extraction methods based on the kernel mapping outperform the original linear feature extraction methods. Three algorithms, namely orthogonal discriminant locality preserving projections, discriminative common vectors and kernel uncorrelated space method, are effective methods for feature extraction, but they are linear feature extraction methods. Therefore three nonlinear feature extraction methods are developed in the paper, namely kernel orthogonal discriminant locality preserving projections, kernel discriminative common vectors and kernel uncorrelated space method. To three nonlinear feature extraction methods through the ingenious transformation, they are realized in the process only to calculate the inner product of the input samples, not only avoid the algorithm computation complexity, simultaneously also effectively enhance the algorithm recognition performance.
(4) A kernel feature extraction optimization model based on the compression transformation for small sample sizes problem is developed in the paper. Firstly, according to the fisher criterion, the original samples are compressed into a lower dimensional space, then the kernel feature extraction algorithms are implemented on the compressed samples. The optimized methods guarantee recognition performance of the original methods, simultaneously save the computation load and the memory expenses, also enhance the algorithms usability.
(1)不相关鉴别分析方法是一种有效的特征提取方法,但是将其应用到人脸识别中将遇到所谓的小样本问题,而且由于采用迭代求解方式,算法运算速度缓慢。基于图像矩阵模型的特征提取方法可有效地解决小样本问题,故此提出了一种基于图像矩阵模型的二维不相关鉴别矢量集方法,该方法由于采用了图像矩阵模型,避免了小样本问题,通过对类内散布矩阵的白化变换,可以非迭代的求得二维不相关鉴别矢量集,不但求解速度快且数值解稳定；
(2)对基于图像向量模型的不相关鉴别分析方法进行了深入的研究,以不相关空间方法为理论基础,提出了一种改进的不相关空间方法,其思想是将原始数据空间降到一个低维的子空间,从而避免了总体散布矩阵奇异；另外根据散布矩阵的对称性,引入了一种快速的矩阵分解方法,进一步提高了求解不相关鉴别矢量集的速度。该方法不但在理论上有效地解决了小样本问题,同时具有较快的计算速度；
(3)基于核映射的方法是一种广泛使用的非线性方法。已有的实验结果表明：基于核映射的特征提取方法可有效提高原线性方法的识别性能。正交鉴别保局投影、鉴别通用矢量集和不相关空间方法是三种具有较好识别性能的特征提取方法,但它们都是线性方法,故此针对三种线性方法进行了研究,分别提出了其相应的非线性方法,即核正交鉴别保局投影、核鉴别通用矢量集和核不相关空间方法。三种核特征提取方法通过巧妙的变换,使其在实现过程中转化成样本的内积形式,然后用核函数替换内积计算即可完成非线性特征的提取,不但降低了算法的计算复杂性,同时也提高了原相应线性特征提取方法的识别性能；
(4)针对核特征提取方法解决高维小样本问题存在的缺点,提出了一种基于压缩变换的核特征提取优化模型。该模型的求解思想是首先对高维的训练样本根据Fisher准则进行降维处理,然后再将降维后的训练样本按核特征提取方法进行非线性特征提取。优化后的方法在保证原方法的识别性能的同时,将有效地节省算法的计算量与存储开销,增强算法的实用性。
Face recognition is a biological recognition technology with great developable potential, which is believed to have a great deal of potential applications in information security, public security and financial security. In face recognition, feature extraction is one of the key steps. In the passed decade years, many correlated algorithms have been proposed to solve this problem. Linear feature extraction methods, such as Linear Discriminant Analysis (LDA), Principal Component Analysis (PCA) and Locality Preserving Projections (LPP), are developed to solve linear problem, and nonlinear feature extraction methods, such as kernel function methods based on support vector machine (SVM), are proposed to solve nonlinear problem. In this paper, linear and nonlinear methods on feature extraction field are both deeply analyzed. Not only are effectiveness and performance considered in our proposed methods, but the propsed methods can effectively overcome small size samples problem. The researchs of the dissertation are:
(1) The uncorrelated discriminant analysis is a effective method for feature extraction, but it may encounter the small size sample problem when this method is applied in face recognition task. This algorithm, which is solved by recursive method, has low speed of computation. Feature extraction methods based on image matrix model can effectively solve the small sample size problem, so a new algorithm based on image matrix model is proposed, which is called two-dimensional uncorrelated discriminant vectors. Being based on image matrix model, the new algorithm avoids small sample sizes problem. Through whitening transform of within-class scatter matrix, uncorrelated discriminant vectors can be obtained non-recursively.The new method computes faster while maintaining numerical stability.
(2) The uncorrelated discriminant analysis based on image vector model is deeply analyzed. An improved uncorrelated space method is proposed. The main idea of the proposed algorithm is to map the original space into a low dimensional subspace, and then the singularity of the total-scatter matrix can be avoided in this low dimensional subspace. In addition, according to the symmetry of scatter matrix, a fast method is introduced in order to further improve speed of computing uncorrelated discriminant vectors. The new method not only effectively solves the small size sample problem but also computes faster.
(3) Kernel method as a non-linear dimension reduction method is widely used. The existed results show that the feature extraction methods based on the kernel mapping outperform the original linear feature extraction methods. Three algorithms, namely orthogonal discriminant locality preserving projections, discriminative common vectors and kernel uncorrelated space method, are effective methods for feature extraction, but they are linear feature extraction methods. Therefore three nonlinear feature extraction methods are developed in the paper, namely kernel orthogonal discriminant locality preserving projections, kernel discriminative common vectors and kernel uncorrelated space method. To three nonlinear feature extraction methods through the ingenious transformation, they are realized in the process only to calculate the inner product of the input samples, not only avoid the algorithm computation complexity, simultaneously also effectively enhance the algorithm recognition performance.
(4) A kernel feature extraction optimization model based on the compression transformation for small sample sizes problem is developed in the paper. Firstly, according to the fisher criterion, the original samples are compressed into a lower dimensional space, then the kernel feature extraction algorithms are implemented on the compressed samples. The optimized methods guarantee recognition performance of the original methods, simultaneously save the computation load and the memory expenses, also enhance the algorithms usability.
引文
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