基于线性子空间及环形对称GABOR变换的人脸识别算法研究
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摘要
本文所开展的基于线性特征子空间和环形对称Gabor变换的人脸识别方法的研究，主要从两个方面进行，一方面是对主成分分析和线性判别分析等基于线性特征子空间的人脸识别方法的研究，另一方面是对基于环形对称Gabor变换特征的人脸识别方法的研究。研究的主要目的，是提高算法对于人脸成像过程中存在的诸多变化因素的鲁棒性，这些因素包括成像环境的光照和成像角度的变化、识别对象的表情和姿态的变化，以及人脸图像的旋转和平移等。
本文中所做的主要工作包括：
对基于线性特征子空间的人脸识别方法进行了深入的理论和方法研究，其中包括主成分分析方法和线性判别分析方法，在此基础上，分别提出了基于加权主成分分析的方法、基于图像校正和位平面融合的广义主成分分析方法、特征块方法以及结合主成分分析与分步线性判别分析的方法等四种人脸识别的新方法；在对基于Gabor变换特征的人脸识别方法的研究基础上，从理论和实验方面对环形对称Gabor变换进行了详细的研究，分析了其用于人脸识别的可能性，提出了采用环形对称Gabor变换的人脸识别方法。通过在ORL、AR、Yale和UMIST等人脸数据库上的实验，验证了本文所提出的改进方法或新方法相对于现有方法的优越性。
本文的创新之处在于：
1)提出了基于加权主成分分析的人脸识别方法
通过深入研究主成分分析方法，我们从理论和实验出发，观察分析了特征脸空间中不同的特征分量，即特征脸对于人脸图像的重建和分类的作用的不同，提出了在加权的主成分空间中进行人脸识别的改进方法。
通过对传统的主成分空间进行与本征值矩阵有关的加权，使各分量具有相等的方差，从而归一化的加权主成分空间，从而使判别性能得以改善。我们证明了加权主成分空间中的一些有用性质，指出，在加权的主成分分析中，采用欧氏距离测度进行分类，等价于在传统主成分分析空间中采用马氏距离测度进行分类，这就从理论上给出了所提出的方法能够提高识别性能的原因，此外，用于重建目的时，采用较大的本征值所对应的本征向量构成变换矩阵，其重建与传统的主成分分析相同。
通过实验，我们还分析了不同特征分量分别在传统的主成分分析和加权的主成分分析中的分布情况，并指出，在传统的主成分分析中，某些对分类意义不大但取值很大的分量，主导了特征距离的计算，使其它取值较小但对分类重要的分量的作用被淹没。另外，实验结果也说明，即使在加权的主成分分析中，特征的选取也要按照本征值由大到小的顺序进行。在AR和ORL两个数据库上的实验结果说明，本文所提出的方法在识别率方面明显超过传统方法；
2)提出了基于图像校正和位平面融合的广义主成分分析人脸识别方法
根据人脸的左右对称特性，提出了对图像中光照方向的变化进行校正和补偿的方法，从图像预处理的角度对人脸图像在成像过程中存在的光源向左或右偏移引起光照左右强弱变化的问题进行初步校正和补偿。同时，通过对人脸图像的位平面分解，分析了各个位平面不同的特性，及其对于图像结构和纹理的不同贡献，并将其与类间和类内差异相联系。我们指出，经过了直方图均衡处理的图像，其0、1、5、6、7位平面主要表现结构特征，而2、3、4位平面主要表现纹理特征。结构特征代表了同一个体所有不同图像的共性，即类间差异，而纹理特征则代表了同一个体不同图像间的差异，即类内差异。以此为基础，本文提出了一种基于图像校正和位平面融合的广义主成分分析方法。我们在训练阶段构造出主要由样本的结构信息形成的只与类别有关的类标志，并结合纹理信息将样本投影到复数空间，并在此空间中形成虚拟人脸样本，最终通过在该复数空间上的广义主成分分析实现有效的特征提取，从而提高了算法对于光照和表情等的不变性；
3)提出了人脸识别的特征块方法
由于需要将人脸图像表示为向量形式，传统的主成分分析方法会遇到大规模的矩阵和向量相乘等复杂的计算问题，同时，作为一种基于整幅人脸图像的方法，传统的主成分分析方法对于遮挡和表情变化等局部变形非常敏感。为此，我们研究了基于图像分块的主成分分析方法，仿照特征脸方法的概念，提出了人脸识别的特征块方法。通过实验验证，在适当尺寸的图像分块下，算法的速度得到了显著的提高，同时，结合我们提出的与此配合的基于块匹配的分类规则，在一定程度上提高了算法对于遮挡和表情等局部变形的鲁棒性；
4)提出了结合主成分分析与分步线性判别分析的人脸识别方法
通过对线性判别分析方法的深入研究，分析了其存在的两个主要问题，首先是小样本问题，即在训练样本的数目小于图像的像素数目时，类内散布矩阵为奇异矩阵，因此，线性判别分析中的广义本征方程无法求解的问题，其次是由于类间散布矩阵的经典定义中不区分不同类的贡献大小，从而导致通常的线性判别分析准则函数的最优化与识别率的最大化不直接相关的问题。
解决上述两个问题的有效方法之一就是采用基于加权类间散布矩阵的变形的准则函数。但是，研究中发现，系统的识别性能在很大程度上依赖与加权函数的选择，为此，我们借助于近来提出的解决加权Fisher准则函数权函数选择问题的分步线性判别分析方法，结合主成分分析降维方法，提出了结合主成分分析与分步线性判别分析的人脸识别方法，解决了F-LDA方法由于计算复杂性问题不能直接用于人脸识别的问题，在实验中取得了优于现有方法的识别结果；
5)提出了采用环形对称Gabor变换的人脸识别方法
由于其良好的空域和频域局部分析特性，以及与哺乳动物视觉响应特性的一致性，Gabor变换在人脸识别中受到了人们的广泛关注。
我们深入研究了现有的基于Gabor变换特征的人脸识别方法，分析了其中两种主要的特征提取方法，即首先进行亚取样，然后形成增广矩阵的方法和提取关键点或基准点的方法。作为一种有意义的探讨，我们在本文中首次提出了采用环形对称Gabor变换的人脸识别方法。在对环形对称Gabor变换的定义、概念和性质进行全面分析和讨论的基础上，我们对人脸图像在环形对称Gabor变换域中的表现性质进行了比较全面的理论和实验分析与观察，并与传统的Gabor变换进行了对比分析，通过采用环形对称Gabor变换进行简单的眼睛定位等实验，发现环形对称Gabor变换比传统的Gabor变换在变换的旋转不变性和数据的冗余性方面都具有明显的优势。
在此基础上，我们对采用环形对称Gabor变换的人脸识别方法进行了全面深入的研究，提出了按照变换域中的局部极点的大小或高度确定人脸模型图基准点或节点的研究思路，并给出了基于对称Gabor变换的人脸识别系统的概念框图，进一步地，本文提出了基于环形对称Gabor变换的三种具体的人脸识别实现方案，分别是按图像分块局部极值排序的单通道识别算法、按图像分块局部极值排序的多通道特征融合识别算法和按图像分块局部极值排序的多通道分类器融合识别算法，在ORL人脸库上的识别实验中，最高识别率高达98.5％，比采用传统Gabor变换的算法有显著的提高。
This work involves in the research on robust approaches for face recognition. The research is conducted in two phases. One is on such linear feature subspaces as principal component analysis (PCA) and linear discriminant analysis (LDA) based approaches. The other is on approaches based on circular symmetric Gabor transforms (CSGT). The main objective is to increase the robustness of face recognition approaches to the variable factors in the imaging process of face images, which include variation in illumination and shooting angles determined by the imaging condition, variation in expression and poses and the rotation and translation in face images.
The main works we have done include what follows. Studies are conducted to the face recognition approaches based on linear feature subspaces both in theory and in algorithms, including PCA and LDA. On this basis, four new approaches are proposed, which are weighted PCA space based face recognition, generalized PCA combining image correction and bit plane fusion, Eigenblock approach and PCA plus Fractional LDA (F-LDA). Furthermore, through the study on Gabor transform (GT) based approaches, a completely new method using CSGT is presented. Experiments on ORL, AR, Yale and UMIST databases are conducted and it is verified that the new approaches are superior to existing ones.
The main innovations of this work lie in the following new approaches proposed in this thesis.
1) Weighted PCA space based face recognition
In the study of the traditional PCA approach, the different effects of different features, e.g. eigenfaces in the eigenface space are observed and analyzed by theoretical analysis and experimental observation. It is proposed to perform face recognition in a weighted PCA space.
By weighting the traditional PCA space according to the eigenvalue matrix, equal variances are obtained for each feature component. Thus the traditional PCA space is converted to a normalized weighted PCA space and the discriminant performance is improved. Some good characteristics are theoretically proven. It is pointed out that classification by Euclidian distances in the new space is equivalent to that by Mahalanobis distances in the traditional PCA space. Thus, the reason behind the performance improvement of the new approach is given in theory. In addition, when used for reconstruction purpose, the reconstruction error is the same with that of the traditional PCA space if the transform matrix is formed by eigenvectors corresponding to bigger eigenvalues in the weighted PCA space.
In the experiment, distributions of the feature components in the traditional PCA space and in the weighted PCA space respectively are demonstrated and analyzed. It is indicated that, in the traditional PCA space, some features with big values but not significant to classification dictate the computation of the distance metrics. While the role of some other features with small values but indeed significant to classification is submerged. Experiment results also indicate that, even in the weighted PCA space, features should be selected in a descending order of eigenvalues as in the traditional PCA space. The proposed approach is superior to the traditional PCA in recognition accuracy in the experiments.
2) Generalized PCA combining image correction and bit plane fusion
According to the symmetry of human faces, an image correction approach is given to complement the variable illumination existed in the images. Primary correction and complementation is carried out from the image preprocessing phases to the illumination variance existed in the imaging process caused bias light sources. Meanwhile, images are decomposed into bit planes and different characteristics and contributions to image structure and textures of different planes are analyzed. This is further related to the within-class scatter and the between-class scatter. We argue that after histogram equalization, the planes 0, 1, 5, 6 and 7 mainly show structural characteristics, while plane 2, 3 and 4 mainly textural characteristics. Structural characteristics contribute to common properties of all the different images from the same subject, that is, between-class scatter. While textural characteristics emphasize the differences between different image from the same subject, that is, within-class scatter. Based on the analysis, we propose a face recognition approach of combining image correction and bit plane fusion. In the training stage, a class mark mainly composed of structural information from the samples of the same class is established. Together with the texture information, the samples are thus mapped to a complex space to form virtual samples. Finally, effective feature extraction is achieved using generalized PCA in the complex space and in this way, the invariance of the algorithm to variable illumination and expression is increased.
3) Eigenblock approach for face recognition
Computation between big matrices and vectors is inevitable due to the big size of face images in traditional PCA. At the same time, as a whole image based approach, traditional PCA is sensitive to local distortion such as occlusion and expression variance in images. To cope with this problem, we propose to partition the face images into blocks first and then perform PCA on the basis of the position sensitive blocks, which we call eigenblock approach. In the experiment, the algorithm is speeded up and its robustness to occlusion is increased by using the block based matching criterion specifically designed for the new approach.
4) PCA plus F-LDA approach
LDA is carefully studied and two main problems are analyzed. One is the small sample size (SSS) problem, that is, when the number of training samples is less than that of the pixels in the face image, the within-class scatter matrix is singular and thus the generalized eigenequation has no solution in the LDA. The other is that, because in the classical definition of the between-class scatter matrix, the contribution differences of different classes are ignored and this leads to the problem that the criterion function is not directly related to the recognition accuracy in the conventional LDA.
One of the effective approaches to cope with above two problems is to apply an modified criterion function based on weighted between-class scatter matrix. However, it is found in research that, the performance of such face recognition systems is greatly dependant on the choice of the weigh functions. To solve the problem, we combine F-LDA, which was proposed recently to solve the problem of choosing weight functions for the weighted Fisher criterion function with PCA dimension reduction technique to propose a new PCA plus F-LDA approach. In this way, the problem of applying F-LDA to high dimensional face images is solve. Better results than existing approaches are achieved in the experiment.
5) Circularly symmetric Gabor transform based face recognition
Because its good locality both in spatial and frequency domains and good agreement with the mammalian visual characteristics, GT is widely used in face recognition.
Research is conducted on GT based face recognition. Two principal feature selection methods are analyzed. One is to sub-sample the transform domain and then form augmented feature vectors. The other is to extract key points or fiducial points. As a helpful exploration, we propose to use CSGT in face recognition. On the basis of complete analysis and discussion to the definition, concept and properties of CSGT, we examined the characteristics of faces in CSGT domain both in theory and in experiment. By comparing to the traditional GT with the help of experiment in locating eyes in face images, it is found that the former is remarkably superior in rotation invariance and data redundancy.
We carry out a complete study to the problem of applying CSGT to face recognition based on above-mentioned research. Technical route of determine the fiducial points according to local extremes in the transform domain is proposed and a conceptual block diagram of face recognition based on CSGT is presented. Moreover, three algorithms are designed for face recognition, which include single channel recognition algorithm using ordered local extremes in image blocks, multiple channel feature fusion algorithm using ordered local extremes and multiple channel classifier fusion algorithm. In the experiments on ORL database, recognition rate of up to 98.5% is achieved, which is significantly higher than existing GT based approaches.
本文中所做的主要工作包括：
对基于线性特征子空间的人脸识别方法进行了深入的理论和方法研究，其中包括主成分分析方法和线性判别分析方法，在此基础上，分别提出了基于加权主成分分析的方法、基于图像校正和位平面融合的广义主成分分析方法、特征块方法以及结合主成分分析与分步线性判别分析的方法等四种人脸识别的新方法；在对基于Gabor变换特征的人脸识别方法的研究基础上，从理论和实验方面对环形对称Gabor变换进行了详细的研究，分析了其用于人脸识别的可能性，提出了采用环形对称Gabor变换的人脸识别方法。通过在ORL、AR、Yale和UMIST等人脸数据库上的实验，验证了本文所提出的改进方法或新方法相对于现有方法的优越性。
本文的创新之处在于：
1)提出了基于加权主成分分析的人脸识别方法
通过深入研究主成分分析方法，我们从理论和实验出发，观察分析了特征脸空间中不同的特征分量，即特征脸对于人脸图像的重建和分类的作用的不同，提出了在加权的主成分空间中进行人脸识别的改进方法。
通过对传统的主成分空间进行与本征值矩阵有关的加权，使各分量具有相等的方差，从而归一化的加权主成分空间，从而使判别性能得以改善。我们证明了加权主成分空间中的一些有用性质，指出，在加权的主成分分析中，采用欧氏距离测度进行分类，等价于在传统主成分分析空间中采用马氏距离测度进行分类，这就从理论上给出了所提出的方法能够提高识别性能的原因，此外，用于重建目的时，采用较大的本征值所对应的本征向量构成变换矩阵，其重建与传统的主成分分析相同。
通过实验，我们还分析了不同特征分量分别在传统的主成分分析和加权的主成分分析中的分布情况，并指出，在传统的主成分分析中，某些对分类意义不大但取值很大的分量，主导了特征距离的计算，使其它取值较小但对分类重要的分量的作用被淹没。另外，实验结果也说明，即使在加权的主成分分析中，特征的选取也要按照本征值由大到小的顺序进行。在AR和ORL两个数据库上的实验结果说明，本文所提出的方法在识别率方面明显超过传统方法；
2)提出了基于图像校正和位平面融合的广义主成分分析人脸识别方法
根据人脸的左右对称特性，提出了对图像中光照方向的变化进行校正和补偿的方法，从图像预处理的角度对人脸图像在成像过程中存在的光源向左或右偏移引起光照左右强弱变化的问题进行初步校正和补偿。同时，通过对人脸图像的位平面分解，分析了各个位平面不同的特性，及其对于图像结构和纹理的不同贡献，并将其与类间和类内差异相联系。我们指出，经过了直方图均衡处理的图像，其0、1、5、6、7位平面主要表现结构特征，而2、3、4位平面主要表现纹理特征。结构特征代表了同一个体所有不同图像的共性，即类间差异，而纹理特征则代表了同一个体不同图像间的差异，即类内差异。以此为基础，本文提出了一种基于图像校正和位平面融合的广义主成分分析方法。我们在训练阶段构造出主要由样本的结构信息形成的只与类别有关的类标志，并结合纹理信息将样本投影到复数空间，并在此空间中形成虚拟人脸样本，最终通过在该复数空间上的广义主成分分析实现有效的特征提取，从而提高了算法对于光照和表情等的不变性；
3)提出了人脸识别的特征块方法
由于需要将人脸图像表示为向量形式，传统的主成分分析方法会遇到大规模的矩阵和向量相乘等复杂的计算问题，同时，作为一种基于整幅人脸图像的方法，传统的主成分分析方法对于遮挡和表情变化等局部变形非常敏感。为此，我们研究了基于图像分块的主成分分析方法，仿照特征脸方法的概念，提出了人脸识别的特征块方法。通过实验验证，在适当尺寸的图像分块下，算法的速度得到了显著的提高，同时，结合我们提出的与此配合的基于块匹配的分类规则，在一定程度上提高了算法对于遮挡和表情等局部变形的鲁棒性；
4)提出了结合主成分分析与分步线性判别分析的人脸识别方法
通过对线性判别分析方法的深入研究，分析了其存在的两个主要问题，首先是小样本问题，即在训练样本的数目小于图像的像素数目时，类内散布矩阵为奇异矩阵，因此，线性判别分析中的广义本征方程无法求解的问题，其次是由于类间散布矩阵的经典定义中不区分不同类的贡献大小，从而导致通常的线性判别分析准则函数的最优化与识别率的最大化不直接相关的问题。
解决上述两个问题的有效方法之一就是采用基于加权类间散布矩阵的变形的准则函数。但是，研究中发现，系统的识别性能在很大程度上依赖与加权函数的选择，为此，我们借助于近来提出的解决加权Fisher准则函数权函数选择问题的分步线性判别分析方法，结合主成分分析降维方法，提出了结合主成分分析与分步线性判别分析的人脸识别方法，解决了F-LDA方法由于计算复杂性问题不能直接用于人脸识别的问题，在实验中取得了优于现有方法的识别结果；
5)提出了采用环形对称Gabor变换的人脸识别方法
由于其良好的空域和频域局部分析特性，以及与哺乳动物视觉响应特性的一致性，Gabor变换在人脸识别中受到了人们的广泛关注。
我们深入研究了现有的基于Gabor变换特征的人脸识别方法，分析了其中两种主要的特征提取方法，即首先进行亚取样，然后形成增广矩阵的方法和提取关键点或基准点的方法。作为一种有意义的探讨，我们在本文中首次提出了采用环形对称Gabor变换的人脸识别方法。在对环形对称Gabor变换的定义、概念和性质进行全面分析和讨论的基础上，我们对人脸图像在环形对称Gabor变换域中的表现性质进行了比较全面的理论和实验分析与观察，并与传统的Gabor变换进行了对比分析，通过采用环形对称Gabor变换进行简单的眼睛定位等实验，发现环形对称Gabor变换比传统的Gabor变换在变换的旋转不变性和数据的冗余性方面都具有明显的优势。
在此基础上，我们对采用环形对称Gabor变换的人脸识别方法进行了全面深入的研究，提出了按照变换域中的局部极点的大小或高度确定人脸模型图基准点或节点的研究思路，并给出了基于对称Gabor变换的人脸识别系统的概念框图，进一步地，本文提出了基于环形对称Gabor变换的三种具体的人脸识别实现方案，分别是按图像分块局部极值排序的单通道识别算法、按图像分块局部极值排序的多通道特征融合识别算法和按图像分块局部极值排序的多通道分类器融合识别算法，在ORL人脸库上的识别实验中，最高识别率高达98.5％，比采用传统Gabor变换的算法有显著的提高。
This work involves in the research on robust approaches for face recognition. The research is conducted in two phases. One is on such linear feature subspaces as principal component analysis (PCA) and linear discriminant analysis (LDA) based approaches. The other is on approaches based on circular symmetric Gabor transforms (CSGT). The main objective is to increase the robustness of face recognition approaches to the variable factors in the imaging process of face images, which include variation in illumination and shooting angles determined by the imaging condition, variation in expression and poses and the rotation and translation in face images.
The main works we have done include what follows. Studies are conducted to the face recognition approaches based on linear feature subspaces both in theory and in algorithms, including PCA and LDA. On this basis, four new approaches are proposed, which are weighted PCA space based face recognition, generalized PCA combining image correction and bit plane fusion, Eigenblock approach and PCA plus Fractional LDA (F-LDA). Furthermore, through the study on Gabor transform (GT) based approaches, a completely new method using CSGT is presented. Experiments on ORL, AR, Yale and UMIST databases are conducted and it is verified that the new approaches are superior to existing ones.
The main innovations of this work lie in the following new approaches proposed in this thesis.
1) Weighted PCA space based face recognition
In the study of the traditional PCA approach, the different effects of different features, e.g. eigenfaces in the eigenface space are observed and analyzed by theoretical analysis and experimental observation. It is proposed to perform face recognition in a weighted PCA space.
By weighting the traditional PCA space according to the eigenvalue matrix, equal variances are obtained for each feature component. Thus the traditional PCA space is converted to a normalized weighted PCA space and the discriminant performance is improved. Some good characteristics are theoretically proven. It is pointed out that classification by Euclidian distances in the new space is equivalent to that by Mahalanobis distances in the traditional PCA space. Thus, the reason behind the performance improvement of the new approach is given in theory. In addition, when used for reconstruction purpose, the reconstruction error is the same with that of the traditional PCA space if the transform matrix is formed by eigenvectors corresponding to bigger eigenvalues in the weighted PCA space.
In the experiment, distributions of the feature components in the traditional PCA space and in the weighted PCA space respectively are demonstrated and analyzed. It is indicated that, in the traditional PCA space, some features with big values but not significant to classification dictate the computation of the distance metrics. While the role of some other features with small values but indeed significant to classification is submerged. Experiment results also indicate that, even in the weighted PCA space, features should be selected in a descending order of eigenvalues as in the traditional PCA space. The proposed approach is superior to the traditional PCA in recognition accuracy in the experiments.
2) Generalized PCA combining image correction and bit plane fusion
According to the symmetry of human faces, an image correction approach is given to complement the variable illumination existed in the images. Primary correction and complementation is carried out from the image preprocessing phases to the illumination variance existed in the imaging process caused bias light sources. Meanwhile, images are decomposed into bit planes and different characteristics and contributions to image structure and textures of different planes are analyzed. This is further related to the within-class scatter and the between-class scatter. We argue that after histogram equalization, the planes 0, 1, 5, 6 and 7 mainly show structural characteristics, while plane 2, 3 and 4 mainly textural characteristics. Structural characteristics contribute to common properties of all the different images from the same subject, that is, between-class scatter. While textural characteristics emphasize the differences between different image from the same subject, that is, within-class scatter. Based on the analysis, we propose a face recognition approach of combining image correction and bit plane fusion. In the training stage, a class mark mainly composed of structural information from the samples of the same class is established. Together with the texture information, the samples are thus mapped to a complex space to form virtual samples. Finally, effective feature extraction is achieved using generalized PCA in the complex space and in this way, the invariance of the algorithm to variable illumination and expression is increased.
3) Eigenblock approach for face recognition
Computation between big matrices and vectors is inevitable due to the big size of face images in traditional PCA. At the same time, as a whole image based approach, traditional PCA is sensitive to local distortion such as occlusion and expression variance in images. To cope with this problem, we propose to partition the face images into blocks first and then perform PCA on the basis of the position sensitive blocks, which we call eigenblock approach. In the experiment, the algorithm is speeded up and its robustness to occlusion is increased by using the block based matching criterion specifically designed for the new approach.
4) PCA plus F-LDA approach
LDA is carefully studied and two main problems are analyzed. One is the small sample size (SSS) problem, that is, when the number of training samples is less than that of the pixels in the face image, the within-class scatter matrix is singular and thus the generalized eigenequation has no solution in the LDA. The other is that, because in the classical definition of the between-class scatter matrix, the contribution differences of different classes are ignored and this leads to the problem that the criterion function is not directly related to the recognition accuracy in the conventional LDA.
One of the effective approaches to cope with above two problems is to apply an modified criterion function based on weighted between-class scatter matrix. However, it is found in research that, the performance of such face recognition systems is greatly dependant on the choice of the weigh functions. To solve the problem, we combine F-LDA, which was proposed recently to solve the problem of choosing weight functions for the weighted Fisher criterion function with PCA dimension reduction technique to propose a new PCA plus F-LDA approach. In this way, the problem of applying F-LDA to high dimensional face images is solve. Better results than existing approaches are achieved in the experiment.
5) Circularly symmetric Gabor transform based face recognition
Because its good locality both in spatial and frequency domains and good agreement with the mammalian visual characteristics, GT is widely used in face recognition.
Research is conducted on GT based face recognition. Two principal feature selection methods are analyzed. One is to sub-sample the transform domain and then form augmented feature vectors. The other is to extract key points or fiducial points. As a helpful exploration, we propose to use CSGT in face recognition. On the basis of complete analysis and discussion to the definition, concept and properties of CSGT, we examined the characteristics of faces in CSGT domain both in theory and in experiment. By comparing to the traditional GT with the help of experiment in locating eyes in face images, it is found that the former is remarkably superior in rotation invariance and data redundancy.
We carry out a complete study to the problem of applying CSGT to face recognition based on above-mentioned research. Technical route of determine the fiducial points according to local extremes in the transform domain is proposed and a conceptual block diagram of face recognition based on CSGT is presented. Moreover, three algorithms are designed for face recognition, which include single channel recognition algorithm using ordered local extremes in image blocks, multiple channel feature fusion algorithm using ordered local extremes and multiple channel classifier fusion algorithm. In the experiments on ORL database, recognition rate of up to 98.5% is achieved, which is significantly higher than existing GT based approaches.
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