人脸识别中特征提取方法的研究
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摘要
特征提取是人脸识别的关键技术,其优劣直接影响到整个人脸识别系统的性能。其中,基于Fisher准则的线性鉴别分析(LDA)是特征提取中最为经典和广泛使用的一种方法,它以模式数据的可分性为目标,寻找最佳鉴别矢量使类内离散度最小的同时,类间离散度达到最大。但作为一种基于统计的代数特征提取技术,传统LDA在小样本情况下会碰到2个实际问题：一是分布矩阵“奇异性”问题；二是分布矩阵估计误差问题。
最近的FRVT2006测试结果表明：在受控和配合的观测条件下,目前最好算法的识别率相比FRVT2002有了一个数量级以上的提高,已超过人类本身的识别能力。但是,在非控制和非配合条件下识别率却将近有一个数量级的下降。这些影响识别性能的非控制因素很多如：光照变化、姿态、表情等等,其中光照变化的影响尤其明显,如何提取对这些因素鲁棒的特征仍是一个极具挑战性的问题。
本文的工作紧紧围绕克服上述3个问题而展开,并提出了有效的解决方案,主要贡献总结如下：
1.综述了各种基于LDA的扩展方法
在小样本情况下,传统LDA由于类内离散矩阵Sw的奇异性而无法计算。近年来提出了许多LDA扩展方法,如克服奇异性问题的方法：Fisherfaces、直接LDA、零空间LDA、正交LDA等,和降低估计误差问题影响的方法：扰动LDA法、双空间LDA、三空间正则法等。本文详细介绍了这些扩展方法,并作了一定的分析。
2.理论分析了各种克服奇异性问题的LDA扩展方法之间的关系和特性
从代数理论层面分析了各种LDA扩展方法之间的关系和特性,并得出结论如下：GSVD-LDA等价于ULDA; DLDA存在理论缺陷,其几乎没利用Sw零空间中的信息,若保留全部的鉴别矢量,DLDA将退化为类间离散矩阵的保留所有非零主成分的PCA,而没利用Sw,在类内数据变化大于类间变化的应用场合(如人脸识别),从分类意义上讲DLDA并非最优选择的方法。
3.研究了降低分布矩阵估计误差影响的方法
一些正则方法从类内离散矩阵Sw的特征谱角度出发认为分布矩阵估计误差引起的扰动对小和零特征值区域影响很大,那么,对其进行正则处理可降低分布矩阵估计误差影响,提高算法的稳定性。基于此思想,所研究算法采用了广义Fisher准则函数,以总体离散矩阵St为主要处理对象,将其非零特征空间进行分割并作加权处理,保留了St的小特征值部分中的鉴别信息,降低了分布矩阵估计误差的影响,达到了提高算法稳定性的目的。在PIE人脸库上的实验比较结果也表明其具有兼顾识别精度和计算代价的优点。
4.提出了基于多尺度梯度角和LDA的鲁棒特征提取新方法
正如在FERET测试和FRVT测试的结果所反映的,光照条件、姿态、表情、噪声等因素对识别性能的影响很大。从频域的角度讲,光照变化一般反映在低频部分,而表情、噪声等因素主要分布在高频部分,本文所提出的多尺度梯度角特征同时具备了小波的局部性、多分辨率特性和梯度角的抑制光照影响优点。在实现上,利用了反对称双正交小波的导数特性,可方便地计算多尺度梯度角。并且与LDA结合,使算法所提取的特征对各种因素的影响更鲁棒、更稳定。在人脸库Yale和YaleB上的对比实验结果表明：该方法不但可以有效抑制光照、表情、噪声等因素的影响,而且识别精度也比其它光照不变特征方法有了较大提高。
Feature extraction is a key technique for the face recognition, which directly impact on the performance of the entire system. Among them, linear discriminant analysis (LDA) based on Fisher criteria is the most classic and widely used method, which takes the separability of the patterns as its goal, and seeks an optimal linear transformation by maximizing the ratio of the between-class and within-class scatter matrices. However, as an algebra feature extraction based on statistical techniques, the traditional LDA in the case of small sample size will encounter two practical problems:one arises from the "singularity" of the distribution matrix; the other is due to the estimation error of the distribution matrix.
The recent FRVT2006 test results showed that:face recognition performance on still frontal images taken under controlled and cooperative conditions has improved by an order of magnitude since the FRVT 2002, and were more accurate than humans. However, under non-controlled and non-cooperative conditions there is almost an order of magnitude of the decline. There are a lot of non-controlled factors such as change in the illumination, post variation, expression variation, and so on, in which the effects of illumination variation is particularly serious. So, how to extract the robust features against these factors is still a challenging problem.
In this thesis, we closely focused on our work to overcome the above-mentioned 3 problems, and to present an effective solution. And the main contributions are summarized as follows:
1. Provided an overview of the LDA-based extensions
In the case of small sample size, the traditional LDA fails due to the singularity of the within-class scatter matrix Sw. Recently, many LDA-based methods have been proposed:the ones overcoming the singularity problem such as Fisherfaces, direct LDA, null space LDA, orthogonal LDA, and etc, and the others reducing the impact of the estimation error of the distribution matrix such as Perturbation LDA, dual-space LDA, three space regularization method, and etc. This thesis described these extensions in detail and presented a certain analysis.
2. Theoretical analysis of the characteristics and the relationship among LDA-based extensions dealing with the singularity problem
We carried on the theoretical analysis of the characteristics and the relationship among LDA-based extensions and concluded as follows:GSVD-LDA is equivalent to ULDA; In undersampled cases DLDA nearly can make no use of the null space of Sw and may result in the loss of important discriminative information; DLDA is degenerated as PCA of the between-class scatter with all nonzero principal components if it keeps the complete projection vectors. As a result, DLDA is not an optimal choice for dimensionality reduction from the classification sense.
3. Studied on the method reduced the impact of the estimation error of the distribution matrix
From the matrix Sw's eigenspectrum analytic point of view, Some regularization methods thought that the perturbation caused by the estimation error of the distribution matrix has a large impact on the corresponding eigenspace of the small and zero eigenvalues, then the regularized process for these subspace can reduce the effect of the estimation error, and improves the stability of algorithm. Based on this idea, we adopted the generalized Fisher criteria, and used the total scatter matrix St as an operational object. Then the corresponding eigenspace of non-zero eigenvalues of St is partitioned and used different weighting factor. So the discriminant information inside the eigenspace of the small eigenvalues of St is reserved, and the algorithm stability is improved. The comparison results on PIE face database also showed that our algorithm can take into account the recognition accuracy and computational cost.
4. Proposed an approach based on the multi-scale gradient angle and LDA for
robust feature extraction
As showed in the results of FERET and FRVT, the recognition performance will suffer from the effect of some factors such as illumination variation, expression variation, pose variation and noise. From the frequency domain point of view, the illumination variation generally reflected in the low-frequency part, and expression variation and noise are mainly distributed in the high-frequency part. The multi-scale gradient angular feature proposed in this thesis possessed two advantages:the localization and multi-resolution of wavelet transform and the illumination invariant of the gradient angle. Using the derivative characteristics of anti-symmetric biorthogonal wavelet, the multi-scale gradient angle can be calculated easily. Combined with the LDA, our algorithm based on the multi-scale gradient angle was more robust and stable. The experimental comparison results on Yale and YaleB showed that:our algorithm can decrease effectively the effect of illumination variation, expression variation and noise, and outperformed the other methods based on illumination invariant feature in the recognition accuracy.
最近的FRVT2006测试结果表明：在受控和配合的观测条件下,目前最好算法的识别率相比FRVT2002有了一个数量级以上的提高,已超过人类本身的识别能力。但是,在非控制和非配合条件下识别率却将近有一个数量级的下降。这些影响识别性能的非控制因素很多如：光照变化、姿态、表情等等,其中光照变化的影响尤其明显,如何提取对这些因素鲁棒的特征仍是一个极具挑战性的问题。
本文的工作紧紧围绕克服上述3个问题而展开,并提出了有效的解决方案,主要贡献总结如下：
1.综述了各种基于LDA的扩展方法
在小样本情况下,传统LDA由于类内离散矩阵Sw的奇异性而无法计算。近年来提出了许多LDA扩展方法,如克服奇异性问题的方法：Fisherfaces、直接LDA、零空间LDA、正交LDA等,和降低估计误差问题影响的方法：扰动LDA法、双空间LDA、三空间正则法等。本文详细介绍了这些扩展方法,并作了一定的分析。
2.理论分析了各种克服奇异性问题的LDA扩展方法之间的关系和特性
从代数理论层面分析了各种LDA扩展方法之间的关系和特性,并得出结论如下：GSVD-LDA等价于ULDA; DLDA存在理论缺陷,其几乎没利用Sw零空间中的信息,若保留全部的鉴别矢量,DLDA将退化为类间离散矩阵的保留所有非零主成分的PCA,而没利用Sw,在类内数据变化大于类间变化的应用场合(如人脸识别),从分类意义上讲DLDA并非最优选择的方法。
3.研究了降低分布矩阵估计误差影响的方法
一些正则方法从类内离散矩阵Sw的特征谱角度出发认为分布矩阵估计误差引起的扰动对小和零特征值区域影响很大,那么,对其进行正则处理可降低分布矩阵估计误差影响,提高算法的稳定性。基于此思想,所研究算法采用了广义Fisher准则函数,以总体离散矩阵St为主要处理对象,将其非零特征空间进行分割并作加权处理,保留了St的小特征值部分中的鉴别信息,降低了分布矩阵估计误差的影响,达到了提高算法稳定性的目的。在PIE人脸库上的实验比较结果也表明其具有兼顾识别精度和计算代价的优点。
4.提出了基于多尺度梯度角和LDA的鲁棒特征提取新方法
正如在FERET测试和FRVT测试的结果所反映的,光照条件、姿态、表情、噪声等因素对识别性能的影响很大。从频域的角度讲,光照变化一般反映在低频部分,而表情、噪声等因素主要分布在高频部分,本文所提出的多尺度梯度角特征同时具备了小波的局部性、多分辨率特性和梯度角的抑制光照影响优点。在实现上,利用了反对称双正交小波的导数特性,可方便地计算多尺度梯度角。并且与LDA结合,使算法所提取的特征对各种因素的影响更鲁棒、更稳定。在人脸库Yale和YaleB上的对比实验结果表明：该方法不但可以有效抑制光照、表情、噪声等因素的影响,而且识别精度也比其它光照不变特征方法有了较大提高。
Feature extraction is a key technique for the face recognition, which directly impact on the performance of the entire system. Among them, linear discriminant analysis (LDA) based on Fisher criteria is the most classic and widely used method, which takes the separability of the patterns as its goal, and seeks an optimal linear transformation by maximizing the ratio of the between-class and within-class scatter matrices. However, as an algebra feature extraction based on statistical techniques, the traditional LDA in the case of small sample size will encounter two practical problems:one arises from the "singularity" of the distribution matrix; the other is due to the estimation error of the distribution matrix.
The recent FRVT2006 test results showed that:face recognition performance on still frontal images taken under controlled and cooperative conditions has improved by an order of magnitude since the FRVT 2002, and were more accurate than humans. However, under non-controlled and non-cooperative conditions there is almost an order of magnitude of the decline. There are a lot of non-controlled factors such as change in the illumination, post variation, expression variation, and so on, in which the effects of illumination variation is particularly serious. So, how to extract the robust features against these factors is still a challenging problem.
In this thesis, we closely focused on our work to overcome the above-mentioned 3 problems, and to present an effective solution. And the main contributions are summarized as follows:
1. Provided an overview of the LDA-based extensions
In the case of small sample size, the traditional LDA fails due to the singularity of the within-class scatter matrix Sw. Recently, many LDA-based methods have been proposed:the ones overcoming the singularity problem such as Fisherfaces, direct LDA, null space LDA, orthogonal LDA, and etc, and the others reducing the impact of the estimation error of the distribution matrix such as Perturbation LDA, dual-space LDA, three space regularization method, and etc. This thesis described these extensions in detail and presented a certain analysis.
2. Theoretical analysis of the characteristics and the relationship among LDA-based extensions dealing with the singularity problem
We carried on the theoretical analysis of the characteristics and the relationship among LDA-based extensions and concluded as follows:GSVD-LDA is equivalent to ULDA; In undersampled cases DLDA nearly can make no use of the null space of Sw and may result in the loss of important discriminative information; DLDA is degenerated as PCA of the between-class scatter with all nonzero principal components if it keeps the complete projection vectors. As a result, DLDA is not an optimal choice for dimensionality reduction from the classification sense.
3. Studied on the method reduced the impact of the estimation error of the distribution matrix
From the matrix Sw's eigenspectrum analytic point of view, Some regularization methods thought that the perturbation caused by the estimation error of the distribution matrix has a large impact on the corresponding eigenspace of the small and zero eigenvalues, then the regularized process for these subspace can reduce the effect of the estimation error, and improves the stability of algorithm. Based on this idea, we adopted the generalized Fisher criteria, and used the total scatter matrix St as an operational object. Then the corresponding eigenspace of non-zero eigenvalues of St is partitioned and used different weighting factor. So the discriminant information inside the eigenspace of the small eigenvalues of St is reserved, and the algorithm stability is improved. The comparison results on PIE face database also showed that our algorithm can take into account the recognition accuracy and computational cost.
4. Proposed an approach based on the multi-scale gradient angle and LDA for
robust feature extraction
As showed in the results of FERET and FRVT, the recognition performance will suffer from the effect of some factors such as illumination variation, expression variation, pose variation and noise. From the frequency domain point of view, the illumination variation generally reflected in the low-frequency part, and expression variation and noise are mainly distributed in the high-frequency part. The multi-scale gradient angular feature proposed in this thesis possessed two advantages:the localization and multi-resolution of wavelet transform and the illumination invariant of the gradient angle. Using the derivative characteristics of anti-symmetric biorthogonal wavelet, the multi-scale gradient angle can be calculated easily. Combined with the LDA, our algorithm based on the multi-scale gradient angle was more robust and stable. The experimental comparison results on Yale and YaleB showed that:our algorithm can decrease effectively the effect of illumination variation, expression variation and noise, and outperformed the other methods based on illumination invariant feature in the recognition accuracy.
引文
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