面向人脸识别的子空间分析和分类方法研究
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摘要
人脸识别作为生物特征识别中最自然最直接的手段,受到越来越多的研究和产业关注。如何有效的从人脸图像中提取鉴别特征是人脸识别需要解决的关键问题。在众多特征提取技术中,子空间分析方法因其实施性好、有效性高等特点,成为人脸图像特征提取和识别的主流方法之一。本文针对子空间方法在人脸识别应用中的高维计算代价问题、约束问题、单样本问题和分类机制设计问题等,进行了若干具体子空间方法分支的理论和应用研究,主要完成以下工作:
①提出了主成分分析变换空间上的鉴别共同向量算法(PCA+DCV)。该方法通过在主成分分析变换空间上实施两次Gram-Schmidt正交化过程进行最优求解。在保留原算法数值稳定性高的优点的同时,利用主成分分析变换空间的低维特性降低了算法复杂度,提高了求解速度,更适合高维人脸样本分析计算应用。
②基于本文PCA+DCV算法中的主成分分析过程,进一步提出了依据主成分对应特征值进行权重处理的鉴别共同向量识别算法(WPCA+DCV)。该算法把对样本主成分的权重预处理工作融合在最优投影矩阵的求解工作中,弱化了受光照等条件影响严重的主成分的判决作用。实验结果证明该方法提升了基于鉴别共同向量实现的人脸辨识的效果。
③提出了一种在非负矩阵分解框架下传统子空间方法的统一形式和收敛算法。在该统一形式下,进行了主成分分析、Fisher线性判别和局部邻域保持投影方法思想的非负约束实现,完成了“非减性、加合性”的基学习,跳出了一般子空间基线性组合时常见的正负抵消的产生模式的局限。该方法可为多种子空间学习算法提供更好的视觉和心理解释性,反映人类思维中“局部构成整体”的概念。
④面向单样本人脸识别任务,提出了基于光流检测权重的模块二维主成分分析方法。针对一般子空间方法面对单样本情况性能退化明显的问题,本文利用模块二维主成分分析的特性,在实现保留样本局部信息、更稳定估计数据协方差矩阵的基础上,提出了利用光流度量人脸图像之间的直观区域差别,并通过权重方法将其作为先验知识定量地引入子空间鉴别过程的思想方法。实验结果验证了该方法在解决单样本问题时,相对于一般子空间方法在识别正确率及稳定性方面具有显著提升。
⑤建立了一个基于单个二次规划问题进行各类样本整体优化的多类支持向量分类器算法。该算法具有优化问题规模不随目标分类类别数增长的特性,解决了现有基于整体优化的多类分类支持向量机在大规模样本学习中的算法复杂度限制问题。相比最近邻分类方法,该方法可为样本特征在子空间中提供更好的分类超平面决策,丰富了子空间方法在人脸识别应用中的分类决策设计手段。
Face recognition,as the most natural and explicit approach of biological feature recognition,has attracted more academic and industrial concentration in recent decades.A central issue to a successful approach for face recognition is how to extract discriminative feature from the facial images.Many feature extraction methods have been proposed and among them the subspace analysis has received extensive attention owing to its appealing properties of efficiency.This dissertation focuses on the subspace analysis and classification methods in case of face recognition.The main contributions of the dissertation can be noted as following:
①An algorithm named Discriminative Common Vectors in the PCA transformed space(PCA+DCV) was proposed.Based on the analysis that the optimal projections of DCV can be searched within the more compact subspace,PCA+DCV performs two Gram-Schmidt orthogonalization procedures in the PCA transformed space to obtain the same optimal projection matrix as original DCV algorithm.PCA+DCV is a fast algorithm calculating the discriminative common vectors,which makes the DCV method more feasible to the high dimensional pattern classification such as face recognition.
②Furthermore,with the facility offered by PCA analysis procedure in PCA+DCV,we gave a Weighted PCA+DCV algorithm.The algorithm subtly weights the facial components in PCA space while calculating optimal projection matrix,which is potential to enrich the representative information and thus improves DCV's recognition performance.
③The dissertation established an unified framework and corresponding converging iterative update algorithm for Nonnegative Matrix Factorization subspace analysis.Under this framework,the basic principle of major subspace analysis such as PCA,Fisher LDA,Local Preserving Projection can be applied subjecting to non-negativity constraints in learning basis.This ensures that the components are combined to form a whole in the non-subtractive way.For this reason,the NMF unified framework yields a series of subspace analysis learning a parts-based representation,which maybe better consistent with the human being intuitive meaning of adding parts to form a whole.
④Aiming to face recognition one sample problem,the dissertation proposed the weighted modular 2DPCA(two-dimensional principal component analysis) method.Due to the fact that the PCA's performance can be considered as an upper limit for most of 1D image vector based subspace methods in one sample problem,the new method firstly performs 2DPCA feature extraction for sub-image-blocks.In this way,the scatter matrix of data can be estimated more stably than PCA,as well as local information was retained.Then optical flow method was used to quantitatively estimate the difference of blocks between face images,which is introduced as prior knowledge for enforcing a local-depended classification.The experiment results indicate that,in one sample problem,the weighted modular 2DPCA method is superior to conventional 1D-data-based subspace analysis method in terms of recognition accuracy and robustness.
⑤The dissertation developed a novel multi-class support vector classifier (SVC) called MLMC,which considers all classes data in one QP optimization formulation without increasing the size of the problem proportional to the number of classes.MLMC overcomes the computational efficiency limitation for multi-class SVCs of one QP problem in case of large scale samples learning.Compared with the nearest neighbor classifier(NNC) which is widely adopted by subspace method for classification after feature extraction, MLMC could give better decision hyperplanes in the feature space,thus offers a new alternative decision mechanism for the large scale face recognition application.
①提出了主成分分析变换空间上的鉴别共同向量算法(PCA+DCV)。该方法通过在主成分分析变换空间上实施两次Gram-Schmidt正交化过程进行最优求解。在保留原算法数值稳定性高的优点的同时,利用主成分分析变换空间的低维特性降低了算法复杂度,提高了求解速度,更适合高维人脸样本分析计算应用。
②基于本文PCA+DCV算法中的主成分分析过程,进一步提出了依据主成分对应特征值进行权重处理的鉴别共同向量识别算法(WPCA+DCV)。该算法把对样本主成分的权重预处理工作融合在最优投影矩阵的求解工作中,弱化了受光照等条件影响严重的主成分的判决作用。实验结果证明该方法提升了基于鉴别共同向量实现的人脸辨识的效果。
③提出了一种在非负矩阵分解框架下传统子空间方法的统一形式和收敛算法。在该统一形式下,进行了主成分分析、Fisher线性判别和局部邻域保持投影方法思想的非负约束实现,完成了“非减性、加合性”的基学习,跳出了一般子空间基线性组合时常见的正负抵消的产生模式的局限。该方法可为多种子空间学习算法提供更好的视觉和心理解释性,反映人类思维中“局部构成整体”的概念。
④面向单样本人脸识别任务,提出了基于光流检测权重的模块二维主成分分析方法。针对一般子空间方法面对单样本情况性能退化明显的问题,本文利用模块二维主成分分析的特性,在实现保留样本局部信息、更稳定估计数据协方差矩阵的基础上,提出了利用光流度量人脸图像之间的直观区域差别,并通过权重方法将其作为先验知识定量地引入子空间鉴别过程的思想方法。实验结果验证了该方法在解决单样本问题时,相对于一般子空间方法在识别正确率及稳定性方面具有显著提升。
⑤建立了一个基于单个二次规划问题进行各类样本整体优化的多类支持向量分类器算法。该算法具有优化问题规模不随目标分类类别数增长的特性,解决了现有基于整体优化的多类分类支持向量机在大规模样本学习中的算法复杂度限制问题。相比最近邻分类方法,该方法可为样本特征在子空间中提供更好的分类超平面决策,丰富了子空间方法在人脸识别应用中的分类决策设计手段。
Face recognition,as the most natural and explicit approach of biological feature recognition,has attracted more academic and industrial concentration in recent decades.A central issue to a successful approach for face recognition is how to extract discriminative feature from the facial images.Many feature extraction methods have been proposed and among them the subspace analysis has received extensive attention owing to its appealing properties of efficiency.This dissertation focuses on the subspace analysis and classification methods in case of face recognition.The main contributions of the dissertation can be noted as following:
①An algorithm named Discriminative Common Vectors in the PCA transformed space(PCA+DCV) was proposed.Based on the analysis that the optimal projections of DCV can be searched within the more compact subspace,PCA+DCV performs two Gram-Schmidt orthogonalization procedures in the PCA transformed space to obtain the same optimal projection matrix as original DCV algorithm.PCA+DCV is a fast algorithm calculating the discriminative common vectors,which makes the DCV method more feasible to the high dimensional pattern classification such as face recognition.
②Furthermore,with the facility offered by PCA analysis procedure in PCA+DCV,we gave a Weighted PCA+DCV algorithm.The algorithm subtly weights the facial components in PCA space while calculating optimal projection matrix,which is potential to enrich the representative information and thus improves DCV's recognition performance.
③The dissertation established an unified framework and corresponding converging iterative update algorithm for Nonnegative Matrix Factorization subspace analysis.Under this framework,the basic principle of major subspace analysis such as PCA,Fisher LDA,Local Preserving Projection can be applied subjecting to non-negativity constraints in learning basis.This ensures that the components are combined to form a whole in the non-subtractive way.For this reason,the NMF unified framework yields a series of subspace analysis learning a parts-based representation,which maybe better consistent with the human being intuitive meaning of adding parts to form a whole.
④Aiming to face recognition one sample problem,the dissertation proposed the weighted modular 2DPCA(two-dimensional principal component analysis) method.Due to the fact that the PCA's performance can be considered as an upper limit for most of 1D image vector based subspace methods in one sample problem,the new method firstly performs 2DPCA feature extraction for sub-image-blocks.In this way,the scatter matrix of data can be estimated more stably than PCA,as well as local information was retained.Then optical flow method was used to quantitatively estimate the difference of blocks between face images,which is introduced as prior knowledge for enforcing a local-depended classification.The experiment results indicate that,in one sample problem,the weighted modular 2DPCA method is superior to conventional 1D-data-based subspace analysis method in terms of recognition accuracy and robustness.
⑤The dissertation developed a novel multi-class support vector classifier (SVC) called MLMC,which considers all classes data in one QP optimization formulation without increasing the size of the problem proportional to the number of classes.MLMC overcomes the computational efficiency limitation for multi-class SVCs of one QP problem in case of large scale samples learning.Compared with the nearest neighbor classifier(NNC) which is widely adopted by subspace method for classification after feature extraction, MLMC could give better decision hyperplanes in the feature space,thus offers a new alternative decision mechanism for the large scale face recognition application.
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