【作者】 刘俊；

【导师】 陈松灿；

【作者基本信息】 南京航空航天大学 ， 计算机应用技术， 2007， 博士

【摘要】 上世纪90年代以来,以主成分分析(Principal Component Analysis, PCA)和线性判别分析(Linear Discriminant Analysis, LDA)为代表的子空间方法有力地促进了人脸识别技术的发展,并成为事实上的基准方法。在子空间人脸识别中,两个主要问题是小样本和面部大变化。本文旨在深入分析和比较一些子空间方法以利于后续研究,并提出一些克服小样本和大变化问题的有效算法。本文的主要贡献在于:(1)对基于主成分分析的方法展开了四个方面研究。第一,深入分析了二维主成分分析(two-Dimensional PCA, 2DPCA),指出2DPCA是具有Kronecker积约束的PCA;第二,重新审视了推广低秩逼近(Generalized Low Rank Approximations of Matrices, GLRAM),主要研究结果包括:(a)给出了GLRAM的一些基本性质,(b)导出了GLRAM准则函数的一个下界,并回答了Ye提出的两个公开问题,(c)探讨了GLRAM在什么时候和为什么能取得较好的压缩(重建)性能。第三,提出了非迭代的GLRAM算法,主要工作在于,构造并优化近似的GLRAM准则以导出非迭代算法,并给出一个确定投影方向数的准则。第四,提出了一个渐进主成分分析算法,主要特点在于,利用图像子模式之间的上下文信息,渐进地读取图像样本以计算PCA的投影向量。(2)对基于线性判别分析的方法展开了四个方面研究。第一,揭示了判别公共向量(Discriminant Common Vectors, DCV)、近邻成分分析(Neighborhood Component Analysis, NCA)、拉普拉斯脸(Laplacianfaces, LAP)和加权最大间隔准则(weighted Maximal Margin Criterion, wMMC)的性质。第二,为正则化判别分析(Regularized Discriminant Analysis, RDA)、wMMC、伪逆法线性判别分析(Pseudo-inverse Linear Discriminant Analysis, PLDA)和核PLDA提出了快速算法。第三,揭示了DCV与NCA、LAP、wMMC和RDA的关系,主要结论是:(a) DCV能取得NCA和LAP准则函数的最优解;(b) DCV是wMMC和RDA的特殊情形;(c)当平均标准差异准则(Mean Standard Variance, MSV)较小时,DCV能取得好的识别性能。第四,运用重采样技术提高了Fisherfaces和基于QR分解的线性判别分析(LDA via QR decomposition, LDA/QR)的识别性能。(3)提出了人脸图像的分数阶奇异值分解表示(Fractional order Singular Value Decomposition Representation, FSVDR)。FSVDR能缓和人脸面部大变化,并可作为人脸图像和子空间方法之间的中间级表示。实验表明,FSVDR能显著提高PCA、DCV和LDA/QR等子空间方法在人脸面部大变化下的识别性能。(4)提出了单图像子空间(Single Image Subspace, SIS)表示方法。在SIS中,把每幅(训练和测试)人脸图像表示成由其虚拟样本所张成的子空间,并通过所定义的能处理不同子空间维数的子空间距离来度量人脸图像的不相似度。此外,为了更好地对付人脸面部大变化,SIS采用了将人脸图像划分为若干子模式的方法。最后,基于单图像子空间表示,定义了几种人脸图像之间的核。更多还原

【Abstract】 Since the 1990s, the face recognition technology has been greatly promoted by subspace methods such as PCA (Principal Component Analysis) and LDA (Linear Discriminant Analysis), which have become the de facto baseline methods. Two major problems with regard to face recognition by subspace methods are Small Sample Size (SSS) and Great Facial Variations (GFV). This paper is focused on two aspects, namely, on one hand, conducting comparative studies among some existing subspace methods to facilitate future studies, and on the other hand, proposing some effective methods to deal with the aforementioned problems. The major contributions in this paper are that:(1) On PCA, the following four researches are conducted. First, an in-depth analysis is given to 2DPCA (two-dimensional PCA), with the main result being that 2DPCA is indeed PCA subjected to the Kronecker product constraint. Second, the GLRAM (Generalized Low Rank Approximations of Matrices) method is revisited, with the main results being that: (a) some basic properties of GLRAM are revealed, (b) a lower bound of the objective function of GLRAM is derived to answer the two open problems raised by Ye, and (c) when and why GLRAM can obtain good compression (reconstruction) performance is explored. Third, the GLRAM method is extended to its non-iterative version, NIGLRAM (Non-Iterative GLRAM). NIGLRAM constructs and optimizes an approximate objective function of GLRAM, and enjoys an automatic criterion in determining the number of projection vectors. Fourth, a PrPCA (Progressive PCA) method is proposed. PrPCA makes use of the contextual information among the image blocks, and reads face images progressively to compute the principal components(2) On LDA, the following four researches are carried out. First, some properties of DCV (Discriminant Common Vectors), NCA (Neighborhood Component Analysis), LAP (Laplacianfaces) and wMMC (weighted Maximal Margin Criterion) are revealed. Second, efficient algorithms are proposed for RDA (Regularized Discriminant Analysis), wMMC, PLDA (Pseudo-inverse LDA) and KPLDA (Kernelized PLDA). Third, DCV’s relationships with NCA, LAP, wMMC and RDA are revealed, with the main results being that: (a) DCV can obtain the optimal result of the objective functions of both NCA and LAP, (b) DCV is a special case of both wMMC and RDA, and (c) when the MSV (Mean Standard Variation) criterion is relatively small, DCV can obtain good classification performance. Fourth, the resampling technique is employed to improve the classification performance of Fisherfaces (or PCA+LDA) and LDA/QR ((LDA via QR decomposition).(3) The FSVDR (Fractional order Singular Value Decomposition Representation) is proposed to alleviate the great facial variations, and to offer an intermediate representation between the original face images and subspace methods. Empirical results show that, FSVD can obviously improve the classification performance of subspace methods such as PCA, DCV and LDA/QR under great facial variations.(4) The SIS (Single Image Subspace) representation is proposed. The core of SIS is to represent each (training, testing) image as a subspace spanned by its synthesized virtual images. To measure the dissimilarity of face images under SIS representation, a new subspace distance that can deal with unequal number of subspace dimensions is developed. To deal with the great facial variations, face images are divided into a set of sub-images, on which SIS is employed. Finally, some new kernels based on SIS are defined.更多还原