二维主元分析在人脸识别中的应用研究

结合二维主元分析（two-dimensional principal component analysis,2DPCA）的特点,将2DPCA算法用于人脸识别。它与主元分析（principal component analysis,PCA）的不同之处在于,2DPCA算法以图像矩阵为分析对象;而PCA算法以图像的一维向量为分析对象。2DPCA算法是直接利用原始图像矩阵构造图像的协方差矩阵。而PCA算法需对原始图像矩阵先降维、再将降维矩阵转换成列向量,然后构造图像的协方差矩阵。为了测试和评估2DPCA算法的性能,在ORL（olivetti research laboratory）与Yale人脸数据库上进行了实验,结果表明,2DPCA算法用于人脸识别的正确识别率高于PCA算法。同时,也显示了2DPCA算法在特征提取方面比PCA算法更有效。     

Two-dimensional PCA: a new approach to appearance-based face representation and recognition

In this paper, a new technique coined two-dimensional principal component analysis (2DPCA) is developed for image representation. As opposed to PCA, 2DPCA is based on 2D image matrices rather than 1D vectors so the image matrix does not need to be transformed into a vector prior to feature extraction. Instead, an image covariance matrix is constructed directly using the original image matrices, and its eigenvectors are derived for image feature extraction. To test 2DPCA and evaluate its performance, a series of experiments were performed on three face image databases: ORL, AR, and Yale face databases. The recognition rate across all trials was higher using 2DPCA than PCA. The experimental results also indicated that the extraction of image features is computationally more efficient using 2DPCA than PCA.     

BDPCA plus LDA: a novel fast feature extraction technique for face recognition.

Appearance-based methods, especially linear discriminant analysis (LDA), have been very successful in facial feature extraction, but the recognition performance of LDA is often degraded by the so-called "small sample size" (SSS) problem. One popular solution to the SSS problem is principal component analysis (PCA) + LDA (Fisherfaces), but the LDA in other low-dimensional subspaces may be more effective. In this correspondence, we proposed a novel fast feature extraction technique, bidirectional PCA (BDPCA) plus LDA (BDPCA + LDA), which performs an LDA in the BDPCA subspace. Two face databases, the ORL and the Facial Recognition Technology (FERET) databases, are used to evaluate BDPCA + LDA. Experimental results show that BDPCA + LDA needs less computational and memory requirements and has a higher recognition accuracy than PCA + LDA.     

关于二维主成分分析方法的研究

The principal component analysis (PCA), or the eigenfaces method, is a de facto standard in human face recognition. Numerous algorithms tried to generalize PCA in different aspects. More recently, a technique called two-dimensional PCA (2DPCA) was proposed to cut the computational cost of the standard PCA. Unlike PCA that treats images as vectors, 2DPCA views an image as a matrix. With a properly defined criterion, 2DPCA results in an eigenvalue problem which has a much lower dimensionality than that of PCA. In this paper, we show that 2DPCA is equivalent to a special case of an existing feature extraction method, i.e., the block-based PCA. Using the FERET database, extensive experimental results demonstrate that block-based PCA outperforms PCA on datasets that consist of relatively simple images for recognition, while PCA is more robust than 2DPCA in harder situations.     

模块二维主成分分析——人脸识别新方法

提出了模块二维主成分分析(M2DPCA)线性鉴别分析方法。M2DPCA方法先对图像矩阵进行分块，对分块得到的子图像矩阵直接进行鉴别分析。其特点是：能有效地降低模式原始特征的维数；可以完全避免使用矩阵的奇异值分解，特征抽取方便；此外，2DPCA是M2DPCA的特例。在ORL人脸库上试验结果表明，M2DPCA方法在识别性能上优于PCA，比2DPCA更具有鲁棒性。     

基于模块2DPCA的人脸识别方法

提出了模块2DPCA（two-dimensional principal component analysis）的人脸识别方法。模块2DPCA方法先对图像矩阵进行分块，将分块得到的子图像矩阵直接用于构造总体散布矩阵，然后利用总体散布矩阵的特征向量进行图像特征抽取。与基于图像向量的鉴别方法（比如PCA）相比，该方法在特征抽取之前不需要将子图像矩阵转化为图像向量，能快速地降低鉴别特征的维数，可以完全避免使用矩阵的奇异值分解，特征抽取方便；此外，模块2DPCA是2DPCA的推广。在ORL和NUST603人脸库上的试验结果表明，模块2DPCA方法在识别性能上优于PCA，比2DPCA更具有鲁棒性。     

An adaptive neural networks formulation for the two-dimensional principal component analysis

This study, for the first time, developed an adaptive neural networks (NNs) formulation for the two-dimensional principal component analysis (2DPCA), whose space complexity is far lower than that of its statistical version. Unlike the NNs formulation of principal component analysis (PCA, i.e., 1DPCA), the solution with lower iteration in nature aims to directly deal with original image matrices. We also put forward the consistence in the conceptions of ‘eigenfaces’ or ‘eigengaits’ in both 1DPCA and 2DPCA neural networks. To evaluate the performance of the proposed NN, the experiments were carried out on AR face database and on 64 × 64 pixels gait energy images on CASIA(B) gait database. The less reconstruction error was exploited using the proposed NN in the condition of a large sample set compared to adaptive estimation of learning algorithms for NNs of PCA. On the contrary, if the sample set was small, the proposed NN could achieve a higher residue error than PCA NNs. The amount of calculation for the proposed NN here could be smaller than that for the PCA NNs on the feature extraction of the same image matrix, which represented an efficient solution to the problem of training images directly. On face and gait recognition tasks, a simple nearest neighbor classifier test indicated a particular benefit of the neural network developed here which serves as an efficient alternative to conventional PCA NNs.     

An efficient algorithm for Kernel two-dimensional principal component analysis

Recently, a new approach called two-dimensional principal component analysis (2DPCA) has been proposed for face representation and recognition. The essence of 2DPCA is that it computes the eigenvectors of the so-called image covariance matrix without matrix-to-vector conversion. Kernel principal component analysis (KPCA) is a non-linear generation of the popular principal component analysis via the Kernel trick. Similarly, the Kernelization of 2DPCA can be benefit to develop the non-linear structures in the input data. However, the standard K2DPCA always suffers from the computational problem for using the image matrix directly. In this paper, we propose an efficient algorithm to speed up the training procedure of K2DPCA. The results of experiments on face recognition show that the proposed algorithm can achieve much more computational efficiency and remarkably save the memory-consuming compared to the standard K2DPCA.     

基于二维主分量分析的面部表情识别

提出了一种直接基于图像矩阵的二维主分量分析(2DPCA)和多分类器联合的面部表情识别方法。首先利用2DPCA进行特征提取,然后用基于模糊积分的多分类器联合的方法对七种表情(生气、厌恶、恐惧、高兴、中性、悲伤、惊讶)进行识别。在JAFFE人脸表情静态图像库上进行实验,与传统主分量分析(PCA)相比,采用2DPCA进行特征提取,不仅识别率比较高,而且运算速度也有很大的提高。     

融合WMD矩阵与2DPCA的人脸特征抽取与识别

提出了一种融合小波矩描述子(WMD)矩阵与二维主成分分析(2DPCA)的人脸特征抽取与识别算法。该方法抽取描述人脸本质特征的WMD矩阵,利用2DPCA对该矩阵进行投影压缩降维,抽取人脸最终鉴别特征,利用最近邻分类器对特征进行分类识别。NUST603人脸库上的实验结果验证了算法的有效性。     

基于改进灰狼算法优化支持向量机的人脸识别

针对二维主成分分析法(2DPCA)与主成分分析法(PCA)相结合提取人脸特征时效率不高的问题,提出一种2DPCA和快速PCA结合与改进灰狼算法(EGWO)共同优化支持向量机的人脸识别方法。该方法在特征提取方面运用2DPCA与快速PCA相结合,以减少提取特征的维数和提取时间,从而缩短了SVM所需的识别时间。为了提高灰狼算法的全局搜索能力,引用精英反向学习策略初始化种群个体,有效增强GWO的勘探和开采能力,再将其使用到SVM中,迭代获取最佳核参数和惩戒参数,将训练得到的最终分类器应用于人脸识别中。通过6个基准测试函数与GWO和反向学习灰狼算法(OGWO)进行性能比较,改进灰狼算法的收敛精度和收敛速度更优;经ORL和Yale中的人脸图像实验,证明了改进算法相对于GWO、粒子群算法(PSO)和差分进化算法(DE)结合SVM模型的识别结果更佳且稳定性更强。     

概率二维主分量分析

二维主分量分析是一种直接面向图像矩阵表达方式的特征抽取与降维方法. 提出了一个基于二维主分量分析的概率模型. 首先, 通过对此产生式概率模型参数的最大似然估计得到主分量(矢量); 然后, 考虑到缺失数据问题, 利用期望最大化算法迭代估计模型参数和主分量. 混合概率二维主分量分析模型在人脸聚类问题上的应用表明概率二维主分量分析模型能作为图像矩阵的密度估计工具. 含有缺失值的人脸图像重构实验阐述了此模型及迭代算法的有效性.     

Horizontal and Vertical 2DPCA-Based Discriminant Analysis for Face Verification on a Large-Scale Database

This paper first discusses some theoretical properties of 2D principal component analysis (2DPCA) and then presents a horizontal and vertical 2DPCA-based discriminant analysis (HVDA) method for face verification. The HVDA method, which applies 2DPCA horizontally and vertically on the image matrices (2D arrays), achieves lower computational complexity than the traditional PCA and Fisher linear discriminant analysis (LDA)-based methods that operate on high dimensional image vectors (1D arrays). The horizontal 2DPCA is invariant to vertical image translations and vertical mirror imaging, and the vertical 2DPCA is invariant to horizontal image translations and horizontal mirror imaging. The HVDA method is therefore less sensitive to imprecise eye detection and face cropping, and can improve upon the traditional discriminant analysis methods for face verification. Experiments using the face recognition grand challenge (FRGC) and the biometric experimentation environment system show the effectiveness of the proposed method. In particular, for the most challenging FRGC version 2 Experiment 4, which contains 12thinspace776 training images, 16 028 controlled target images, and 8014 uncontrolled query images, the HVDA method using a color configuration across two color spaces, namely, the YIQ and the YCbCr color spaces, achieves the face verification rate (ROC III) of 78.24% at the false accept rate of 0.1%.     

基于DCT融合2DPCA与DLDA的人脸识别

传统的基于主成分分析的人脸识别需要将图像矩阵转化为向量,特征提取需要花费大最时间.二维主成分分析直接利用图像矩阵,特征提取速度快,但特征数量大,影响分类速度.因此,提出了一种基于离散余弦变换(DCT)的二维主成分分析(2DPCA)和直接线性判决分析(DLDA)结合的人脸识别方法.算法首先用DCT对人脸图像进行压缩并重建,然后利用2DPCA和DLDA对人脸图像进行特征提取.最后选用最近邻分类器进行分类.在ORL人脸库上的测试结果表明,与DLDA或2DPCA算法相比,算法具有更高的识别率.     

二阶分块PCA的人脸特征提取方法研究

为了提取更为有效的鉴别特征,在已有的二阶特征脸方法和分块主成分分析(PCA)方法上,提出了二阶分块PCA人脸特征提取方法.该方法对原始人脸图像和经重建得到的剩余图像分别运用分块PCA,将提取的一阶和二阶特征线性组合为一个特征矩阵,再进行分类识别.此特征能更充分反映人脸图像的低频和高频特性.采用ORL人脸库和FERET人脸库的实验结果表明该二阶分块PCA正确识别率优于普通分块PCA算法,具有较强的特征提取能力.     

二维投影与PCA相结合的人脸识别算法

传统的特征抽取算法是基于向量的,在模式是图像时并不方便。二维投影方法利用图像矩阵直接计算,虽然抽取特征速度快,但抽取出的特征是矩阵,对应的特征数量大,影响分类速度。该文结合二者的优点,先用二维投影处理原始图像,降维后再做主分量分析,抽取出少量的特征进行分类,识别率和分类速度均有提高。在ORL人脸库上20次实验的平均识别率达95.83%。     

改进的基于Gabor-LDA的人脸识别方法

鉴于Gabor特征对光照、表情等变化比较鲁棒,并已在人脸识别领域取得成功应用,提出了一种改进的Gabor-LDA算法.首先对人脸图像进行多方向、多尺度Gabor小渡滤波,然后对得到的特征向量使用改进的主成分分析方法(PCA)变换降维,采用自适应加权原理重建类内散布矩阵和类间散布矩阵,从而改进了最佳鉴别分析(LDA)判别函数,有效地解决了训练样本类均值与类中心的偏离问题.对Yale人脸库的数值试验表明,该算法比传统算法有更好的性能.     

基于多级纹理频谱特征与PCA的人脸识别算法

针对主成分分析(PCA)算法在人脸识别中识别率低的问题,提出一种图像纹理频谱特征与PCA相结合的人脸识别算法。该算法利用纹理单元算子提取人脸图像纹理频谱特征,然后用PCA对所提取的特征降维,最后利用最近邻(KNN)分类器进行人脸识别。在ORL人脸库和Yale人脸库上对所提出的算法进行了测试,识别率均高于PCA、模块化二维PCA(M2DPCA)等方法,分别为96.5%和95%。实验结果表明了该算法的有效性和准确性。     

A self-adaptive image normalization and quaternion PCA based color image watermarking algorithm

This paper proposes a novel robust digital color image watermarking algorithm which combines color image feature point extraction, shape image normalization and QPCA (quaternion principal component algorithm) based watermarking embedding (QWEMS) and extraction (QWEXS) schemes. The feature point extraction method called Mexican Hat wavelet scale interaction is used to select the points which can survive various attacks and also be used as reference points for both watermarking embedding and extraction. The normalization shape image of the local quadrangle image of which the four corners are feature points of the original image is invariant to translation, rotation, scaling and skew, by which we can obtain the relationship between the feature images of the original image and the watermarked image which has suffered with geometrical attacks. The proposed QWEMS and QWEXS schemes which denote the color pixel as a pure quaternion and the feature image as a quaternion matrix can improve the robustness and the imperceptibility of the embedding watermarking. To simplify the eigen-decomposition procedure of the quaternion matrix, we develop a calculation approach with which the eigen-values and the corresponding eigen-vectors of the quaternion matrix can be computed. A binary watermark image is embedded in the principal component coefficients of the feature image. Simulation results demonstrate that the proposed algorithm can survive a variety of geometry attacks, i.e. translation, rotation, scaling and skew, and can also resist the attacks of many signal processing procedures, for example, moderate JPEG compression, salt and pepper noise, Gaussian filtering, median filtering, and so on.     

Multi-directional two-dimensional PCA with matching score level fusion for face recognition

The traditional matrix-based feature extraction methods that have been widely used in face recognition essentially work on the facial image matrixes only in one or two directions. For example, 2DPCA can be seen as the row-based PCA and only reflects the information in each row, and some structure information cannot be uncovered by it. In this paper, we propose the directional 2DPCA that can extract features from the matrixes in any direction. To effectively use all the features extracted by the D2DPCA, we combine a bank of D2DPCA performed in different directions to develop a matching score level fusion method named multi-directional 2DPCA for face recognition. The results of experiments on AR and FERET datasets show that the proposed method can obtain a higher accuracy than the previous matrix-based feature extraction methods.