一种双向压缩的二维特征抽取算法及其应用*

针对二维主分量分析（2DPCA）在最优投影轴上的投影是一个向量,其抽取出的图像特征是一个矩阵,特征数据量大,不便于直接分类的弱点,提出了一种特征抽取新方法。首先用2DPCA作一次横向压缩,对抽取出的特征矩阵再作一次2DPCA进行纵向压缩。这样抽取出的特征数量大大减少,可加快分类速度。ORL人脸库的试验结果表明了该方法的有效性。     

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。     

基于多子空间直和特征融合的人脸识别算法

多个子空间直和能保证多个子空间数据融合时多个子空间得到的特征向量相互两两正交,融合数据采用该特征表示时冗余最小,更有利于分类识别。本文基于多子空间直和进行特征融合,提出了一种新的人脸识别算法。通过 2DPCA算法,首先分别计算所有训练样本归一化后正脸、左侧脸及右侧脸图像的协方差矩阵的各P个最大特征值对应的P个相互正交的特征向量,然后通过选取3个子空间的部分满足直 和条件的特征向量组成各自的特征空间(投影空间),再将样本正脸、左侧脸及右侧脸图像分别向各自特征空间投影得到3个特征矩阵,最后将此3个特征矩阵融合为该样本的特征矩阵用于最近邻分类器进行分类识别。最终通过本文3组实验数据的对比说明了该 算法能减少计算量并且提高了识别率。     

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。     

一种基于人脸垂直对称性的变形2DPCA算法

本文分析了人脸的对称性和主成分分析法(PCA)、二维主成分分析法(2DPCA)的特性,证明了2DPCA协方差矩阵就是PCA协方差矩阵的主角线的平均值,同时表明2DPCA减少了对人脸识别有用的协方差信息。提出了一种基于人脸垂直对称性的变形2DPCA算法(S2DPCA),该算法最大程度地利用了协方差鉴别信息,用更少的系数表示一张人脸图像。通过在ORL的实验比较表明,该算法与PCA算法相比降低了计算复杂性,与2DPCA方法和PCA方法相比提高了人脸识别率,在识别率方面优于传统算法(PCA(Eigenfaces)、ICA、Kernel Eigenfaces),同时也压缩了人脸的存储空间。     

基于特征选择的二维主分量分析

提出了一种基于分类性能的二维主分量特征选择方法.即将二维主分量分析中图像总体散布矩阵的特征向量在二维线性鉴别分析的目标函数上进行投影,并选择分类性更好的特征向量进行投影.另外,为了保持原有的二维主分量分析主特征的优点,对最后的投影特征向量进行组合,也就是最后的投影特征向量选取对图像重建和图像分类分别起着重要作用的特征进行组合.在XM2VTS标准人脸库上的试验结果表明,所提出的方法融合了两种具有互补性的图像并行特征,在识别性能上优于传统的二维主分量分析方法.     

改进的2DPCA人脸识别算法

在对2DPCA人脸识别方法研究的基础上,提出一种改进的2DPCA人脸识别算法,该算法对训练集进行两次2DPCA特征提取,以此重建散布矩阵,从而大大降低特征矩阵的存储空间.并在标准Yale与ORL人脸识别数据库上进行对比实验,改进的2DPCA人脸算法能有效改善识别性能,优于传统的2DPCA方法.最后,再通过和PCA,LD...     

二维投影非负矩阵分解算法及其在人脸识别中的应用

建立在最小化非负矩阵分解损失函数上的人脸识别算法需同时计算基矩阵和系数矩阵, 导致求解这类问题十分耗时. 本文把非负属性引入二维主成分分析(2-dimensional principal component analysis, 2DPCA)中, 提出了一种新的二维投影非负矩阵分解(2-dimensional projective non-negative matrix factorization, 2DPNMF)人脸识别算法. 该算法在保持人脸图像的局部结构情况下, 突破了最小化非负矩阵分解损失函数的约束, 仅需计算投影矩阵(基矩阵), 从而降低了计算复杂度. 本文从理论上证明了所提出算法的收敛性, 同时, 使用了YALE、FERET和AR三个人脸库进行实验, 结果表明2DPNMF不仅识别率高, 而且速度优于非负矩阵分解和二维主成分分析.     

基于分块2DPCA的人脸识别方法

为进一步提高分块二维主成分分析(2DPCA)算法在人脸识别的识别率,提出一种人脸识别算法.将训练样本人脸矩阵按光照等相似条件进行分块并进行类内平均归一化;采用2DPCA算法构造特征空间,将分块矩阵在特征空间中进行投影得到训练样本识别特征,利用支持向量机(SVM)在分类上的优势,对训练样本识别特征和经过归一化分块2DPCA的测试样本识别特征进行分类,对人脸图像进行识别.选取ORL人脸数据库的图片进行实验,将该算法与传统2DPCA、2DPCA+SVM等算法进行比较,验证了该算法的性能优于其它算法.     

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。     

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.     

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.     

Structural two-dimensional principal component analysis for image recognition

In this paper, a new technique called structural two-dimensional principal component analysis (S2DPCA) is proposed for image recognition. S2DPCA is a subspace learning method that identifies the structural information for discrimination. Different from conventional two-dimensional principal component analysis (2DPCA) that only reflects within-row information of images, the goal of S2DPCA is to discover structural discriminative information contained in both within-row and between-row of the images. By contrast with 2DPCA, S2DPCA is directly based on the augmented images encoding corresponding row membership, and the projection directions of S2DPCA are obtained by solving an eigenvalue problem of the augmented image covariance matrix. Computationally, S2DPCA is straightforward and comparative with 2DPCA. Like 2DPCA, the singularity problem is completely avoided in S2DPCA. Experiments on face recognition and handwritten digit recognition are presented to show the effectiveness of the proposed approach.     

二维主成分分析方法的推广及其在人脸识别中的应用

提出了分块二维主成分分析(分块2DPCA)的人脸识别方法。分块2DPCA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:能方便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;与2DPCA方法相比,使用低维的鉴别特征矩阵,而达到较高(至少是不低)的正确识别率。此外,2DPCA是分块2DPCA的特例。在ORL和NUST603人脸库上的试验结果表明,所提出的方法在识别性能上优于2DPCA方法。     

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.     

Cross grouping strategy based 2DPCA method for face recognition

Grouping strategy exactly specifies the form of covariance matrix, therefore it is very essential. Most 2DPCA methods use the original 2D image matrices to form the covariance matrix which actually means that the strategy is to group the random variables by row or column of the input image. Because of their grouping strategies these methods have two main drawbacks. Firstly, 2DPCA and some of its variants such as A2DPCA, DiaPCA and MatPCA preserve only the covariance information between the elements of these groups. This directly implies that 2DPCA and these variants eliminate some covariance information while PCA preserves such information that can be useful for recognition. Secondly, all the existing methods suffer from the relatively high intra-group correlation, since the random variables in a row, column, or a block are closely located and highly correlated. To overcome such drawbacks we propose a novel grouping strategy named cross grouping strategy. The algorithm focuses on reducing the redundancy among the row and the column vectors of the image matrix. While doing this the algorithm completely preserves the covariance information of PCA between local geometric structures in the image matrix which is partially maintained in 2DPCA and its variants. And also in the proposed study intra-group correlation is weak according to the 2DPCA and its variants because the random variables spread over the whole face image. These make the proposed algorithm superior to 2DPCA and its variants. In order to achieve this, image cross-covariance matrix is calculated from the summation of the outer products of the column and the row vectors of all images. The singular value decomposition (SVD) is then applied to the image cross-covariance matrix. The right and the left singular vectors of SVD of the image cross-covariance matrix are used as the optimal projective vectors. Further in order to reduce the dimension LDA is applied on the feature space of the proposed method that is proposed method + LDA. The exhaustive experimental results demonstrate that proposed grouping strategy for 2DPCA is superior to 2DPCA, its specified variants and PCA, and proposed method outperforms bi-directional PCA + LDA.     

基于Gabor小波和二维主元分析的人脸识别

论文提出了一种基于Gabor小波和二维主元分析(2DPCA)的人脸识别方法。该方法首先对人脸图像进行Gabor小波变换,将小波变换的系数作为人脸图像的特征向量;然后,用2DPCA对所得的人脸图像特征进行降维,并采用最近邻法进行分类;最后,利用AT&T人脸库,对基于Gabor小波和二维主元分析(2DPCA)的人脸识别方法和基于Gabor小波和PCA的人脸识别方法进行了仿真比较实验。仿真实验表明,基于Gabor小波和2DPCA的人脸识别方法具有较好的识别性能。