一种对角LDA算法及其在人脸识别上的应用

2维特征抽取方法(如2DPCA、2DLDA),因为其抽取特征的速度和识别率要比1维的方法好,所以在人脸识别中得到了广泛的应用。最近基于2DPCA又提出了对角主成份分析(diagonal principal component analysis,DiaPCA),该方法由于保持了图像的行变化和图像的列变化之间的相关性,从而克服了2DPCA仅能反映图像行之间的变化,而忽略了图像列之间变化的缺点。但是,由于DiaPCA并没在特征抽取中融入鉴别信息,同时2DLDA也具有与2DPCA同样的缺点,从而分别影响了DiaPCA与2DLDA两种方法的识别性能。针对这一问题,提出了一种对角线性鉴别分析(diagonal linear dicriminant analysis,DiaLDA)的新算法,该新算法是基于对角人脸图像来求解最优鉴别向量。该新算法在ORL和FERET人脸库进行了实验,并与PCA、Fisherface、DiaPCA、2DLDA等方法进行了比较。实验结果表明,该方法比其他方法的识别性能要好。     

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.     

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.     

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。     

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。     

Color face recognition based on quaternion matrix representation

There are several methods to recognize and reconstruct a human face image. The principal component analysis (PCA) is a successful approach because of its effective extraction of the global feature and excellent reconstruction of face image. However, the crucial shortcomings of PCA are its low recognition rate and overfitting of feature extraction which leads to the dependence of training data on training samples. In this paper, a modified two-dimension principal component analysis (2DPCA) and bidirectional principal component analysis (BDPCA) methods based on quaternion matrix are proposed to recognize and reconstruct a color face image. In these methods, the spatial distribution information of color images is used to represent a color face, and the 2DPCA or BDPCA feature of color face image is extracted by reducing the dimensionality in both column and row directions. A method obtaining orthogonal eigenvector set of quaternion matrix is proposed. Numerous experiments show that the present approach based on quaternion matrix can effectively smooth the overfitting issue and substantially enhance the recognition rate.     

基于方向极傅里叶频谱2DPCA 的尾迹检测

针对航空图像中的水面尾迹, 提出了一种基于方向极傅里叶频谱二维主成分分析(Two-dimensional principal component analysis, 2DPCA)的尾迹自动检测算法. 该方法根据子图像的纹理方向, 对傅里叶频谱进行极坐标变换, 使得到的方向极傅里叶频谱具有平移和旋转不变性. 相对于文献中对极频谱的直接划分作为纹理特征, 本文对它进行一次列二维主成分分析, 一次行二维主成分分析和两次二维主成分分析, 实验结果表明本文方法具有更高的分类识别率, 其中两次二维主成分分析的分类识别率最高. 对40幅图像的测试结果表明, 本文的方法能够有效地自动检测航空图像中的水面尾迹纹理.     

A novel matrix-based method for face recognition

Two-dimensional principal component analysis (2DPCA) is one of the representative techniques for image representation and recognition. However, it fails in detecting the local variation of images, which characterizes the most important modes of variability of face images. Motivated by the fact that the local spatial geometric structure of images is effectual in learning the representative image space, we assign different weight to each training image and then present a novel method, namely local two-dimensional principal component analysis (L2DPCA), which explicitly considers the variations among nearby data. Finally, we describe an effective algorithm L2DPCA+2DPCA to further reduce dimensionality reduction. Extensive experimental results on two-face databases (Yale and AR) show the efficiency of the proposed method.     

非负二维主成分分析及在人脸识别中的应用

二维主成分分析是一种基于整体脸的方法,保留人脸部件之间的拓扑关系.而非负矩阵分析是基于局部特征的识别,是通过提取局部信息来实现分类.文中将两种思想的优点融合在一起,提出非负二维主成分分析.该方法改善传统非负矩阵分解只是从矩阵分解的角度考虑,没有加强分类的问题.此外,该方法在矩阵分解之前不需要将图像矩阵转换为图像向量,能快速降低鉴别特征的维数.在ORL和FERET人脸库上的实验结果表明,该方法在识别性能上优于其它方法,且更具有鲁棒性.     

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.     

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.     

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。     

一种基于共同向量结合2DPCA的人脸识别方法

提出了一种基于共同向量结合2维主成分分析(2-dimen-sional principal component analysis, 2DPCA)的人脸识别方法. 共同向量由图像通过Gram-Schmidt正交变换而求得, 具有该类图像共同不变的性质. 原始图像与该类共同向量之间的差分向量通过2DPCA处理, 依据最小距离测试得到识别结果. 实验在ORL和Yale人脸数据库进行测试, 结果表明本文提出的方法有较好的识别性能.     

一种基于Gabor小波特征的人脸表情识别新方法

近来,表情识别成为人机交互研究的热点.将Gabor小波变换与2DPCA结合提出了一种表情识别的新方法.首先对静态灰度表情图片进行预处理,然后对其进行Gabar小波变换,通过2DPCA进行降维,根据Gabor不同尺度不同方向的变换结果训练不同的分类器,由校验集得到分类器权值,通过隶属度函数将各个分类结果模糊化,实现了分类器集成和表情特征数据的融合.实验证明了Gabor小渡与2DPCA结合在表情识别中的有效性,以及基于Gabor小波模糊分类器集成的方法能够进一步提高识别率.     

Probabilistic two-dimensional principal component analysis and its mixture model for face recognition

Recently, two-dimensional principal component analysis (2DPCA) as a novel eigenvector-based method has proved to be an efficient technique for image feature extraction and representation. In this paper, by supposing a parametric Gaussian distribution over the image space (spanned by the row vectors of 2D image matrices) and a spherical Gaussian noise model for the image, we endow the 2DPCA with a probabilistic framework called probabilistic 2DPCA (P2DPCA), which is robust to noise. Further, by using the probabilistic perspective of P2DPCA, we extend the P2DPCA to a mixture of local P2DPCA models (MP2DPCA). The MP2DPCA offers us a method of being able to model faces in unconstrained (complex) environment. The model parameters could be fitted on the basis of maximum likelihood (ML) estimation via the expectation maximization (EM) algorithm. The experimental recognition results on UMIST, AR face database, and the face recognition (FR) data collected at University of Essex confirm the effectivity of the proposed methods.     

基于传感器模式噪声特性的图像篡改检测方法

针对传统基于传感器模式噪声特性的图像篡改检测算法由于需要知道参考图像数据库因而应用局限性大的问题,提出了一种基于噪声子空间投影的图像篡改检测框架,分别采用主成分分析（ PCA）、二维主成分分析（2DPCA）和核主成分分析（KPCA）实现了基于图像噪声特性的篡改检测,并通过实验验证了此方法的有效性。     

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.     

Improved discriminant locality preserving projections for face and palmprint recognition

We propose in this paper two improved manifold learning methods called diagonal discriminant locality preserving projections (Dia-DLPP) and weighted two-dimensional discriminant locality preserving projections (W2D-DLPP) for face and palmprint recognition. Motivated by the fact that diagonal images outperform the original images for conventional two-dimensional (2D) subspace learning methods such as 2D principal component analysis (2DPCA) and 2D linear discriminant analysis (2DLDA), we first propose applying diagonal images to a recently proposed 2D discriminant locality preserving projections (2D-DLPP) algorithm, and formulate the Dia-DLPP method for feature extraction of face and palmprint images. Moreover, we show that transforming an image to a diagonal image is equivalent to assigning an appropriate weight to each pixel of the original image to emphasize its different importance for recognition, which provides the rationale and superiority of using diagonal images for 2D subspace learning. Inspired by this finding, we further propose a new discriminant weighted method to explicitly calculate the discriminative score of each pixel within a face and palmprint sample to duly emphasize its different importance, and incorporate it into 2D-DLPP to formulate the W2D-DLPP method to improve the recognition performance of 2D-DLPP and Dia-DLPP. Experimental results on the widely used FERET face and PolyU palmprint databases demonstrate the efficacy of the proposed methods.     

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。     

基于最大相关熵准则的2维主成分分析

目的 本文针对基于最小均方差准则的主成分分析算法(如2DPCA-L₂(two-dimensional PCA with L₂-norm)算法和2DPCA-L₁(two-dimensional PCA with L₁-norm)算法)对外点敏感、识别率低的问题,结合信息论中的最大相关熵准则,提出了一种基于最大相关熵准则的2DPCA(2DPCA-MCC)。方法 2DPCA-MCC算法采用最大相关熵表示目标函数,通过半二次优化技术解决相关熵问题,降低了外点在目标函数评价中的贡献,从而提高了算法的鲁棒性和识别精度。结果 通过对比2DPCA-MCC算法和2DPCA-L₂、2DPCA-L₁在ORL人脸数据库上的识别效果,表明了2DPCA-MCC算法的识别率比2维主成分分析算法的识别率最低提高了近10%,最高提高了近30%。结论 提出了一种基于最大相关熵的2DPCA算法,通过半二次优化技术解决非线性优化问题,实验结果表明,本算法能够较好地解决外点问题,显著提高识别精度,适用于解决人脸识别中的外点问题。