CN102982322A - Face recognition method based on PCA (principal component analysis) image reconstruction and LDA (linear discriminant analysis) - Google Patents

Face recognition method based on PCA (principal component analysis) image reconstruction and LDA (linear discriminant analysis) Download PDF

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CN102982322A
CN102982322A CN2012105251172A CN201210525117A CN102982322A CN 102982322 A CN102982322 A CN 102982322A CN 2012105251172 A CN2012105251172 A CN 2012105251172A CN 201210525117 A CN201210525117 A CN 201210525117A CN 102982322 A CN102982322 A CN 102982322A
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face
matrix
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周昌军
王兰
张强
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大连大学
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Abstract

The invention discloses a face recognition method based on PCA image reconstruction and LDA and belongs to the technical field of computer image processing and pattern recognition. The face recognition method is based on a principal component analysis algorithm; an intra-class covariance matrix serves as a generation matrix for acquiring face feature subspaces of individuals; then an image to be recognized maps the feature subspaces to extract features; the image is reconstructed according to feature values; a residual image is subjected to the linear discriminant analysis; and finally, face recognition is realized by a minimum distance classification recognition algorithm. Compared with the prior feature subspace method, the face recognition method can better extract the face features of different people, and the face recognition rate is increased effectively. In addition, when a face database is required to be expanded, only the newly added faces are required for feature face training; not all the face feature subspaces are retrained; and the face recognition method also has good extendibility.

Description

基于PCA图像重构和LDA的人脸识别方法 Face Recognition Based on PCA and LDA of image reconstruction

技术领域 FIELD

[0001] 本发明涉及一种基于PCA图像重构和LDA的人脸识别方法,属于计算机图像处理与模式识别技术领域。 [0001] The present invention relates to a method for face recognition PCA and LDA based image reconstruction, image processing and computer belonging to the technical field of pattern recognition.

背景技术 Background technique

[0002] 人脸识别技术是利用计算机分析人脸图像,从中提取有效的识别信息,辨别个人身份的一门技术,对于输入的人脸图像,首先判断其中是否存在人脸,若存在人脸,则进一步的给出每个人脸的位置、大小和各个主要面部器官的位置信息,并根据这些信息,进一步提取每个人脸中所包含的身份特征,并将其与己知人脸库中的人脸进行对比,从而识别每个人脸的身份。 [0002] The face recognition technology using computer analysis of the face image, to extract effective identification information to identify a personal identification technology, for the input face image, which first determines whether there is a human face, if there is a face, it is further given to each face position, size, and position information of each major face parts, and based on this information, further characterized in extracting the identity of each face included, and the library has Appreciating face which faces the person compared to identify the identity of each person's face. 人脸识别技术涉及到模式识别、图像处理、计算机视觉、生理学、认知学等诸多学科的知识,并与其他生物特征的识别方法以及计算机人机感知交互的研究领域都有密切联系。 Face recognition technology involves the knowledge of pattern recognition, image processing, computer vision, physiology, cognitive science and many other disciplines, and with other biometric identification methods as well as human computer interaction research perception are closely linked. 同时人脸识别作为一种生物特征识别,有着其他生物特征识别方法(如指纹、虹膜、DAN检测等)所无法比拟的优点: Meanwhile, as a biometric face recognition, biometric recognition with other methods (such as fingerprint, iris, the DAN detection) unmatched advantages:

[0003] (I)非侵犯性,人脸图像的获取不需要和被检测人发生身体接触,可以在不惊动被检测人的情况下进行识别; [0003] acquisition need not occur and the detected human body contacting (I) a non-invasive, face image, may not disturb the identification of the person is detected;

[0004] (2)低成本、易安装,人脸识别系统只需要采用普通的摄像头、数码摄像机等被广泛使用的摄像设备即可,而且对用户来说也没有特别的安装要求; [0004] (2) low cost, easy to install, using only the face recognition system to the imaging apparatus is widely used ordinary camera, a digital camera and the like, but also for users no particular installation requirements;

[0005] (3)无人工参与,整个人脸识别过程不需要用户或被检测人的主动参与,计算机可以根据用户的预先设置自动进行。 [0005] (3) without human intervention, or the entire recognition process does not require the user's active participation detecting a human, a computer may automatically according to a preset user.

[0006] 由于人脸识别技术具有以上的优势,人脸识别技术被广泛的应用到多个领域,t匕如司法部门领域,公安部门可通过犯罪嫌疑人的照片或者面部特征,迅速调取档案系统中的人脸照片进行比对,可以提高刑侦破案的效率;公共安全领域,在车站、机场、宾馆等人群密集的地方,若想发现特定的目标是非常困难的,采用人脸识别系统和智能视频监控系统相连接,就可以非常快速的从人群密集的地方找到特定目标;门禁系统领域,传统的门禁系统的身份识别技术存在着伪造、冒用等风险,而人脸识别系统作为生物特征识别的一种,不存在着这些风险,而且还会给用户带来更多的方便;信息安全领域,如各类银行卡、金融卡的持卡人身份验证,而且随着网络信息化的发展,电子银行被使用的越来越频繁,但是目前的电子银行的安全机制主要是依赖于 [0006] Since the face recognition technology has more advantages, face recognition technology has been widely applied to many fields, t dagger areas such as the judiciary, public security departments through photographs or facial features of the suspect, rapid retrieval of files the system faces in the photo for comparison, can improve the detection efficiency of criminal investigation; public safety in railway stations, airports, hotels and other crowded places, if you want to find a specific target is very difficult, and the use of face recognition system intelligent video surveillance system is connected, you can very quickly find a specific target from crowded places; the field of access control systems, access control systems of traditional identification technology exists forgery, fraudulent use of other risks, and as a biometric face recognition system a recognition, there is no such risk, but also bring more convenience to the user; information security field, such as cardholder authentication various bank cards, debit cards, and with the development of information technology network , electronic banking more and more frequently being used, but the current security mechanisms of e-banking is mainly dependent on the 号、密码、数字证书等,这些信息容易被复制、传播、人脸识别技术是一种更为安全可靠的身份认证技术,因此其在信息安全,民事领域大有用武之地。 Numbers, passwords, digital certificates, this information can easily be copied, distributed, face recognition technology is a more secure authentication technology, its information security, civil spheres come in handy.

[0007] 虽然人类可以毫不困难地由人脸辨别一个人,但利用计算机进行完全自动的人脸识别仍存在许多困难,其表现在:人脸是一类具有相当复杂的细节变化的自然结构目标,夕卜貌、表情、肤色等不同;人脸随年龄增长而变化;发型、眼镜、胡须等装饰对人脸造成遮挡;人脸所成图像受光照、成像角度、成像距离等影响。 [0007] While humans can without difficulty to identify a person by the face, but the use of computer fully automated face recognition there are still many difficulties in its performance: the natural structure of the face is a kind of insight is very complex changes goal, Xi Bu appearance, facial expressions, skin color, such as different; face changes with age; hair, glasses, beards and other decorations on the face caused by occlusion; the facial image into the affected light, angle imaging, imaging distance. 此外人脸识别技术研究与相关学科的发展及人脑的认识程度紧密相关,这诸多因素使得人脸识别研究成为一项极富挑战性的课题。 Also closely related to the development and the level of awareness of the human brain's Face Recognition technology and related disciplines, and many other factors make this face recognition can become a major challenging. 因此,如果能够找到解决这些问题的方法,成功构造出人脸自动识别系统,将为解决其它类似的复杂模式识别问题提供重要的启示。 Therefore, if we can find a way to solve these problems successfully constructed automatic face recognition system, provide important inspiration for solving other similarly complex pattern recognition problems.

[0008] 子空间分析方法是统计模式识别中一类重要的方法,它本质上是一种特征提取与选择的方法,比较典型的方法包括主成分分析(PCA)、线性判别分析(LDA)、独立成分分析(ICA)、奇异值分解(SVD)、非负矩阵因子(NMF)、局部保持映射(LPP)和基于核的非线性子空间分析等等。 [0008] subspace statistical pattern recognition analysis is an important class of methods, which essentially is a feature extraction and selection methods, typical methods include principal component analysis (the PCA), linear discriminant analysis (LDA), independent component analysis (ICA), Singular value decomposition (SVD), the non-negative matrix factorization (NMF), a local holding map (LPP) and core-based linear subspace analysis and the like. 近年来,基于子空间的模式识别方法得到了快速的发展,由于其具有计算代价小、描述能力强、可分性好等特点,使得该方法在人脸识别等模式识别以及特征提取中得到了广泛的研究和应用。 In recent years, a pattern recognition method based on subspace has been rapid development, since it has a low computational cost description ability, and good characteristics can be divided, so that the method was like in the face recognition feature extraction and pattern recognition extensive research and application.

发明内容 SUMMARY

[0009] 本发明针对以上问题的提出,而研制基于PCA图像重构和LDA的人脸识别方法。 [0009] The present invention is directed to the above issues raised, developed PCA face recognition method based on image reconstruction and the LDA.

[0010] 本发明采取的技术方案如下; [0010] The present invention takes the following technical solutions;

[0011] 1、基于PCA图像重构和LDA的人脸识别方法包括如下几个步骤: [0011] 1, face recognition method of PCA and LDA-based image reconstruction comprises the following steps:

[0012] 步骤1、图像预处理 [0012] Step 1, an image pre-processing

[0013] 步骤二、从ORL人脸库中随机选取图像作为训练集,剩下的图像作为测试集,读取训练库人脸图像成灰度矩阵形式,并将训练样本以个人进行分类存储成Vj ; [0013] Step two randomly selected images from the ORL database as the training set, the rest of the image as the test set, the training corpus read face image to grayscale matrix and individual training sample storage to categorize Vj;

[0014] 步骤三、以个人的人脸图像协方差矩阵Sj = Ε[(Χ-μ(X-Uj)tJ作为产生矩阵,采用PCA方法提取其特征子空间Wj ; [0014] Step three, the face image to the covariance matrix of individual Sj = Ε [(Χ-μ (X-Uj) tJ as generate a matrix, wherein the extraction method using PCA subspaces of Wj;

[0015] 步骤四、重复步骤二至三,提取出所有人脸的特征子空间W」」=1,2,. . .,m,其中m为用于训练及识别的人脸类别数量 [0015] Step 4 Repeat steps two to three, all the extracted face feature subspace W ' "= 1,2 ,..., The number of m, where m is the human face for training and recognition category

[0016]步骤五、将训练图像 Xi 根据公式Hij= (X1-Uj) Xffj,! = 1,2,-,N, j = 1,2,…,m提取其特征Hij,所述Hij = (X1-Uj) Xffj, i = 1,2,···,Ν,j = l,2r..,m; [0016] Step five, the training images Xi according to the formula Hij = (X1-Uj) Xffj ,! = 1,2, -, N, j = 1,2, ..., m which extract Hij, said Hij = ( X1-Uj) Xffj, i = 1,2, ···, Ν, j = l, 2r .., m;

[0017] 步骤六、将特征向量Hij向W」进行反求,根据公式Yij = WjXHij+μ」,i =1,2,…,N,j = I, 2,…,m重构得到新的人脸图像Yij ; [0017] Step 6 Hij feature vector W for the "reverse, according to the formula Yij = WjXHij + μ", i = 1,2, ..., N, j = I, 2, ..., m are reconstructed to obtain new face image Yij;

[0018] 步骤七、从原始图像Xi中减去重构图像Yij,得到残差图像X,即! [0018] Step 7 subtracted from the original image Y ij Xi reconstructed image, the residual image to obtain X, i.e.,! = 1,- > = 1, ->

[0019] 步骤八、在残差图像中运用线性判别分析(LDA)方法进行特征向量提取根据公式 [0019] Step 8 using linear discriminant analysis (LDA) method in the residual image feature vector extraction is performed according to the formula

Figure CN102982322AD00051

得到系数矩阵,其中, To give the coefficient matrix, wherein

St> Sb和Sw分别为总体散布矩阵、类间散布矩阵和类内散布矩阵。 St> Sb and Sw respectively total scatter matrix and the between-class scatter matrix within-class scatter matrix.

[0020] 步骤九、将测试图像映射到特征子空间内,然后以与训练图像同样的步骤5-8提取测试图像; [0020] Step 9, the test image is mapped to the subspace, then the same training image step 5-8 extracts a test image;

[0021] 步骤十、计算训练图像与测试图像在特征脸空间中对应点之间的欧式距离,以最小欧氏距离作为判据对人脸图像进行识别; [0021] Step 10, calculating the training image and the test image corresponding to the Euclidean distance between the feature points in the face space to a minimum Euclidean distance to a face image recognition criterion;

[0022] 以上所述步骤三中以个人的人脸图像协方差矩阵Sj作为产生矩阵,计算产生矩阵的特征值及对应的特征向量,并把特征值从大到小的顺序进行排序,同时对应的特征向量也进行排序,进而求出所有40个人的人脸图像特征子空间Wj, j = 1,2,. . .,40。 [0022] The above three steps to the individual face images generated covariance matrix as matrix Sj, calculated to produce an eigenvalue matrix and corresponding characteristic values ​​of the order and the descending sort, while the corresponding the eigenvectors are also sorted, and then find all 40 individuals face image feature subspace Wj, j = 1,2 ,..., 40.

[0023] 以上所述步骤七中重构图像的获取过程是针对单个人的特征子空间而获得的,其具体方法为,首先将训练图像Xi根据公式Hu = (X1- μ j) Xffj提取其特征Hu ;其次将特征向量Hij向Wj进行反求,根据公式Yij = Wj XHij+ μ j重构得到新的人脸图像Yij ;再从原始图像Xi中减去重构图像Yij,得到残差图像。 [0023] Step VII above said reconstructed image acquisition process for a subspace obtained by a single person, which is a specific method, the first training images extracted according to the equation Xi Hu = (X1- μ j) Xffj characterized in Hu; secondly Hij feature vector Wj for the reverse, according to the formula Yij = Wj XHij + μ j new reconstructed face image obtained Yij; Yij reconstructed image is subtracted from the original image Xi to obtain a residual image.

[0024] 以上所述步骤八中将LDA方法应用于人脸残差图像中提取人脸图像的特征向量,并实现人脸图像的识别。 [0024] The above eight step method is applied in the face LDA residual image feature vector extracting face images, and to achieve recognition of the face image.

[0025] 本发明与现有技术相比具有以下优点: [0025] The present invention and the prior art has the following advantages:

[0026] I、传统的主成分分析(PCA)人脸识别的方法,多是采用总体散布矩阵作为产生矩阵,这样获取的大多是人脸的共性特征而忽略了每个人不同的人脸特性,虽然每个人脸都有一定的相似性及规则,但是不同的人脸存在着明显的区别,而且不同的人脸的特征恰恰是人脸识别中最有用的信息。 [0026] I, traditional principal component analysis (PCA) face recognition method, is used more as a total scatter matrix to produce the matrix, thus acquired most common features of a face while ignoring different facial characteristics of each person, Although each face has a certain similarity and rules, but different face there is a clear difference, and features different face recognition is precisely the most useful information. 因此,基于主成分分析算法,我们以类内协方差矩阵作为产生矩阵获取单个人的人脸特征子空间,然后将待识别图像对每个特征子空间进行映射提取特征,并以此特征值进行图像重构,然后对残差图像运用线性判别分析方法。 Thus, based on principal component analysis algorithm, we class generating the covariance matrix as matrix obtaining a single individual face feature subspaces, then the map image to be recognized for each feature extracting feature subspace, and thus eigenvalue image reconstruction, and then the residual image using linear discriminant analysis method. 最后我们采用最小距离分类识别算法实现人脸识别,该方法与以往的特征子空间方法相比,能够更好提取 Finally, we use the minimum distance classifier recognition face recognition algorithm, compared with the conventional method wherein the subspace method, it is possible to extract better

出不同人的人脸特征,有效的提高了人脸识别率。 Facial features of different people, effectively improve the recognition rate.

[0027] 2、该方法具有良好的可扩展性;由于不同人的特征脸是相对独立的,当往人脸数据库里添加新的人脸时,只需要对新添加的人脸进行特征脸的训练,而不用像传统的特征子空间方法那样重新训练特征子空间,因此该方法具有更好的可扩展性。 [0027] 2, the method has good scalability; Due to the different features of the person face is relatively independent, when a new face to face database is added, only human newly added facial feature face training, rather than like a traditional subspace methods such as re-training feature subspace, this method has better scalability.

附图说明 BRIEF DESCRIPTION

[0028] 图1本发明的系统流程图。 [0028] The system of the present invention a flowchart of FIG.

具体实施方式 Detailed ways

[0029] 下面结合附图对本发明做进一步说明; [0029] The accompanying drawings illustrate the present invention further binding;

[0030] 本发明的一个实施例: An embodiment [0030] of the present invention:

[0031] 如图1所示:本分明包括如下步骤: [0031] Figure 1: This clearly includes the steps of:

[0032] 步骤I、图像预处理 [0032] Step I, the image pre-processing

[0033] 对人脸图像I (大小为wXh)进行一定的预处理,主要包括图像平滑以及图像灰度和方差的归一化处理,尽量去除尺度大小、光线明暗等因素给识别过程带来的不利影响; [0033] The face image I (WXH size) certain pretreatment, including image smoothing and normalizing image intensity and variance, try to remove the scale size, light shade and other factors to bring recognition process Negative Effects;

[0034] 图像平滑是为了消除图像噪声,改善图像质量。 [0034] The image smoothing to eliminate image noise and improve image quality. 数字图像的平滑技术分化为两类:一类是全局处理,即对噪声图像的整体或大的块进行校正;另一类平滑技术是对噪声图像使用局部算子,当对某一像素进行平滑处理时,仅对它的局部小领域的一些像素加以运算,可以对多个像素并行处理。 Smoothing differentiation of the digital image into two categories: one is the overall process, i.e., the whole or a large block noise correcting image; the other smoothing technique is a noise image using the local operator, when a certain pixel of the smoothing when the processing operation to be only some of the pixels of its small local areas of a plurality of pixels to be processed in parallel. 平滑模板的思想是通过一点和周围几个点的运算来去除突然变化的点,从而滤掉一定的噪声,一般情况下,通过选择不同的模版来消除不同的噪声,常用的模板有: Thought the template is smooth operation and by one o'clock several points around the point to remove the sudden changes to filter out some of the noise, in general, to eliminate different noise by selecting a different template, the templates used are:

[0035] [0035]

Figure CN102982322AD00061

[0036] 归一化的目标是取得尺寸一致、灰度取值范围相同的标准化人脸。 [0036] The normalized size to obtain the same goal, the same grayscale range normalized face. 为了去除一定的光照对灰度分布的影响,需要对目标图像进行灰度归一化,比较典型的一种灰度归一化方法是直方图均衡化。 In order to remove certain light intensity distribution on impact, the target image needs gradation normalization, a typical gradation normalization method is histogram equalization.

[0037] 直方图是用于表达图像灰度分布情况的统计图表,其横坐标是灰度值,纵坐标是出现这个灰度值的概率。 [0037] The histogram is a graph for expressing the statistical distribution of the image gradation, which gray value is the abscissa, the ordinate is the gray value of the probability of occurrence. 设图像f(x,y)的灰度值为:T1, !T1,…,Iv1, IiCri)为灰度级像素出现的概率,则图像直方图为: Provided gray value image f (x, y) is:! T1, T1, ..., Iv1, IiCri) is the probability of occurrence of gray level pixels, the image histogram:

[0038] [0038]

Figure CN102982322AD00071

[0039] 式中,N是一幅图像的总像素点,L是图像像素的灰度级数,且1-1 [0039] In the formula, N is the total pixels of an image, L is a gray image pixel series, and 1-1

[0040] [0040]

Figure CN102982322AD00072

(2) (2)

[0041] 此时图像像素分布的累计概率为 [0041] At this time, the cumulative probability distribution of the pixel image

[0042] [0042]

Figure CN102982322AD00073

[0043] 取累计概率Pf(A)作为图像像素灰度变换函数T (ri),则输出图像像素灰度值Si由下式决定: [0043] Take cumulative probability Pf (A) as an image pixel gradation conversion function T (ri), the output image pixel gray value Si is determined by the formula:

[0044] [0044]

Figure CN102982322AD00074

[0045] 步骤二、从ORL人脸库中随机选取图像作为训练集,剩下的图像作为测试集,读取训练库人脸图像成灰度矩阵形式,并将训练样本以个人进行分类存储成Vj ; [0045] Step two randomly selected images from the ORL database as the training set, the rest of the image as the test set, the training corpus read face image to grayscale matrix and individual training sample storage to categorize Vj;

[0046] 将单个人的每一幅图像矩阵I按行或列展开成n = wXh维的向量X,并将向量x进行去均值处理以及白化处理,使得白化后的变量协方差矩阵为单位矩阵,利用协方差进行特征值分解,即E (XXT) =PEPt,其中E是正交矩阵E (XXt)的特征值,P是对应的特征向量,得到的白化矩阵为: [0046] Each one of the single individual image matrix I by row or column expanded to n = wXh dimensional vector X, and the vector x to be processed and the average whitening, whitening such that the matrix of covariance matrix using eigenvalue decomposition of the covariance, i.e., E (XXT) = PEPt, wherein E is an orthogonal matrix E (XXT) characteristic value, P is the corresponding eigenvector, whitening matrix is ​​obtained:

[0047] M = PE^172Pt (5) [0047] M = PE ^ 172Pt (5)

[0048] 得到白化后的数据: [0048] After the obtained whitening data:

[0049] χ = Μχ (6) [0049] χ = Μχ (6)

[0050] 将个人的所有训练图像以nXs (s是一个人的所有人脸训练图像数量)矩阵Vj表 [0050] The personal training of all images nXs (s owner is a person's face, the number of training images) matrix Vj table

/Jn ο / Jn ο

[0051] 步骤三、以个人的人脸图像协方差矩阵Sj = Ε[(Χ-μ(X-Uj)tJ作为产生矩阵,采用PCA方法提取其特征子空间Wj ; [0051] Step three, the face image to the covariance matrix of individual Sj = Ε [(Χ-μ (X-Uj) tJ as generate a matrix, wherein the extraction method using PCA subspaces of Wj;

[0052]训练样本中的样本均值为,以及协方差矩阵S = E [ (X- μ ) (Χ_μ )Τ]=XXTo [0052] The sample mean of the training sample, and the covariance matrix S = E [(X- μ) (Χ_μ) Τ] = XXTo

[0053] 通常情况下,图像列矢量的维数η都较高,直接通过样本协方差矩阵计算其特征向量较为困难,而相对来说,训练样本集中训练样本的个数N却相对较少,根据矩阵论的知识,XXt和XtX有相同的特征值,且XXt对应于特征值λ i的特征向量Ui与XtX相应的特征向量\具有下列关系: [0055] 因此可以利用求解NXN维内积矩阵XtX的特征矢量来间接计算协方差矩阵的特征矢量。 [0053] Typically, the image dimension column vectors η are high, which is difficult to directly calculate a feature vector by a sample covariance matrix, relatively speaking, the training set of training sample number N is relatively small, the knowledge of matrix theory, XXT XTX and have the same characteristic value and XXT corresponding eigenvectors corresponding to eigenvalues ​​λ i of the feature vector XTX Ui \ the following relationship: [0055] NXN can be solved using the product matrix within the dimensions calculated indirectly eigenvectors of the covariance matrix of the feature vector XtX. 根据KL变换,假设S的特征值为λ j(j = 1,2,. . .,η),且A1 ≥λ2 ≥ ....≥λη>0,相应的特征向量为μ」,则对任意X中的样本Xi可表示为: The KL transform, assuming feature value S λ j (j = 1,2 ,..., Η), and A1 ≥λ2 ≥ .... ≥λη> 0, the corresponding feature vectors μ "of the X Xi in any sample can be expressed as:

Figure CN102982322AD00081

[0057]其中 y」=Xi1UjU = 1,2,· · ·,η), y = Iiy1, y2, · · ·,yn]T。 [0057] where y '= Xi1UjU = 1,2, · · ·, η), y = Iiy1, y2, · · ·, yn] T. 选取y 的前d 个分量 Select the previous th component of y d

#作为特征,则可证-为方差最大(即能量最大)的d个分量,且G=ένο在所 # As a characteristic, you can permit - a maximum variance (i.e., the maximum energy) of d components, and in the G = ένο

有以S的d个特征向量的重构中具有最小的均方误差,因而ί通常被称为主成份,与^对应的子空间被称为信号子空间。 D reconstructed to have the feature vector S with the smallest mean square error, and thus generally referred to as main component ί, ^ the corresponding sub-space is called the signal subspace.

[0058] 据此来计算个人的人脸图像协方差矩阵的特征值及对应的特征向量ω」,并把特征值从大到小的顺序进行排序,同时对应的特征向量也进行排序,再选择其中一部分构造特征子空间。 [0058] According to calculate the individual face image covariance eigenvalues ​​and the corresponding eigenvectors ω ", and the eigenvalues ​​in descending order of sort, while the corresponding eigenvectors are also sorted, selected and then wherein a portion of the structural features subspace.

[0059] 步骤四、重复步骤2-3,提取出所有人脸的特征子空间W」,j = 1,2,. . .,m,其中m为用于训练及识别的人脸类别数量,其包括以下步骤; [0059] Step 4 Repeat steps 2-3, all faces of the extracted feature subspace W ', j = 1,2 ,..., M, where m is used for training people to identify the number and categories of faces, comprising the steps of;

[0060] 每一幅人脸图像投影到子空间以后,就对应于子空间中的一个点,即子空间中的任一点也对应于一幅图像。 [0060] Each face image is projected onto a subspace after it corresponds to a point in a subspace, i.e., any one of the subspaces is also corresponds to an image. 这些子空间中的点重构以后的图像很像“人脸”,所以称为“特征脸”。 After these sub-points in space reconstructed image much like the "human face", so called "characteristic face." 因此,任何一张人脸图像都可以向特征脸做投影并获得一组坐标系数:y = WTx,这组系数表明了该图像在子空间中的位置,便可作为人脸识别的依据,也就是这张人脸图像的特征脸特征。 Therefore, any one person can do to a face image feature projection face and get a set of coordinates coefficient: y = WTx, this set of coefficients indicate the location of the image in the sub-space, it can be used as the basis of face recognition, but also this feature is the facial feature facial image.

[0061] 步骤五、将训练图像Xi根据公式(9)提取其特征Hij ; [0061] Step five, the training images Hij wherein Xi extracted according to the equation (9);

Figure CN102982322AD00082

[0063] 步骤六、将特征向量Hij向%进行反求,根据公式(10)重构得到新的人脸图像Yij ; [0063] Step 6 Hij feature vector for the reverse%, (10) to obtain a new reconstruction Yij face image according to the formula;

Figure CN102982322AD00083

[0065] 步骤七、从原始图像Xi中减去重构图像Yij,得到残差图像! [0065] Step seven, minus the reconstructed image from the original image Yij Xi, the residue image! = •' = • '

[0066] 步骤八、在残差图像中运用线性判别分析(LDA)方法,根据公式(14) (15) (16)得到系数矩阵; [0066] Step 8 using linear discriminant analysis (LDA) method in the residual image, the coefficient matrix obtained according to the equation (14) (15) (16);

[0067] LDA的目的是寻找一个矩阵W,使得在某种意义上,类间离散度和类内离散度的比值最大,而离散度的一种简单的标量度量就是散布矩阵的行列式的值。 [0067] LDA aim is to find a matrix W, such that in a sense, a ratio of dispersion between classes and the class of the maximum dispersion, and a simple scalar value is a measure of the dispersion of scatter of Matrices . 因此,若类内散布矩阵3¥是非奇异的,则可以得到最优投影矩阵为: Thus, if the spread is non-singular matrix. 3 ¥ inner class, the optimal projection matrix can be obtained as follows:

Figure CN102982322AD00084

[0069] 通过求解下面广义特征方程的特征值问题就可以求出最优投影矩阵,Wopt = [W1WfWJ即为广义特征方程的最大特征值所对应的特征向量,即 [0069] By solving the following equation generalized characteristic feature value problem can be determined optimal projection matrix, Wopt = [W1WfWJ is the maximum eigenvalue of generalized eigenvalue equation corresponding feature vector, i.e.,

[0070] SbWj = λ JSwWj, j = 1,2,…,m (12) [0070] SbWj = λ JSwWj, j = 1,2, ..., m (12)

[0071] 因为Sw是非奇异的,特征方程(8)可以转化为 [0071] Since Sw is nonsingular, the characteristic equation (8) can be converted to

[0072] S^1SbWi = XjWj J = I,2,-'-,m (13) [0072] S ^ 1SbWi = XjWj J = I, 2, -'-, m (13)

[0073] 但是当LDA用于人脸特征提取时,样本图像的维数往往是远大于样本数,造成Sw是奇异的,所以很难根据特征方程(12)求解最优投影矩阵。 [0073] However, when LDA for facial feature extraction, the sample image dimension is much larger than the number of samples is often caused Sw is singular, it is difficult to find the optimal projection matrix from the characteristic equation (12).

[0074] 为解决此小样本问题,采用PCA和LDA相结合的方法,先利用PCA对人脸图像进行降维,使Sw满秩,再运用LDA进行特征提取,进而实现人脸识别,通过此方法求解的最优投影矩阵可描述为: [0074] In order to solve this small sample, the method combining PCA and LDA, the first use of PCA face image dimension reduction, so Sw full rank, then use the LDA feature extraction, thus achieving recognition through this the method for solving the optimal projection matrix can be described as:

Figure CN102982322AD00091

[0078] 其中,S0 Sb和Sw分别为总体散布矩阵、类间散布矩阵和类内散布矩阵。 [0078] wherein, S0 Sb and Sw respectively total scatter matrix, the between-class scatter matrix and class scatter matrix.

[0079] 步骤九、将测试图像映射到特征子空间内,然后以与训练图像同样的步骤5-8提取测试图像; [0079] Step 9, the test image is mapped to the subspace, then the same training image step 5-8 extracts a test image;

[0080] 步骤十、计算训练图像与测试图像在特征脸空间中对应点之间的欧式距离,以最小欧氏距离作为判据对人脸图像进行识别。 [0080] Step 10, calculating the training image and the test image corresponding to the Euclidean distance between the feature points in the face space to a minimum Euclidean distance as a criterion for the face image recognition.

[0081] 将人脸图像投影到特征子空间,得到相应的人脸特征向量之后,接下来的任务就是如何来判别测试图像所属的类别。 After [0081] The face image projected onto the subspace, the corresponding facial feature vector, the next task is how to determine the category test image belongs. 首先我们要计算出图像之间的相似度,再选择合适的分类器进行分类判别。 First we have to calculate the degree of similarity between the images, and then select the appropriate classifier for classification and discrimination. 这里采用训练图像与测试图像之间的最小欧氏距离作为判据。 Here smallest Euclidean distance between the training image and the test image as a criterion. 欧氏距离也称为欧几里德距离,向量X和Y之间的欧氏距离定义为: Euclidean distance is also referred to as the Euclidean distance, the Euclidean distance between the vectors is defined as X and Y:

Figure CN102982322AD00092

[0083] 假设有m个类别,每类有Ni个样本,则第i类的判别函数为 [0083] Suppose that there are m classes, each class has Ni samples, the class i discriminant function

Figure CN102982322AD00093

[0085] 区别于传统PCA方法以所有人的训练图像协方差矩阵作为产生矩阵,本发明以个人的人脸图像协方差矩阵S」作为产生矩阵,计算产生矩阵的特征值及对应的特征向量,并把特征值从大到小的顺序进行排序,同时对应的特征向量也进行排序,进而求出所有40个人的人脸图像特征子空间W」,j = 1,2,· · ·,40。 [0085] PCA is different from traditional methods to the covariance matrix of all training images is generated as a matrix, the present invention in the individual face image covariance matrix S 'is generated as a matrix, calculated to produce an eigenvalue matrix and corresponding characterized in descending order and the values ​​are sorted, and also the corresponding eigenvectors are sorted, and then find all 40 individuals face image feature subspace W ', j = 1,2, · · ·, 40.

[0086] 步骤七中重构图像的获取过程是针对单个人的特征子空间而获得的,其具体方法为,首先将训练图像Xi根据公式Hij = (X1-Uj) Xffj提取其特征Hij ;其次将特征向量Hij向Wj进行反求,根据公式Yu = WjXHij+μ j重构得到新的人脸图像Yu ;再从原始图像Xi中减去重构图像Yu,得到残差图像。 Obtaining a reconstructed image during VII [0086] Step for the feature subspace is obtained in a single individual, as the specific method, the first training image Xi according to the formula Hij = (X1-Uj) Xffj extract characterized Hij; Second Hij feature vector Wj for the reverse, according to the formula Yu = WjXHij + μ j new reconstructed face image obtained Yu; Yu subtracted from the original image and reconstructed image Xi obtain a residual image.

[0087] 步骤十中将LDA方法应用于权利要求3所述的人脸残差图像中提取人脸图像特征,并实现人脸图像的识别。 Extracting a residual image of the face 3 [0087] Step 10 will be applied to the LDA method claims characterized in face image, and to achieve recognition of the face image.

[0088] 实施例采用了一个公用的人脸数据库,英国剑桥大学的ORL人脸数据库。 [0088] The embodiment employs a public face database, Cambridge University ORL face database. ORL库包含40个人的400幅112X92大小的人脸图像,每人10幅。 ORL library contains 40 individual 400 face images 112X92 size, each 10. 这些图像是在不同时间拍摄的,有姿态、角度、尺度、表情和眼镜等变化。 These images are taken at different times, have attitude, perspective, scale, expression and glasses and other changes. 具体的人脸识别过程归纳如下: Specific recognition process is summarized as follows:

[0089] I、图像预处理 [0089] I, image preprocessing

[0090] 对112X92大小的人脸图像进行预处理,主要包括图像平滑和对比度校正等图像增强以及图像灰度及方差的归一化处理。 [0090] The size of 112X92 face image pre-processing, including the normalization process and gradation image enhancement and image variance image smoothing and contrast correction. 经过预处理之后,所有图像的灰度统一到标准水平,且灰度层次比较分明,同时,为了节省运算的时间及存储量,我们将图像压缩至24X24大小。 After pretreatment, all gray image of unity to the standard level, and relatively distinct gray levels, at the same time, in order to save time and storage operations, we compress the image to 24X24 size.

[0091] 2、特征提取[0092] (I)我们采用随机取数据库中一半图像用于训练,另一半用于识别的做法,即每人的5个样本进行训练的做法,相应剩余的样本进行测试。 [0091] 2, feature extraction [0092] (I) we use randomly half of the image database used for training, the other half is used to identify the practice, i.e., five samples per the practice of the training, the remainder of the respective sample test. 首先对人脸训练图像进行处理,以获取原空间中的原始训练样本矩阵' ;把人脸训练图像按行堆叠为576维的向量,并采用去均值及白化处理将其值归一化为O到I之间。 First, face training image processing, training sample matrix to obtain the original in the original space apos; training the face images in the row vector of 576 dimensions as the stack, and to use the mean value and whitening processing normalized O between I. 这样共形成576X5X40训练样本矩阵V=IV1, V2,, VjI,j = 1,2,. . .,40,式中Vj 为576 X 5 的训练样本矩阵; Such coform 576X5X40 training sample matrix V = IV1, V2 ,, VjI, j = 1,2 ,., 40, where Vj is the training sample matrix of 576 X 5.;

[0093] (2)对应于每个V」,j = 1,2,· · ·,40,以同一类样本的协方差矩阵作为产生矩阵,进而采用PCA方法产生所有人的个人特征脸,即计算产生矩阵的特征值及对应的特征向量,并把特征值从大到小的顺序进行排序,同时对应的特征向量也进行排序,再选择其中一部分构造特征子空间,进而求出所有40类人脸图像的特征子空间W」,j = 1,2,. . .,40。 [0093] (2) corresponding to each V ', j = 1,2, · · ·, 40, to the sample covariance matrix of the same class as the generation matrix using the PCA method of generating further individual characteristics of all faces, i.e., generating calculated eigenvalues ​​and the corresponding eigenvectors and the eigenvalues ​​are sorted in descending order, while also corresponding eigenvectors are sorted, and then select a portion of the structural features subspace, and then find all the humanoid 40 face image feature subspace W ', j = 1,2 ,..., 40.

[0094] (3)将训练图像Xi, i = 1,2,· · ·,200向Wj进行映射,提取其对应于每个特征子空间的图像特征Hij, i = 1,2,..., 200,之后,将Hij, i = 1,2,..., 200向Wj进行反求以获得其自身的重构图像Yu ; [0094] (3) the training images Xi, i = 1,2, · · ·, 200 are mapped to Wj, which extracts the image feature corresponding to each feature subspace Hij, i = 1,2, ... , 200, after which the Hij, i = 1,2, ..., Wj performed to reverse itself in order to obtain a reconstructed image Yu 200;

[0095] (4)从原始图像中减去重构图像,得到残差图像,然后在残差图像中运用LDA方法,根据公式(14) (15) (16)得到系数矩阵; [0095] (4) subtracting the reconstructed image from the original image to obtain a residual image, and residual image using LDA method, a coefficient matrix obtained according to the equation (14) (15) (16);

[0096] (5)将测试图像映射到特征子空间,接下来以与训练图像同样的步骤3-4提取测试图像; [0096] (5) test image feature subspace is mapped to the next step with the same training images 3-4 extracts a test image;

[0097] 3、训练及识别 [0097] 3, and Recognition Training

[0098] 采用最小距离分类器,计算训练图像与测试图像在特征脸空间中对应点之间的欧式距离,训练集中与测试图像间的欧氏距离最小的图像即为最佳匹配,从而实现对人脸图像的识别。 [0098] The minimum distance classifier, the training images computing a test image corresponding to the Euclidean distance between the feature points in the face space, the minimum Euclidean distance between the images in the training set and the test image is the best match to achieve recognize facial image.

[0099]为了更好的说明算法的有效性,我们随机选取每个人的5个样本作为训练图像,剩余的5个样本进行测试。 [0099] In order to better illustrate the effectiveness of the algorithm, we randomly selected five samples of each person as a training image, the remaining five samples tested. 本文实验将重复50次,取其识别率的平均值作为最终的实验结果。 The experiment herein was repeated 50 times, the mean value as the final recognition rate results. 本文的方法与近几年其它的一些人脸识别方法在ORL数据库中的实验结果比较如下表I所示。 The method described herein and in recent years a number of other methods of face recognition results in ORL database comparison shown in Table I below.

Figure CN102982322AD00101

[0101] 表1:不同方法对ORL人脸数据库的识别率比较 [0101] Table 1: Comparison of different methods for the identification of the ORL database

[0102] 通过表I可以看出,在基于ORL的人脸识别实验中,本文提出的人脸识别方法得到的正确识别率为97. 48%,相比于其它的典型的人脸识别方法在识别率上有了较大的提高。 [0102] I can be seen from the table, based on ORL face recognition experiment, recognition obtained by the proposed method 97.48% recognition rate, compared to other typical face recognition method It has been greatly improved the recognition rate. 实验结果说明了该方法能有效的结合PCA和LDA各自的优势,提高人脸识别的准确率[0103] 以上所述,仅为本发明较佳的具体实施方式,但本发明的保护范围并不局限于此,任何熟悉本技术领域的技术人员在本发明揭露的技术范围内,根据本发明的技术方案及其发明构思加以等同替换或改变,都应涵盖在本发明的保护范围之内。 Experimental results show that the method can effectively bind PCA and LDA respective advantages, improve the accuracy of recognition of the [0103] above, the present invention is merely preferred specific embodiments, but the scope of the present invention is not limited thereto, any skilled in the art in the art within the technical scope disclosed by the present invention, according to the present invention and its inventive concept be altered or equivalents should fall within the scope of the present invention.

Claims (4)

1.基于PCA图像重构和LDA的人脸识别方法,其特征在于:包括如下几个步骤: 步骤一、图像预处理对人脸图像I,所述图像I大小为wXh,进行一定的预处理,主要包括图像平滑以及图像灰度和方差的归一化处理,去除尺度大小、光线明暗等因素给识别过程带来的不利影响; 步骤二、从ORL人脸库中随机选取图像作为训练集,剩下的图像作为测试集,读取训练库人脸图像成灰度矩阵形式,并将训练样本以个人进行分类存储成' ; 将单个人的每一幅图像矩阵I按行或列展开成n = wXh维的向量X,并将向量X进行去均值处理以及白化处理,使得白化后的变量协方差矩阵为单位矩阵,利用协方差进行特征值分解,即E(XXT) = PEP1,其中E是正交矩阵E(XXt)的特征值,P是对应的特征向量,得到的白化矩阵为: M = PE-v2Pt (I) 得到白化后的数据: X = Mx (2) 将个人的所有训练图像以nXs (s 1. Face Recognition Based PCA and LDA-based image reconstruction, characterized by: comprising the following steps: Step 1, the face image preprocessing of image I, the image size is WXH I, certain pretreatment , including image smoothing and normalizing the image gray level variance and removed scale size, light shade and other factors to the adverse effects of the recognition process; step two, randomly selected from image ORL database as the training set, the remaining images as the test set, the training corpus read face image to grayscale matrix form, and classify training samples stored as individual '; each of the single individual image matrix I by a row or column to expand into n X = wXh dimensional vector, and the vector X to be processed and the average whitening, such variable covariance matrix is ​​a unit matrix after whitening, covariance eigenvalue decomposition, i.e. E (XXT) = PEP1, wherein E is orthogonal matrix E (XXt) characteristic value, P is the corresponding eigenvector, whitening matrix is ​​obtained: M = PE-v2Pt (I) obtained whitening data: X = Mx (2) all the individual training images to nXs (s 是一个人的所有人脸训练图像数量)矩阵Vj表示。 Is the owner of a number of training face images of people) matrix Vj represents. 步骤三、以个人的人脸图像协方差矩阵Sj = Et(X-Uj) (X-Uj)1]作为产生矩阵,采用PCA方法提取其特征子空间Wj ; 训练样本中的样本均值为# = 毛,以及协方差矩阵S = E[(X-iO (X-iOT] =XXT。 计算每个人的人脸图像协方差矩阵的特征值\及对应的特征向量COp并把特征值从大到小的顺序进行排序,同时对应的特征向量也进行排序,再选择其中一部分构造特征子空间。 步骤四、重复步骤二至步骤三,提取出所有人脸的特征子空间Wj, j = l,2,...,m,其中m为用于训练及识别的人脸类别数量,其包括以下步骤; 每一幅人脸图像投影到子空间以后,就对应于子空间中的一个点,即子空间中的任一点也对应于一幅图像。这些子空间中的点重构以后的图像很像“人脸”,所以称为“特征脸”。因此,任何一张人脸图像都可以向特征脸做投影并获得一组坐标系数:y = WTx,这组系 Step three, individual face image covariance matrix Sj = Et (X-Uj) (X-Uj) 1] as generate a matrix using PCA method for extracting characterized subspace of Wj; sample mean training samples for # = Mao, and covariance matrix S = E [(X-iO (X-iOT] = XXT. calculated for each person's face image co eigenvalues ​​of covariance matrix \ and the corresponding eigenvectors and the eigenvalues ​​in descending COp sorted order, while also corresponding eigenvectors are sorted, and then select a portion configured subspace. step 4 repeat steps two to three step, extracts a feature of all faces subspace Wj, j = l, 2, ..., m, where m is the number of categories used for training and face recognition, comprising the steps of; each face image is projected onto a subspace after it corresponds to a point in the subspace, the subspace i.e. in any point also corresponds to an image. Reconstruction of these points later in the subspace image like "human face", so called "face features". Thus, any one can face image to the face feature do projected and obtaining a set of coefficient coordinates: y = WTx, the set of lines 表明了该图像在子空间中的位置,便可作为人脸识别的依据,也就是这张人脸图像的特征脸特征。 步骤五、将训练图像Xi根据公式(3)提取其特征Hij ; Hij = (Xi-Uj) Xffj, i = 1,2,...,N,j = l,2,...,m (3) 步骤六、将特征向量Hij向Wj进行反求,根据公式(4)重构得到新的人脸图像Yij ; Yij = WjXHi^Uj, i = 1,2,...,N,j = 1,2,…,m (4) 步骤七、从原始图像Xi中减去重构图像Yu,得到残差图像X sBP^ = X->:: 步骤八、在残差图像中运用线性判别分析(LDA)方法进行特征向量提取,根据公式(6)(7) (8)得到系数矩阵; 但是当LDA用于人脸特征提取时,样本图像的维数往往是远大于样本数,造成Sw是奇异的,所以很难根据特征方程SbWj = AjSwWjlJ = 1,2,-,m (5)求解最优投影矩阵。 为解决此小样本问题,采用PCA和LDA相结合的方法,先利用PCA对人脸图像进行降维,使Sw满秩,再运用L Indicate the location of the image in the sub-space, can be used as the basis for face recognition, which is characteristic of this facial feature facial image Step five, the training image Xi (3) extract characterized Hij according to the formula;. Hij = (Xi-Uj) Xffj, i = 1,2, ..., N, j = l, 2, ..., m (3) step 6 Hij feature vector of Wj be the reverse, according to the formula ( 4) Reconstruction of a new face image obtained Yij; Yij = WjXHi ^ Uj, i = 1,2, ..., N, j = 1,2, ..., m (4) step 7 from the original image in Xi subtracting the reconstructed image Yu, to obtain a residual image X sBP ^ = X-> :: step 8 in the residual image using the linear discriminant analysis (LDA) feature vector extraction method, according to the equation (6) (7) ( 8) to give the coefficient matrix; but when the LDA for facial feature extraction, the sample image dimension is much larger than the number of samples is often caused Sw is singular, it is difficult according to the characteristic equation SbWj = AjSwWjlJ = 1,2, - , m (5) to solve the optimal projection matrix. to solve this small sample, the method combining PCA and LDA, first face image using PCA to reduce the dimensionality, so Sw full rank, then the use of L DA进行特征提取,进而实现人脸识别,通过此方法求解的最优投影矩阵可描述为: W1 = W1 W1 ( 6) rvOpt rrIdarv pea =OTgmaxWrS^ (7) WI WtWt SWW jjr v¥ Vy pea vvPcayr / Q\ U ; =argmax~——--18〕 W1KAjvpcaW 其中,S0 Sb和Sw分别为总体散布矩阵、类间散布矩阵和类内散布矩阵。 DA feature extraction, and then face recognition, solved by this process can be described as the optimal projection matrix: W1 = W1 W1 (6) rvOpt rrIdarv pea = OTgmaxWrS ^ (7) WI WtWt SWW jjr v ¥ Vy pea vvPcayr / Q \ U; = argmax ~ ---- 18] W1KAjvpcaW wherein, S0 Sb and Sw respectively total scatter matrix, the between-class scatter matrix and class scatter matrix. 步骤九、将测试图像映射到特征子空间内,然后以与训练图像同样的步骤5-8提取测试图像; 步骤十、计算训练图像与测试图像在特征脸空间中对应点之间的欧式距离,以最小欧氏距离作为判据对人脸图像进行识别。 Step 9, the test image is mapped to the subspace, then the same test procedure as training images to extract image 5-8; Step 10, calculating the training image and the test image corresponding to the Euclidean distance between the feature points in the face space, minimum Euclidean distance to the face image identified as the criterion. 将人脸图像投影到特征子空间,得到相应的人脸特征向量之后,我们采用训练图像与测试图像之间的最小欧氏距离作为判据。 After the face image projected subspace, to give the corresponding face feature vector, we use the minimum Euclidean distance between the training image and the test image as a criterion. 欧氏距离也称为欧几里德距离,向量X和Y之间的欧氏距离定义为: D{XJ) = ^fd(Xi-Vt)1 (9) 假设有m个类别,每类有Ni个样本,则第i类的判别函数为尺.(X) = min X - X1:,/c = I,2,…,N1 (10) k ' Euclidean distance is also referred to as the Euclidean distance, the Euclidean distance between the vectors is defined as X and Y: D {XJ) = ^ fd (Xi-Vt) 1 (9) assuming that there are m classes, each class has Ni samples, the class i discriminant function ft (X) = min X - X1:., / c = i, 2, ..., N1 (10) k '
2.根据权利要求I所述基于PCA图像重构和LDA的人脸识别方法,其特征在于:以个人的人脸图像协方差矩阵I作为产生矩阵,计算产生矩阵的特征值及对应的特征向量,并把特征值从大到小的顺序进行排序,同时对应的特征向量也进行排序,进而求出所有40个人的人脸图像特征子空间W」,j = 1,2,• • •,40。 2. The method according to claim I PCA face recognition and image reconstruction based on the LDA, wherein: the facial image of the covariance matrix I as individual generate a matrix, calculates the feature vector generation eigenvalues ​​and the corresponding , and the characteristic values ​​of the order of descending sort, while the corresponding eigenvectors are also sorted, and then find all 40 individuals face image feature subspace W ', j = 1,2, • • •, 40 .
3.根据权利要求I所述的基于PCA图像重构和LDA的人脸识别方法,其特征在于:步骤七中重构图像的获取过程是针对单个人的特征子空间而获得的,其具体方法为,首先将训练图像Xi根据公式Hij = (Xi-Uj) Xffj提取其特征Hij ;其次将特征向量Hij向Wj进行反求,根据公式Yu = WjXHij+uj重构得到新的人脸图像Yu ;再从原始图像Xi中减去重构图像Yu,得到残差图像。 The recognition method of claim I PCA and LDA-based image reconstruction, as claimed in claim wherein: the reconstructed image acquisition process step VII is for the subspace obtained by a single person, the specific method , for the first training image Xi according to the formula Hij = (Xi-Uj) Xffj extract characterized Hij; secondly Hij eigenvectors of Wj be the reverse, according to the formula Yu = WjXHij + uj obtained reconstructed Yu new face image; minus the reconstructed image from the original image Xi Yu, the residue image.
4.根据权利要求3所述的基于PCA图像重构和LDA的人脸识别方法,其特征在于:步骤八中将LDA方法应用于人脸残差图像中提取人脸图像的特征向量,并实现人脸图像的识别。 4. The method of face recognition PCA and LDA-based image reconstruction, wherein the claim 3: Step Eight LDA method will be applied to the residual image extracting face feature vector of the face image, and to achieve recognize facial image.
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