CN101329724B - An optimized face recognition method and device - Google Patents

Abstract

The invention discloses an optimized human face recognition method and device, which improves the recognition rate of human face images. Its technical solution is: the present invention solves this problem by combining principal component analysis and linear discriminant analysis, that is, principal component analysis is performed before linear discriminant analysis to obtain a relatively low-dimensional space, and then linear analysis is performed on this space. Discriminant analysis, so that the linear discriminant process is effective without causing the within-class scatter matrix to be singular. The present invention first uses principal component analysis to obtain the best description features, and then uses linear discriminant analysis to obtain the best identification features on this basis, thereby greatly reducing the dimension of the face feature space, and finally uses the minimum distance method to classify Recognition, which significantly improves the recognition rate of face images. The invention is applied to face recognition.

Description

An optimized face recognition method and device

technical field

The invention relates to the optimization of a face recognition algorithm, in particular to a face recognition method and device combining principal component analysis (PCA) and linear discriminant analysis (LDA) in face recognition.

Background technique

With the development of society and the advancement of technology, especially the rapid improvement of computer software and hardware performance in recent years, the requirements for fast and efficient automatic identity verification are increasingly urgent. Biometric technology has gained great attention and development in the field of scientific research. Because biological characteristics are the inherent attributes of human beings, they have strong self-stability and individual differences, so they are the most ideal basis for identity verification. Among them, the use of face features for identity verification is the most natural and direct means. Compared with other human biometric identification systems such as fingerprints, iris, and palm prints, face recognition systems are more friendly, convenient, and easy to be accepted by users. Wide range of applications, such as public security monitoring, prison monitoring, judicial certification, civil aviation security inspection, port access control, customs identity verification, bank security, smart ID card, smart access control, smart video surveillance, smart access control, driver Driver's license verification, various bank cards, debit cards, credit cards, savings card holders' identity verification, social insurance identity verification and many other aspects can also be applied to medical care and video conferencing, showing its strong vitality. Face Recognition (Face Recognition) is a technology that uses computers to analyze face images and extract effective identification information from them to identify identities. That is, after the known faces are standardized, they are compared with the face samples in the database by a certain method to find the corresponding face in the database and the relevant information of the face.

Face recognition technology includes face detection, face preprocessing, feature extraction and face recognition. How to effectively extract and recognize features is an important problem in face recognition.

There are two methods of principal component analysis (PCA) and linear discriminant analysis (LDA) in the traditional face recognition technology.

The idea of principal component analysis (PCA) comes from the K-L transformation, the purpose is to find a set of optimal unit orthogonal vectors as the basis of the subspace, and then use their linear combination to reconstruct the original sample, and make the reconstruction in the mean square error It is optimal in the smallest sense; that is, the image area of the entire face is regarded as a random vector, and the high-dimensional vector representing the face is mapped to the subspace formed by several feature vectors through K-L transformation. A linear combination of these eigenfaces is used to describe, express and approximate human face images.

The main parameters involved in principal component analysis are as follows: It is known that there are c types of different people, and each type of people has N _i (i=1, 2, ..., c) face images respectively, then there are a total of training images, that is, there are N known samples of class c, and each class has N _i (i=1, 2, ..., c) face images, that is, N ₁ samples belong to X ₁ class, and N ₂ Samples belong to class X ₂ , N _i samples belong to class X _i , and X _i is the i-th class sample set. Assuming that each face image is w×h pixels, first expand it into a column vector of n=w×h dimension by row or column, then N samples can be simply expressed as: x _i (i=1, 2, ..., N).

The average face of the training sample set is defined as: (Formula 1)

(式2)The vector after training sample centering

(Formula 2)

The covariance matrix C of the training samples: (Formula 3)

The specific steps of principal component analysis are:

(1) Expand each image into a row (or column) of vectors to form a face image matrix, then obtain the average face of the image and center it, and finally obtain the covariance matrix of the samples, that is, Equation 3.

(2) Calculate the eigenvalues and eigenvectors of the covariance matrix C, and arrange the corresponding eigenvectors u _i in the order of the non-zero eigenvalues λ _i from large to small, and the first k eigenvector matrices formed are Eigenface space (projection matrix) U, each column of U is an eigenvector: U=[u ₁ , u ₂ , . . . , u _k ].

投影到投影空间，得到其相应的投影系数，组成投影系数矩阵

此时原本n维的人脸图像就经投影后变成了k维，达到了降维的效果。(3) Each centered training image

Project to the projection space, get its corresponding projection coefficient, and form a projection coefficient matrix

At this time, the original n-dimensional face image becomes k-dimensional after projection, achieving the effect of dimensionality reduction.

也投影到投影空间，得到投影系数矩阵M为测试样本数目，最后用最小欧氏距离进行判别。(4) After centering each test sample, get

Also projected to the projection space, the projection coefficient matrix is obtained M is the number of test samples, and finally the minimum Euclidean distance is used for discrimination.

From the effect of principal component analysis, principal component analysis is based on the least mean square criterion, which minimizes the energy loss of the image and minimizes the error between the reconstructed image and the original image. It has the best representation ability, but not the best Discrimination ability. The principal component analysis method is statistically optimal, which minimizes the mean square error before and after compression, and retains the data component with the largest variance in the original sample (ie, the principal component), which makes the transformed low-dimensional space have a good representation ability , but the training of principal component analysis is unsupervised, that is, the category information of the training samples cannot be used, and the problems of intra-class and inter-class are not considered, but all samples are used together, and there is no best discrimination ability.

Linear discriminant analysis aims at the best separability of samples, trying to find a set of linear transformations to minimize the intra-class scatter of each class and maximize the inter-class scatter, which has the best discrimination ability. That is, after the samples are projected into the linear change space, the samples of the same class can be gathered as much as possible, and the samples of different classes can be separated as much as possible.

The main parameters involved in linear discriminant analysis are as follows:

(式4)The mean value of the i-th sample is:

(Formula 4)

(式5)The intra-class dispersion matrix S _w of the sample:

(Formula 5)

(式6)The between-class scatter matrix S _b of the sample:

(Formula 6)

W可以通过解广义特征值问题S_bW＝S_wWΛ求得。Linear discriminant analysis is to find an optimal linear transformation W to minimize the intra-class dispersion and maximize the inter-class dispersion, that is, to satisfy:

W can be obtained by solving the generalized eigenvalue problem S _b W = S _w WΛ.

When the intra-class dispersion matrix S _w is non-singular, the column vector of the optimal linear transformation W is the eigenvector of S _w ^-1 S _b , and this group of vectors is also called the optimal discriminant vector set.

However, the problem encountered in practical application is that the dispersion matrix within the sample class is usually singular, because the number of samples of training samples is often smaller than the number of sample pixels contained in each sample, such as in the ORL face database, The face image has a pixel size of 112×92, which can be as high as 10304 dimensions after being converted into a vector representation, and the number of training samples is usually much smaller than this number. Therefore, under normal circumstances, face recognition always encounters a "small sample", resulting in the singularity of the intra-class scatter matrix, so that linear discriminant analysis cannot be directly used.

Contents of the invention

The purpose of the present invention is to provide an optimized face recognition method, which improves the recognition rate of face images.

Another object of the present invention is to provide an optimized face recognition device, which improves the recognition rate of face images.

The technical solution of the present invention is: the present invention discloses an optimized face recognition method, which combines principal component analysis and linear discriminant analysis, and the method includes:

计算得到协方差矩阵C，其中N为训练样本的总数，

为训练样本中心化后的向量，M为协方差矩阵C的最大特征值的个数；(1) After centering the training sample set x _i of face images, i=1, 2, ... N, according to the formula

Calculate the covariance matrix C, where N is the total number of training samples,

is the vector after the centering of the training samples, and M is the number of the largest eigenvalues of the covariance matrix C;

其中M≤N-c，c为该训练样本集中的不同的人的人数；(2) Calculate the eigenvectors corresponding to the M largest eigenvalues of the covariance matrix C, and the M eigenvectors form the principal component analysis projection matrix:

Where M≤Nc, c is the number of different people in the training sample set;

(3) Using the principal component to analyze the projection matrix, transform the face image space into a dimensionally reduced eigenface space, and obtain the best description features of the face image:

(4) Calculate the intra-class scatter matrix S _w and the inter-class scatter _matrix S _b composed of y _l , .., y _i , ... y N;

(5) Calculate the eigenvectors W _l ^lda , ..., W _i ^lda , ... W _k ^lda corresponding to the k largest eigenvalues of the matrix S _w ^-1 S _b , where k is the matrix S _w ^-1 S _b The number of the largest eigenvalues, the eigenvectors corresponding to the k largest eigenvalues constitute a linear discriminant analysis projection matrix

(6) Use the linear discriminant analysis projection matrix to further reduce the eigenface space to the k-dimensional optimal discriminant space, and obtain the best classification features of the face image: where i = 1, 2, ... N;

(7) Calculate the transformation matrix W=W _pca W _lda as the final projection direction;

(8) Projecting the test sample and the training sample to the transformation matrix W respectively to obtain respective projection coefficients;

(9) Discriminate based on the minimum Euclidean distance.

The face recognition method of above-mentioned optimization, wherein, in step (1), the centralization of training sample further comprises:

Calculate the average face of the training sample set:

Calculate the centered vector of the training samples

The face recognition method of above-mentioned optimization, wherein, step (4) further comprises:

Calculate the mean value of the i-th sample as:

Calculate the sample within-class scatter matrix S _w composed of y _l , .., y _i , ... y _N :

Calculate the between-class scatter matrix S _b of the sample:

The present invention also discloses an optimized face recognition device, which combines principal component analysis and linear discriminant analysis, and the device includes:

计算得到协方差矩阵C，其中N为训练样本的总数，

为训练样本中心化后的向量，M为协方差矩阵C的最大特征值的个数；The covariance matrix calculation module, after centering the training sample set x _i of face images, i=1, 2, ... N, according to the formula

Calculate the covariance matrix C, where N is the total number of training samples,

is the vector after the centering of the training samples, and M is the number of the largest eigenvalues of the covariance matrix C;

其中M≤N-c，c为该训练样本集中的不同的人的人数；The principal component analysis projection matrix calculation module calculates the eigenvectors corresponding to the M largest eigenvalues of the covariance matrix C, and the M eigenvectors form the principal component analysis projection matrix:

Where M≤Nc, c is the number of different people in the training sample set;

The eigenface space acquisition module uses the principal component analysis projection matrix obtained by the principal component analysis projection matrix calculation module to convert the face image space into a dimensionally reduced eigenface space, and obtains the best description features of the face image:

The scatter matrix calculation module calculates the intra-class scatter matrix S _w and the inter-class scatter matrix S _b composed of y _l , .., y _i , ..y _N ;

The linear discriminant analysis projection matrix calculation module calculates the eigenvectors W _l ^lda , ..., W _i ^lda , ... W _k ^lda corresponding to the k largest eigenvalues of the matrix S _w ^-1 S _b , where k is the matrix S _w ^-1 The number of the largest eigenvalues of S _b , and the eigenvectors corresponding to the k largest eigenvalues form a linear discriminant analysis projection matrix

其中i＝1，2，...N；The optimal discriminative space acquisition module uses the linear discriminant analysis projection matrix to further reduce the dimensionality of the eigenface space to the k-dimensional optimal discriminative space, and obtains the best classification features of the face image:

where i = 1, 2, ... N;

The conversion matrix calculation module calculates the conversion matrix W=W _pca W _lda as the final projection direction;

The projection coefficient calculation module projects the test sample and the training sample to the transformation matrix W respectively to obtain respective projection coefficients;

The discriminant module performs discrimination according to the minimum Euclidean distance.

The above-mentioned optimized face recognition device, wherein the covariance matrix calculation module also includes:

The training sample centralization unit further includes:

The average face calculation unit calculates the average face of the training sample set:

上述的优化的人脸识别装置，其中，散布矩阵计算模块进一步包括：Centralized vector calculation unit, which calculates the vector after the training sample is centered

The above-mentioned optimized face recognition device, wherein the scatter matrix calculation module further includes:

The sample mean calculation unit calculates the i-th sample mean as:

The intra-class scatter matrix calculation unit calculates the sample intra-class scatter matrix _{S w} composed of y _l , .., y _i , ... y _N : $S_w=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\Σ}}}\underset{j=1}{\overset{N_i}{\mathrm{\Σ}}}({\mathrm{the\; y}}_{\mathrm{ij}}-m_i){({\mathrm{the\; y}}_{\mathrm{ij}}-m_i)}^T;$

The inter-class scatter matrix calculation unit calculates the inter-class scatter matrix S _b of the sample: $S_b=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\Σ}}}{N}_i(m_i-m){(m_i-m)}^T.$

Compared with the prior art, the present invention has the following beneficial effects: since the linear discriminant analysis is caused by the singular problem of the intra-class scatter matrix, the present invention solves this problem by combining principal component analysis and linear discriminant analysis, that is, when performing linear discriminant analysis Principal component analysis is performed before the analysis to obtain a relatively low-dimensional space, and then linear discriminant analysis is performed on this space, so that the linear discriminant process is effective without causing the intra-class dispersion matrix to be singular. The traditional linear discriminant analysis makes the inter-class dispersion of the projected samples the largest and the intra-class dispersion the smallest, that is to say, the samples of the same class are gathered together in the new space after projection, and the samples of different classes are separated. Has very good separability. The traditional principal component analysis is to retain the data component with the largest variance in the original sample, so the principal component analysis can best represent the original sample and has the best representation ability, but it has no discrimination ability. The present invention first uses principal component analysis to obtain the best description features, and then uses linear discriminant analysis to obtain the best identification features on this basis, thereby greatly reducing the dimension of the face feature space, and finally uses the minimum distance method to classify Recognition, which significantly improves the recognition rate of face images.

Description of drawings

Fig. 1 is a flowchart of a preferred embodiment of the optimized face recognition method of the present invention.

Fig. 2 is a block diagram of a preferred embodiment of the optimized face recognition device of the present invention.

Fig. 3 is a block diagram of a preferred embodiment of the scatter matrix calculation module of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

The main idea of the present invention is to combine principal component analysis and linear discriminant analysis, and Fig. 1 has shown the flow process of the preferred embodiment of the face recognition method of optimization of the present invention, please see Fig. 1, below is to each in the method A detailed description of the steps.

其中N为训练样本集中的样本数量。Step S100: Calculate the average face m of the training sample set x _i , i=1, 2, ... N:

where N is the number of samples in the training sample set.

Step S101: Calculate the centered vector of the training samples

Step S102: Calculate the covariance matrix:

其中M≤N-c，由不同的人的人脸图像组成这个训练样本集，c是人脸图像的类别数。Step S103: Calculate the eigenvectors corresponding to the M largest eigenvalues of the covariance matrix C, and form the principal component analysis (PCA) projection matrix by these M eigenvectors:

Among them, M≤Nc, the training sample set is composed of face images of different people, and c is the number of categories of face images.

i＝1，2，...N。Step S104: Utilize the principal component analysis projection matrix to transform the face image space into a reduced-dimensional eigenface space, and obtain the best description features of each face image:

i=1, 2, . . . N.

Step S105: Calculate the intra-class scatter matrix S _w and the inter-class scatter matrix S _b composed of y _l , .., y _i , ... y _N .

The specific process of calculating the intra-class scatter matrix S _w and the inter-class scatter matrix S _b is:

The first step: Calculate the mean value of the i-th class sample as:

The second step: Calculate the sample intra-class scatter matrix S _w composed of y _l , .., y _i , ... y _N : $S_w=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\Σ}}}\underset{j=1}{\overset{N_i}{\mathrm{\Σ}}}({\mathrm{the\; y}}_{\mathrm{ij}}-m_i){({\mathrm{the\; y}}_{\mathrm{ij}}-m_i)}^T;$

Step 3: Calculate the inter-class scatter matrix S _b of the sample:

Step S106: Calculate the eigenvectors W _l ^lda , ..., W _i ^lda , ... W _k ^lda corresponding to the k largest eigenvalues of the matrix S _w ^-1 S _b , where k is the matrix S _w ^-1 S _b The number of the largest eigenvalues, the eigenvectors corresponding to the k largest eigenvalues constitute a linear discriminant analysis projection matrix

其中i＝1，2，...N。Step S107: Using the linear discriminant analysis projection matrix to further reduce the dimensionality of the eigenface space to the k-dimensional optimal discriminant space, and obtain the best classification features of the face image:

where i=1, 2, . . . N.

Step S108: Calculate the conversion matrix W=W _pca W _lda as the final projection direction.

Step S109: respectively project the test sample and the training sample to the transformation matrix W to obtain respective projection coefficients.

Step S110: Discriminate according to the minimum Euclidean distance.

The training samples and test samples in this embodiment may be derived from the ORL library, which is a face image database produced by the Bell Labs of the University of Cambridge in 1994 for testing face recognition algorithms. The database includes 10 images of each of 40 people taken at different times, a total of 400 images of 256 gray levels, with a size of 112×92. The face images in the ORL database are front-view images, the tilt and rotation changes are about 20%, and the scale changes are about 10%. In addition, the background light of the face image changes to a certain extent, and the facial expressions are also different (including eyes open and closed, smiling and not smiling, and images with and without glasses).

Corresponding to the method embodiment described above, the present invention also provides an optimized face recognition device, which also combines principal component analysis and linear discriminant analysis. Figure 2 shows a preferred implementation of the face recognition device example. 2, the embodiment of the device includes a covariance matrix calculation module 10, a principal component analysis projection matrix calculation module 11, an eigenface space acquisition module 12, a scatter matrix calculation module 13, a linear discriminant analysis projection matrix calculation module 14, an optimal Discrimination space acquisition module 15 , transformation matrix calculation module 16 , projection coefficient calculation module 17 , and discrimination module 18 .

其中N为训练样本的总数，为训练样本中心化后的向量。协方差矩阵计算模块10中还包括训练样本中心化单元100，在训练样本中心化单元100中进一步包括平均脸计算单元1000和中心化向量计算单元1001。平均脸计算单元1000计算训练样本集的平均脸：

中心化向量计算单元1001计算训练样本中心化后的向量

The covariance matrix calculation module 10 calculates the covariance matrix after centering the training sample set x _i of the face image, i=1, 2, ... N:

where N is the total number of training samples, Centered vector for the training samples. The covariance matrix calculation module 10 also includes a training sample centralization unit 100 , and the training sample centralization unit 100 further includes an average face calculation unit 1000 and a centralization vector calculation unit 1001 . The average face calculation unit 1000 calculates the average face of the training sample set:

The centered vector calculation unit 1001 calculates the vector after the training sample is centered

The principal component analysis projection matrix calculation module 11 calculates the eigenvectors corresponding to the M largest eigenvalues of the covariance matrix C, and the M eigenvectors form the principal component analysis projection matrix: Where M≤Nc, c is the number of different people in the training sample set. The eigenface space obtaining module 12 utilizes the principal component analysis projection matrix obtained by the principal component analysis projection matrix calculation module, converts the face image space into the dimensionally reduced eigenface space, and obtains the projection coordinate vector of each face image: ${\mathrm{the\; y}}_i={({\mathrm{the\; y}}_1^i,{\mathrm{the\; y}}_2^i,...,{\mathrm{the\; y}}_m^i)}^T=W_{\mathrm{pca}}^T(x_i-m),i=\mathrm{1,2},...N.$

类内散布矩阵计算单元131计算由y_l，..，y_i，...y_N构成的样本类内散布矩阵S_w：

类间散布矩阵计算单元132计算样本的类间散布矩阵S_b： The scatter matrix calculation module 13 calculates the intra-class scatter matrix S _w and the inter-class scatter matrix S _b composed of y _l , . . . , y _i , ... y _N . The scatter matrix calculation module 13 can be divided into a sample mean calculation unit 130 , an intra-class scatter matrix calculation unit 131 , and an inter-class scatter matrix calculation unit 132 as shown in FIG. 3 . Wherein the sample mean calculation unit 130 calculates the i-th type sample mean as:

The intra-class scatter matrix calculation unit 131 calculates the sample intra-class scatter matrix _S w composed of y _l , .., y _i , ... y _N :

The inter-class scatter matrix calculation unit 132 calculates the inter-class scatter matrix S _b of the sample:

最佳鉴别空间获得模块15利用线性判别分析投影矩阵将该特征脸空间进一步降维到k维最佳鉴别空间，获得

其中i＝1，2，...N。转换矩阵计算模块16计算转换矩阵W＝W_pcaW_lda，以作为最后的投影方向。投影系数计算模块17将测试样本和训练样本分别投影到转换矩阵W，获得各自的投影系数。最后由判别模块18根据最小欧氏距离进行判别。The linear discriminant analysis projection matrix calculation module 14 calculates the eigenvectors W _l ^lda , ..., W _i ^lda , ... W _k ^lda corresponding to the k largest eigenvalues of the matrix S _w ⁻¹ S _b , wherein k is the matrix S _w ^-1 The number of the largest eigenvalues of S _b ; the eigenvectors corresponding to the k largest eigenvalues form a linear discriminant analysis projection matrix

The best discrimination space obtaining module 15 utilizes the linear discriminant analysis projection matrix to further reduce the dimensionality of the eigenface space to the k-dimensional best discrimination space, and obtains

where i=1, 2, . . . N. The transformation matrix calculation module 16 calculates the transformation matrix W=W _pca W _lda as the final projection direction. The projection coefficient calculation module 17 respectively projects the test sample and the training sample to the transformation matrix W to obtain respective projection coefficients. Finally, the discrimination module 18 conducts discrimination according to the minimum Euclidean distance.

Principal component analysis is a simple and practical algorithm based on transform domain coefficients. It is optimal from the perspective of compressing energy. It not only minimizes the mean square error before and after dimension reduction, but also has a low-dimensional space after transformation. Very good face representation ability, but not very good face discrimination ability. Linear discriminant analysis starts from the separability of the samples, and the purpose is to find a space where the samples are projected onto this space to have the best separability, but in practical applications, the "small sample" problem is often encountered. The present invention combines principal component analysis and linear discriminant analysis, solves the small sample problem, and improves the face recognition rate, which is a very good face recognition method.

The above-mentioned embodiments are provided for those of ordinary skill in the art to implement or use the present invention. Those of ordinary skill in the art can make various modifications or changes to the above-mentioned embodiments without departing from the inventive idea of the present invention. Therefore, the present invention The scope of protection of the invention is not limited by the above-mentioned embodiments, but should be the maximum scope consistent with the innovative features mentioned in the claims.

Claims (2)

1. An optimized face recognition method that combines principal component analysis and linear discriminant analysis, the method comprising: (1) The training sample set x _i of the face image, i=1, 2, ... N, the training sample set includes N samples x _i , after centering, according to the formula

Calculate the covariance matrix C, where N is the total number of training samples,

Be the vector after the centering of the training samples, M is the number of the largest eigenvalue of the covariance matrix C, in step (1), the centering of the training samples further includes: Calculate the average face of the training sample set: $m=\frac{1}{N}\underset{i=1}{\overset{N}{\∑}}{x}_i;$ Calculate the centered vector of the training samples

${\stackrel{\&OverBar;}{x}}_i=x_i-m;$ (2) Calculate the eigenvectors corresponding to the M largest eigenvalues of the covariance matrix C, and the M eigenvectors form the principal component analysis projection matrix: $W_{\mathrm{pca}}=[W_1^{\mathrm{pca}},...,W_2^{\mathrm{pca}},...{,W}_m^{\mathrm{pca}}],$ Where M≤Nc, c is the number of categories of face images; (3) Using the principal component to analyze the projection matrix, transform the face image space into a dimensionally reduced eigenface space, and obtain the best description features of the face image: ${\mathrm{the\; y}}_i=W_{\mathrm{pca}}^T(x_i-m),$ i=1,2,...N; (4) Calculating the intra-class scatter matrix S _w and the inter-class scatter matrix S _b composed of y ₁ , ..., y _i , ... y _N , step (4) further includes: Calculate the mean of training samples of class i as: $m_i=\frac{1}{N_i}\underset{\mathrm{the\; y}\&Element;Y_i}{\&Sum;}\mathrm{the\; y},$ N _i is the number of training samples under each type of training samples; Calculate the intra-class scatter matrix S _w of the training samples composed of y ₁ , .., y _i , ... y _N : ${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; \&Sum;</span>}}\underset{\text{<span class="notranslate"> j=1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{<span\; class="notranslate">\; \&Sum;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; ;</span>$ Calculate the inter-class scatter matrix S _b of the training samples: $S_b=\frac{1}{N}\underset{i=1}{\overset{c}{\&Sum;}}{N}_i(m_i-m){(m_i-m)}^T;$ (5) Calculate the eigenvectors _{W 1} ^lda , ..., W _i ^lda , ... W _k ^lda corresponding to the k largest eigenvalues of the matrix S ^{w -1} S _b , where k is the matrix S _w ^-1 S _b The number of the largest eigenvalues, the eigenvectors corresponding to the k largest eigenvalues constitute a linear discriminant analysis projection matrix $W_{\mathrm{lda}}=[W_1^{\mathrm{lda}},...,W_2^{\mathrm{lda}},...,W_k^{\mathrm{lda}}];$ (6) Use the linear discriminant analysis projection matrix to further reduce the eigenface space to the k-dimensional optimal discriminant space, and obtain the best classification features of the face image: $z_i=W_{\mathrm{lda}}^T{\mathrm{the\; y}}_i,$ where i = 1, 2, ... N; (7) Calculate the transformation matrix W=W _pca W _lda as the final projection direction; (8) Projecting the test sample and the training sample to the transformation matrix W respectively to obtain respective projection coefficients; (9) Discriminate based on the minimum Euclidean distance. 2. An optimized face recognition device that combines principal component analysis and linear discriminant analysis, the device includes: The covariance matrix calculation module takes the face image training sample set x _i , i=1, 2, ... N, the training sample set includes N samples x _i , after centering, according to the formula Calculate the covariance matrix C, where N is the total number of training samples,

Be the vector after training sample centering, M is the number of the maximum eigenvalue of covariance matrix C, and this covariance matrix calculation module also includes: The training sample centralization unit further includes: The average face calculation unit calculates the average face of the training sample set: $m=\frac{1}{N}\underset{i=1}{\overset{N}{\&Sum;}}{x}_i;$ Centralized vector calculation unit, which calculates the vector after the training sample is centered ${\stackrel{\&OverBar;}{x}}_i:{\stackrel{\&OverBar;}{x}}_i=x_i-m;$ The principal component analysis projection matrix calculation module calculates the eigenvectors corresponding to the M largest eigenvalues of the covariance matrix C, and the M eigenvectors form the principal component analysis projection matrix: $W_{\mathrm{pca}}=[W_1^{\mathrm{pca}},...,W_2^{\mathrm{pca}},...,W_m^{\mathrm{pca}}],$ Where M≤Nc, c is the number of categories of face images; The eigenface space acquisition module uses the principal component analysis projection matrix obtained by the principal component analysis projection matrix calculation module to convert the face image space into a dimensionally reduced eigenface space, and obtains the best description features of the face image: ${\mathrm{the\; y}}_i=W_{\mathrm{pca}}^T(x_i-m),i=\mathrm{1,2},...N;$ The scatter matrix calculation module calculates the intra-class scatter matrix S _w and the inter-class scatter matrix S _b composed of y ₁ , ..., y _i , ... y _N , and the scatter matrix calculation module further includes: The sample mean value calculation unit calculates the mean value of the i-th type of training samples as: $m_i=\frac{1}{N_i}\underset{\mathrm{the\; y}\&Element;Y_i}{\&Sum;}\mathrm{the\; y},$ N _i is the number of training samples under each type of training samples; The intra-class scatter matrix calculation unit calculates the intra-class scatter matrix S _w of the training samples composed of y ₁ , .., y _i , ... y _N : $S_w=\frac{1}{N}\underset{i=1}{\overset{c}{\&Sum;}}\underset{j=1}{\overset{N_i}{\&Sum;}}({\mathrm{the\; y}}_{\mathrm{ij}}-m_i){({\mathrm{the\; y}}_{\mathrm{ij}}-m_i)}^T;$ The inter-class scatter matrix calculation unit calculates the inter-class scatter matrix S _b of the training samples: ${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; \&Sum;</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; ;</span>$ The linear discriminant analysis projection matrix calculation module calculates the eigenvectors W ₁ ^lda , ..., W _i ^lda , ... W _k ^lda corresponding to the k largest eigenvalues of the matrix S _w ^-1 S _b , where k is the matrix S _w ^-1 The number of the largest eigenvalues of S _b , and the eigenvectors corresponding to the k largest eigenvalues form a linear discriminant analysis projection matrix $W_{\mathrm{lda}}=[W_1^{\mathrm{lda}},...,W_2^{\mathrm{lda}},...,W_k^{\mathrm{lda}}];$ The optimal discriminative space acquisition module uses the linear discriminant analysis projection matrix to further reduce the dimensionality of the eigenface space to the k-dimensional optimal discriminative space, and obtains the best classification features of the face image: $z_i=W_{\mathrm{lda}}^T{\mathrm{the\; y}}_i,$ where i = 1, 2, ... N; The conversion matrix calculation module calculates the conversion matrix W=W _pca W _lda as the final projection direction; The projection coefficient calculation module projects the test sample and the training sample to the transformation matrix W respectively to obtain respective projection coefficients; The discriminant module performs discriminant according to the minimum Euclidean distance.

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