Face recognition technology based on low-rank joint sparse representation algorithm

Abstract

With the improvement of computer computing power and the development of artificial intelligence technology, face recognition technology has made a major breakthrough, and has been popularized and applied in all areas of life. However, different face structure and pose will affect the accuracy of face recognition. To overcome the problem, a low rank joint sparse representation algorithm for face recognition is proposed. The low rank features of images are extracted by structure independent and pairwise rank decomposition methods. The extracted low rank features of the first level image and the low rank features of the second level image are sparsely represented. Finally, the residual rate model is used to classify the images, and the final result of face recognition is obtained. The experimental results show that the proposed SRP algorithm has a recognition accuracy of more than 92% in two different face recognition tests. In the mixed multi face pose test, PRS algorithm performs best in the recognition of 1, 2, 3, 4, and 5 multi face pose types, with recognition rates of 95%, 94%, 93%, 91%, and 90% respectively. The algorithm also has excellent recognition performance and robustness in identifying harsh environments such as fuzzy environments. The research content focuses on complex face recognition scenes, innovatively uses low rank to complete the extraction of face feature data, and combines sparse selection of classification features to improve the overall effect of face recognition. It has important reference value for improving the overall security and recognition rate of face recognition.

Keywords

Low-rank decomposition face recognition s-parse representation feature extraction

1. Introduction

Face recognition technology is an important part of the development of pattern recognition and computer vision. Face recognition technology has a very wide range of applications in medical, security, electronic product security and other fields [1, 2], especially face recognition technology has outstanding advantages and application prospects in the field of security. Due to the differences in the facial contour features of each person, face recognition technology can record the facial feature data of different people, and use the facial feature data as a credential for secure identification [3]. The key of face recognition technology is the extraction and recognition of face contour information, but in the research of face recognition technology, the collection of face information is affected by many factors. Factors such as lighting, facial expression, posture, and extraction environment will affect the entire face recognition effect. With the development of computer artificial intelligence technology and face recognition algorithm technology, modern face recognition technology has been significantly improved [3, 4, 5]. In spite of this, there are still many problems to be solved in the face recognition process, such as rich facial expressions, contour changes will obviously affect the extraction of recognition technical features, and lighting environment and facial occlusion environment will increase the difficulty of face recognition, with low recognition accuracy. Therefore, in order to solve these problems, combined with computer intelligence technology, face feature recognition technology is proposed. Therefore, combined with computer intelligence technology, a face feature recognition technology is proposed. The research uses the current popular low-rank joint sparse expression face recognition algorithm to extract complex contour face features, and expresses the low-rank image features in a sparse form, and realizes the classification of the image through the residual rate model. In the research, the existing face recognition algorithms are studied, and low rank, sparse representation and other technologies are adopted to improve the face recognition effect considering the innovation of face occlusion environment. At the same time, consider lighting, face pose and other scenes, and optimize the face recognition scene through modeling research, so as to effectively improve the effect of face authentication and face recognition in monitoring state.

2. Related work

Face recognition technology is an important development direction in the field of computer vision, and researchers at home and abroad have carried out a lot of research on face recognition technology. Wu [6] found that during the COVID-19 pandemic, wearing a mask is common but affects face recognition. Therefore, an attention mechanism-based masked face recognition algorithm is proposed. And the use of hole convolution to solve the problem of resolution reduction in the sampling process, the results show that the algorithm has a better recognition accuracy. Wang and Deng [7] found that neural networks still face difficulties in face recognition tasks, and proposed a new clustering-based domain adaptation method for face recognition tasks where the source and target domains do not share any classes. The experimental results show that the method has good performance. A novel coupled similarity reference encoding model is proposed for age-invariant face recognition [8], where non-negative constraints and coupled similarity measures are introduced, and experimental results show that the model can be combined with deep networks for better performance. Plichoski et al. [9] found that there are still problems with face-captured images, so the proposed FR framework is defined by an optimizer and a series of preprocessing and feature extraction techniques to find the best set of policies, and experimental results show that this framework is competitive for FR systems. Trigloss et al. [10] proposed a new Generative Adversarial Network (GAN) that can separate identity-related attributes from non-identity-related attributes for better face recognition performance, and the results show that our method is more effective, significantly improving Accuracy of face recognition ability when adding small datasets. Lin et al. [11] proposed a Deep Representation Alignment Network (DRA Net) that considers factors such as lighting and facial recognition expressions. The results show that the proposed DRA-Net algorithm has excellent performance. Zaman [12] found that normalized Gabor features can be well applied in the field of face recognition. However, the large number and size of projected features can affect face recognition, so a streaming learning method called Local Linear Embedding (LLE) is used to optimize this problem by simultaneously and locally reducing Gabor features. The results show that the method improves the feature compression rate of LGFV features to 95% of the total dimension, and the recognition accuracy is greatly improved. Lin et al. [13] found that facial features can exploit photos to fool the recognition system, so the proposed feature extraction method converts thermal images into features to solve this problem. The results show that the RGB image has good recognition performance with an accuracy of only 0.834 and a feature matrix of 0.967. Zhang et al. [14] proposed several joint feature and dictionary learning methods to achieve low misclassification by implicitly assuming that all misclassifications have the same cost. In experimental tests for image-based face recognition, the algorithm outperforms many state-of-the-art methods.

The above analysis shows that face recognition technology has made great progress in recent years, but face recognition algorithms still face many problems in face feature extraction. Based on traditional machine learning, Wright et al. [15] propose a sparse representation face recognition algorithm based on sensor theory. Test data is represented by a sparse linear combination sample dictionary, which can make face recognition samples achieve good training effect and significantly improve face recognition effect. Liu et al. [16] proposed a new image fusion method based on nonlocal low rank tensor approximation and sparse representation. Non local low rank constraints are used to form non local similarity and spatial spectral correlation, and sparse constraints are added to describe the sparsity of abundance. Experiments show that this method can improve the effect of feature extraction of data images and has good performance. Keinert et al. [17] proposed a method based on group sparse representation and applied it to face recognition. The new sparse representation variational model includes the penalty caused by nonconvex sparsity and the robust nonconvex loss function. The loss function is selected to make the algorithm robust to noise, occlusion and camouflage. The final experimental results show that the technology has a good application effect in face recognition. Xue et al. [18] found that the compressed perceptual reconstruction of hyperspectral images faces problems in the field of image recognition. Therefore, a non-local tensor sparse and low rank regularization method was proposed, which can encode the basic structural sparsity of HSI and explore its advantages in face recognition tasks. Ethics tests on various HSI datasets show that the scheme has good performance effects.

In terms of face recognition technology, although sparse representation can improve the effect of face recognition, the overall recognition effect of this technology will significantly decline when the situation is blocked or the light environment is poor. So. In view of the shortcomings of sparse representation in face recognition, Candès et al. [19] proposed a low rank matrix algorithm to recover contaminated data samples from the original test data. The recovered data image can more accurately describe the training sample information, significantly improving the extraction effect of face recognition features. Chen et al. [20] studied the existing man to man recognition technology and found that the matrix regression with kernel norm can improve the recognition effect in the face occlusion environment, but considering the continuity of face recognition and the low rank structure of the image. Therefore, L1 norm can reveal the natural sparsity of the representation better than L2 norm, and a sparse regularization algorithm is proposed. Finally, it is tested in the classic face recognition database, and the scheme can significantly improve the effect of face recognition. At the same time, restoring the low rank error map in the case of severe occlusion and light changes can significantly improve the recognition effect.

It can be seen from relevant domestic research that face recognition technology is currently facing problems such as data security, low recognition rate of facial feature contour, etc. However, the application of deep learning technology in the face field has improved the problems faced by face recognition. Therefore, on this basis, combined with neural network algorithm for in-depth discussion. The low rank sparse representation algorithm is used to optimize the face recognition parameters to improve the current problems faced by face recognition in complex face environments.

3. Construction of face recognition model based on low-rank joint sparse expression algorithm

3.1 Low-rank decomposition and sparse representation model building

In the field of face recognition technology, complex contour feature parameters of faces belong to high-dimensional data. Mapping high-dimensional spatial data to low dimensional space still faces many technical problems. Therefore, principal component analysis (PCA) is a popular dimensionality reduction technology when high-dimensional face data is processed in low dimensions, but PCA is generally used for image denoising. Therefore, considering the robustness, Candès et al. [19] proposed the Robust Component Analysis (RPCA), which is mainly applicable to the processing of low rank and sparse content.

In low rank decomposition, Assume that $X$ is the data matrix, low rank decomposition of the data leads to matrix $E$ and matrix $Z$ respectively. Among them, the matrix $E$ represents the sparse content after $Z$ data decomposition, and represents the low-rank content after data decomposition. RPCA analysis method needs to deal with the problem of data minimization, as shown in Eq. (1).

$\displaystyle\min\textit{rank}(Z)+\|E\|_{0}$ (1)

In Eq. (1), $\textit{rank}(Z)$ the approximation operator of the matrix is expressed $Z$ . In order to understand the solution problem in Eq. (1), the $\ell_{0}$ approximation operator and the parameterization are generally transformed to obtain the $\ell_{1}$ parameterization and the transformed kernel parameterization. The objective function of low rank decomposition is shown in Eq. (2).

$\displaystyle\left\{{\begin{array}[]{l}\mathop{\min}\limits_{Z,E}\|Z\|_{*}+% \lambda\|E\|_{1}\\ s.t.\,X=Z+E\\ \end{array}}\right.$ (2)

In Eq. (2), it $\|Z\|_{*}$ represents the core parameterization of the matrix, which represents the $Z$ sum of all heterogeneous values, and the $\ell_{1}$ parameterization represents the sum of the absolute values of all elements contained in the matrix $Z$ .

In the sparse expression part, usually the image data in image recognition comes from multiple different subspaces. The error matrix of the image can be reconstructed by using the sparsity of multiple image features to improve the face recognition effect. The principle of constructing the sparse matrix is shown in Fig. 1.

Figure 1.

Construction principle of sparse matrix.

Assuming that the sparse classification SRC is as follows, the image to be tested $y$ is represented by the coefficients of the $D$ codebook, where the codebook expression is shown in Eq. (3).

$\displaystyle\left\{{\begin{array}[]{l}D=[{D_{1},D_{2},\ldots D_{K}}]\in R^{d% \times m}\\ D_{k}\in R^{d\times mk}\\ \end{array}}\right.$ (3)

$D_{k}$ A training matrix representing images, where $m k$ represents the number of training samples. Use the SRC algorithm to solve the number of parameters and sparse representation of the training image $\ell_{1}$ , as shown in Eq. (4).

$\displaystyle\mathop{\min}\limits_{a}\|{y-Da}\|^{2}_{2}+\lambda\|a\|_{1}$ (4)

Image recognition is accomplished by inputting image data $y$ , as shown in Eq. (5).

$\displaystyle\mathop{\ell}\limits^{*}=\mathop{\min}\limits_{i}\|{y-D\delta i(a% )}\|_{2}^{2}$ (5)

In Eq. (5), $D\delta i(a)$ a vector is represented. Then, through the $y$ image recognition process, the image is identified as the class with the smallest residual coefficient parameter, and the dictionary is reconstructed. The principle of face recognition based on the low-rank joint sparse expression algorithm is shown in Fig. 2.

Figure 2.

Principle of face recognition based on low-rank joint sparse expression algorithm.

3.2 Construction of multi-pose face recognition model based on low-rank joint sparse representation algorithm

Considering the diversity of facial feature pose in face recognition environment, only low rank decomposition and sparse expression algorithms can not solve this problem well. On this basis, a hybrid pose effective face recognition algorithm is proposed to better judge and recognize similar face data. Two different regular terms are added to the objective function for two effective low order learning, which reduces the impact of similar pose feature data on face recognition, and expands the recognition judgment of different facial category features. Then, the face recognition process of the multi pose face recognition algorithm is shown in Fig. 3.

Figure 3.

The face recognition process of the multi-pose face recognition algorithm.

In Fig. 3, the red block diagram area represents the standard SRC algorithm, and the blue area is the proposed new algorithm. The standard SRC algorithm training dictionary does not carry out the training of image feature extraction, so it is easy to be interfered by multiple pose features of the image when processing the mixed image data. The new algorithm realizes the data recognition of face pose structure and face type through three parts of cooperation. At the same time, regular terms are added to the two low rank feature decomposition of the new algorithm, and the two low rank features are sparsely represented by the dictionary reconstruction residuals in the classification, and the classification effect of image features is achieved through the residual rate model. Then, assuming that it $X=[{X_{1},\ldots,X_{k}}]$ is a multi-pose image feature, a posture data is that each posture data has a $X_{k}\in R^{d\times m_{k}}$ face $m_{k}$ category $c$ in each posture data, is the sample size of each posture data, and $d$ is the vectorization process of each image. aspect. Then, the basic model is shown in Eq. (6).

$\displaystyle\left\{{\begin{array}[]{l}\mathop{\min}\limits_{Z_{c},Z_{v},E}% \textit{rank}(Z_{c})+\textit{rank}(Z_{v})+\lambda\|E\|_{1}\\ s.t.\,X=X(Z_{C}+Z_{V})+E\\ \end{array}}\right.$ (6)

In Eq. (6), the resistance content of the $Z_{c}$ face category structure $Z_{v}$ is represented, and the resistance content of the face pose structure is represented. After the decomposition model of Eq. (6), the obtained low-rank content can better describe the global information of the face, then the principle process of this decomposition is shown in Fig. 4.

Figure 4.

Flow chart of the principle of dual low-rank decomposition.

Figure 4 shows the principle process of pairwise low-rank decomposition, where the same color represents the same attribute face category, and the same shape represents the same face pose. There is an interactive relationship between the two structural features obtained by decomposition. To remove the interference between them, a supervised regularization term is added to the decomposition model to guide the efficient decomposition of low-rank pairs. Positive parameters $\lambda$ , $\lambda_{1}$ , $a$ , and, are added to $\varphi$ the decomposition model to balance the low-rank content of faces, deal with redundant anomalies, determine the parameters of the experimental loop, and deal with the low-rank content poses of faces. The objective optimization model for adding normative terms is shown in Eq. (7).

$\displaystyle\left\{{\begin{array}[]{l}\mathop{\min}\limits_{P,Z_{c},Z_{v},E}% \lambda\|{E_{c}}\|_{*}+\varphi\|{Z_{v}}\|_{*}+\lambda\|E\|_{1}+a\Omega(P,Z_{c}% ,Z_{y})\\ s.t.\,P^{T}X=P^{T}X(Z_{c}+Z_{v})+E,P^{T}P=1_{P}\\ \end{array}}\right.$ (7)

In Eq. (7), $\Omega(P,Z_{c},Z_{y})$ represents the regular term, $P$ represents the subspace learned after processing, and $P^{T}P=1_{P}$ represents the orthogonal constraint, which can avoid redundant solutions. In the low-dimensional learning space, the low-dimensional features of the pose category $Y_{v}=P^{T}XZ_{v}(Y_{v}\in R^{p\times m})$ are defined as, and the low-dimensional features of the face category are defined as $Y_{c}=P^{T}XZ_{c}(Y_{c}\in R^{p\times m})$ . Then the expression of the regular term is $\Omega(P,Z_{c},Z_{y})$ shown in Eq. (8).

$\displaystyle\Omega(P,Z_{c},Z_{y})=tr(P^{T}XZ_{c}L_{c}(P^{T}XZ_{c})^{T})-\beta tr% (P^{T}XZ_{v}L_{v}(P^{T}XZ_{v})^{T})$ (8)

In Eq. (8), it $\beta$ represents the parameter and takes the value 1. The improved expression of the pairwise rank decomposition objective function is shown in Eq. (3.2).

$\displaystyle\mathop{\min}\limits_{P,Z_{c},Z_{v},E,Q}\lambda\|{E_{c}}\|_{*}+% \varphi\|{Z_{v}}\|_{*}+\lambda\|E\|_{1}+a\Omega(P,Z_{c},Z_{y})$ $\displaystyle\quad{}+\langle{Q.P^{T}X-P^{T}X(Z_{c}+Z_{v})-E}\rangle$ (9) $\displaystyle\quad{}+\frac{\mu}{2}\|{P^{T}X-P^{T}X(Z_{c}+Z_{v})-E}\|_{F}^{2}$

In Eq. (3.2), $\mu$ represents the penalty factor, $Q$ represents the Lagrange multiplier, and $\langle\cdot\rangle$ is the matrix inner product. In the optimization of the objective function, considering that the Lagrange multiplier complicates the operation, the objective equations are combined to obtain the transformed objective, as shown in Eq. (10).

$\displaystyle\mathop{\min}\limits_{P,Z_{c},Z_{v},E,Q}\lambda\|{E_{c}}\|_{*}+% \varphi\|{Z_{v}}\|_{*}+\lambda\|E\|_{1}+h(P,Z_{c},Z_{v},E,Q,\mu)-\frac{\mu}{2}$ (10)

In the objective function, the structure-independent low-rank increases the sub-item of the classification content to eliminate the interference of similar poses in the image and improve the face recognition ability. However, in the general face recognition process, the five features of human senses often interfere with the classification results. Therefore, the regularization term of the F parameter is added to the traditional low-rank decomposition model to enhance the recognition ability of the five sensory data of the face and reduce the interference of the similar pose of the face to the classification model. The optimized objective function is expressed as Eq. (11).

$\displaystyle\left\{{\begin{array}[]{l}\mathop{\min}\limits_{Z,E}\sum\limits_{% i=1}^{K}{\{{\|{Z_{i}}\|_{*}+\lambda\|{Z_{i}}\|_{1}}\}+n\sum\limits_{j\neq i}{% \|{Z_{j}^{T}B_{i}}\|_{F}^{2}}}\\ s.t.\,X_{i}=Z_{i}+E_{i},i=1,2,\ldots,k\\ B_{i}=Z_{i}\\ \end{array}}\right.$ (11)

In Eq. (11), $Z_{i}$ represents the low-rank content of face recognition, represents the low-rank content of face recognition $i$ , $B_{i}$ represents $Z_{j}$ sparse $E_{i}$ abnormal data, and $B_{i}$ represents auxiliary variables. When solving the objective, the augmented Lagrange multiplier method is introduced, and the objective function and constraint expressions are shown in Eq. (12).

$\displaystyle\left\{{\begin{array}[]{l}f(A)=\|{Z_{i}}\|_{*}+\lambda\|{E_{i}}\|% _{1}+n\sum\limits_{j\neq i}{\|{Z_{j}^{T}B_{i}}\|_{F}^{2}}\\ h_{1}(A)=X_{i}-Z_{i}-E_{i},h_{2}(A)=B_{i}-Z_{i}\\ h(A)=[{h_{1}(A);h_{2}(A)}]\\ \end{array}}\right.$ (12)

In Eq. (12), let $A=(Z_{i},B_{i},E_{i})$ , then the Lagrangian expansion function expression is obtained, as shown in Eq. (13).

$\displaystyle L(A,Q,\mu)=f(A)+\langle{\Phi,h(A)}\rangle+\frac{\mu}{2}\|{h(A)}% \|_{F}^{2}$ (13)

In Eq. (13), $\mu$ denote the penalty factor, $\Phi$ denoting the Lagrangian multiplier, where $\Phi=(Q_{i},V_{i})$ substituting Eq. (12) into Eq. (13) yields the Lagrangian expansion, as shown in Eq. (14).

$\displaystyle L(Z_{i},B_{i},E_{i},Q,V_{i},\mu)=\|{Z_{i}}\|_{*}+\lambda\|{Z_{i}% }\|_{1}+n\sum\limits_{j\neq i}{\|{Z_{j}^{T}B_{i}}\|_{F}^{2}}{}+\langle{V_{i},B% _{i}-Z_{i}}\rangle+\frac{\mu}{2}\|{h(A)}\|_{F}^{2}{}+\langle{Q_{i},X_{i}-Z_{i}% -E_{i}}\rangle+\frac{\mu}{2}\|{X_{i}-Z_{i}-E_{i}}\|_{F}^{2}$ (14)

It is iteratively updated according to the face recognition type, and the $t+1$ expression of the iteration variable is shown in Eq. (15).

$\displaystyle Z_{i}[{t+1}]=\mathop{\arg\min\psi\|{Z_{i}}\|_{*}+\frac{1}{2}}% \limits_{Z_{i}}\|{A_{a}-Z_{i}}\|_{F}^{2}$ (15)

In Eq. (15), define $\psi=(2\mu[t]^{2})$ and then further derive Eq. (16).

$\displaystyle A_{a}=0.5(X_{i}-E_{i}[t]+(1/\mu)Q[t],B_{i}[t]+(1/\mu[t])V_{i}[t])$ (16)

The core paradigm of Eq. (15) can be solved by singular thresholding and then $E_{i}$ updated as shown in Eq. (17).

$\displaystyle E_{i}[{t+1}]=\mathop{\arg\min{\varepsilon}^{\prime}}\limits_{B_{% i}}\|{E_{i}}\|_{1}+\frac{1}{2}\sum\limits_{j\neq i}{\|{A_{e}-E_{i}}\|}_{F}^{2}$ (17)

In Eq. (17) ${\varepsilon}^{\prime}=(\lambda/\mu^{k})$ , is ${\varepsilon}^{\prime}=(\lambda/\mu^{k})A_{e}=X_{i}-Z_{i}[{t+1}]+(1/\mu^{k})Q_% {i}[t]$ defined, and $B_{i}$ is updated after the shrinkage calculation, as shown in Eq. (3.2).

$\displaystyle B_{i}[{t+1}]=\mathop{\arg\min\eta}\limits_{B_{i}}\sum\limits_{j% \neq i}{\|{Z_{j}^{T}[{t+1}]B_{i}}\|}_{F}^{2}$ (18) $\displaystyle\quad{}+\langle{V_{i}[t],B_{i}-Z_{i}[{t+1}]}\rangle+\frac{\mu[t]}% {2}\|{B_{i}-Z_{i}[{t+1}]}\|_{F}^{2}$

In Eq. (3.2), $\eta$ denote the parameter value. Furthermore, if the spread $B_{i}$ bias is zero, $B_{i}$ an updated expression is obtained, as shown in Eq. (19).

$\displaystyle B_{i}[{t+1}]=\left({2n\sum\limits_{j\neq i}{Z_{j}[{t+1}]}(Z_{j}[% {t+1}]^{T}+\mu[t]{\rm I}}\right)^{-1}(\mu[t]Z_{i}[{t+1}]-V_{i}[t])$ (19)

In the low rank joint sparse representation multi pose face recognition algorithm, the face discrimination basis only uses a single set of features to obtain the minimum residual, so the residual rate comparison model is used to obtain the minimum residual data of two features. The SRC category of the first type of low-rank feature $C_{d}R^{d}_{\min 1}$ is set as the $C_{s}$ minimum residual, and the $R^{s}_{\min 1}$ second $R^{d}_{\min 2}$ small residual is $R^{s}_{\min 2}$ . The mathematical expression of the rate model is shown in Eq. (20).

$\displaystyle\left\{{\begin{array}[]{l}r_{d}=\frac{R^{d}_{\min 2}-R^{d}_{\min 1% }}{R^{d}_{\min 1}}\\ r_{s}=\frac{R^{s}_{\min 2}-R^{s}_{\min 1}}{R^{s}_{\min 1}}\\ \end{array}}\right.$ (20)

The classification recognition corresponding to Eq. (20) is shown in Eq. (21).

$\displaystyle C=\left\{{\begin{array}[]{ll}C_{d}&\mbox{if }r_{d}>r_{s}\\ C_{s}&\mbox{or}\\ \end{array}}\right.$ (21)

In Eq. (21), $C$ is the final classification result obtained.

4. Performance test of face recognition algorithm

4.1 Face recognition test under different feature dimensions

In order to verify the performance of the proposed low-rank joint sparse expression multi-pose face recognition algorithm (PRS), the algorithm performance analysis will be carried out in the AR and CMU PIE C27 face database, and the principal components (PCA) and coefficient expressions (SRC) will be selected. SRC $+$ RPCA (SRP), and Dual Rank Decomposition (DRD) participate in the performance test. The penalty factor $\mu$ is set to 1, the $\beta$ parameter is 1, and the number of iterations is 400. The AR database is a classic face recognition database, which is often used for performance testing in the field of face recognition. There are 126 face images in the database, and the same face data contains multiple face pose images. In the experimental test, a total of 100 face image datasets in 6 different poses will be selected to participate in the performance experimental test. Considering the image size, the related data images will be processed and cropped into 64 $\times$ 64 image data. In order to test the robustness of the algorithm, multiple sets of graphic data will be selected to carry out repeated experiments, repeated 10 times in total, and the average test result will be selected as the final algorithm identification result. The experiment consists of two parts. The first part modifies the image data to obtain two low rank feature dimensions, and tests the recognition effect of the algorithm under different feature dimensions of the image. In the second part, we will select multiple pose faces from different faces for experiments, including adding facial occlusion. As shown in Fig. 5, part of the experimental face image data in the face database.

Figure 5.

Image data of some experimental face database recognition.

Under the AR database, select three poses of each face to calculate the feature dimensions of the image, and use PCA to reduce the dimensions of the image. After using SRC for classification and recognition, the comparison results of image recognition rates under different feature dimensions are obtained, as shown in Fig. 6.

Figure 6.

The recognition rate results of various algorithms under different feature dimensions.

Figure 6 shows the recognition results of different recognition algorithms in the AR database. It can be seen from the data in the figure that with the increase of the image feature dimension, the recognition accuracy of each algorithm has improved. Among them, the face recognition accuracy rates of the proposed PRS face recognition algorithm in feature dimensions 50, 150, 250 and 350 are 82%, 87%, 92% and 94%, respectively, followed by the DRD algorithm, which are 77%, 83% %, 84% and 85%. It can be seen that the proposed PRS face recognition algorithm has the best face recognition accuracy. The recognition results of different recognition algorithms under the CMU PIE C27 database are also tested, as shown in Fig. 7.

Figure 7.

Recognition results of different recognition algorithms in CMU pie chart C27 database.

Figure 7 shows the recognition results of different recognition algorithms in the CMU PIE C27 database. It can be seen from the graph data results that when the feature dimension is 250, the recognition accuracy rates of PCA, SRC, SRP, DRD, and PRS are 71%, 71, 86%, 91%, and 94%, respectively. Each algorithm can achieve the best image recognition results. Considering the lack of image feature data information, when the feature dimension is in the range of 0–250, the recognition accuracy of each algorithm shows an upward trend. Under the feature dimension of 250–400, due to the increase in the amount of image feature data information, the image recognition accuracy of each algorithm gradually decreases. The reason may be that the number of training samples in the small sample data is much smaller than the dimension of the samples, which affects the sparse stability, which in turn leads to a decrease in the recognition rate accuracy of each algorithm.

4.2 Multi pose face recognition test for different faces

Considering the complex scene of face recognition, in the experiment, 3–4 different face pose types will be selected from 6 different types of face pose images for multi-pose face recognition test. Noise and occlusion maps are added to the image, as shown in Fig. 8.

Figure 8.

Shows an image with noise, occlusion, and exposure interference.

In fact, the face recognition scene is very complex. All kinds of noise, occlusion and overexposure interference will be added to face recognition, so as to better simulate the complex scene of face recognition, and test the recognition effect and robustness of the algorithm in the complex face environment. The matching of different facial poses: Type 1, Type 2, Type 3, Type 4, Type 5, Type 6. The recognition effect of each algorithm under different poses of two faces is shown in Fig. 9.

Figure 9.

Recognition accuracy results of each algorithm under two kinds of multi pose combination of faces.

Figure 9 shows the recognition accuracy results of each algorithm under two kinds of face multi pose combination. The proposed PRS algorithm has the best accuracy rate of face recognition. The accuracy rate of the proposed PRS algorithm is higher than 92%, and the accuracy rate of DRD algorithm is higher than 79%. PRS algorithm uses dual rank to realize the separation of complex image feature contour data, including face category and face pose, and takes the obtained face global information as the first low rank feature, reducing the difference between different face image data, and strengthening the algorithm to extract and distinguish different face feature data under the same pose. Decomposition of low rank with different structures can better remove the interference caused by facial features information in face recognition. At the same time, the low rank dictionary is obtained by processing the two types of face feature data, and the sparse representation is used to classify and solve the problem, so that the face information can be well recognized. In the experimental results in Fig. 9, only two different pose face recognition sample data are used to effectively test the excellence of the proposed algorithm. In particular, some classification algorithms also have excellent image recognition effect under the mixture of two poses, but the recognition effect will be significantly affected under multiple poses. Therefore, in combination with the residual rate classification mode designed in the study, more than two types of face recognition pose data are selected for hybrid performance test, namely, Mix 1, Mix 2, Mix 3, Mix 4, and Mix 5. Among them, there are three image poses in Mix 1, four in Mix 2, five in Mix 3, six in Mix 4, and six in Mix 5. The result of multi algorithm face recognition under complex mixed multi face pose is shown in Fig. 10.

Figure 10.

Face recognition results of algorithm in complex mixed multi face posture.

Figure 10 shows the recognition results of each algorithm in the mixed multi face pose environment. It can be seen from the experimental test results in the figure that, with the increase of face pose types, the recognition accuracy of each algorithm is affected and the recognition rate decreases. In feature extraction, PCA algorithm has certain advantages in image feature extraction. The recognition accuracy is less affected when there are fewer pose types, but with the increase of face types, the recognition accuracy is significantly affected. At the same time, SRP algorithm and the proposed PRS algorithm are both hybrid algorithms, which have obvious advantages in the recognition of complex multi pose data. With the increase of face types, there is no problem that the recognition rate drops significantly. The DRD algorithm does not show good robustness when dealing with more than three kinds of mixed attitude. The recognition rate of SRP algorithm is 81%, 80%, 78%, 77% and 74% respectively when the attitude types are 1, 2, 3, 4 and 5, and the recognition rate of PRS algorithm proposed is 95%, 94%, 93%, 91% and 90% respectively. It can be seen that PRS algorithm also has excellent face recognition effect in the mixed multi face and multi pose environment. In order to verify the robustness of the proposed algorithm, noise interference and object occlusion interference are added to the experimental test data. The interference to the test samples is 10%. The experimental results after adding the interference are shown in Table 1.

Table 1

The experimental results of the recognition accuracy of each algorithm after adding 10% occlusion interference

Algorithm type	Type 1	Type 2	Type 3	Type 4	Type 5	Type 6
PCA	64.45%	58.54%	61.45%	67.45%	64.45%	65.45%
SRC	64.45%	65.54%	59.54%	54.55%	65.54%	67.54%
SRP	63.45%	67.45%	61.45%	64.45%	69.54%	68.45%
DRD	74.58%	71.45%	78.45%	74.55%	71.57%	80.24%
PRS	86.25%	85.65%	85.56%	84.58%	86.54%	86.43%

It can be seen from the data in Table 1 that after adding 10% of the interference to the test samples, the proposed PRS algorithm has good robustness in identifying occlusion data, and the recognition rate of the six combinations is above 84.58%. The second is the DRD algorithm, with the recognition rate above 71.45%. The reason is that the proposed algorithm uses low rank decomposition to deal with the content under sparse interference has better robustness, and the interference data and standard face data will be divided as much as possible in the data recognition to ensure that the algorithm achieves good recognition results.

Face recognition is widely used in many fields, but face recognition is limited by the complexity of technology, face recognition environment and face features. Considering the limitations of traditional face recognition algorithms on face feature extraction, we innovatively combined the two face recognition algorithms, used low rank algorithms to extract low rank features of faces, and used kernel norms to solve them, which greatly improved the accuracy of face recognition. Finally, in the experiment, the proposed method has better performance, and has important reference value for the accuracy and security of current face recognition.

5. Conclusion

Face recognition technology is the combination of computer vision technology and biometrics technology. With the continuous development of computing science and hardware processing technology, face recognition technology will have a broader application prospect. In the application of face recognition technology, face recognition technology is affected by such factors as environment, light, face structure and pose, and the accuracy of face recognition will be seriously affected. In order to reduce the accuracy of face recognition in complex scenes, a face recognition algorithm based on low rank joint sparse representation algorithm is proposed. The low rank decomposition of image data is used to obtain two low rank features. The two low rank features obtained are combined with the sparse representation of SRC algorithm to obtain the reconstruction residual. Considering the difference between the classification results of the two features, the residual comparison model is used to achieve the final classification of data. Through the experimental test, in the AR database test, the recognition accuracy of the proposed PRS algorithm for 50, 150, 250 and 350 feature dimensions is 82%, 87%, 92% and 94% respectively, and the DRD algorithm is 77%, 83%, 84% and 85%. It can be seen that the proposed PRS algorithm has the best performance. In the mixed multi pose scene, when the pose types are 3, 4, 5 and 6, the recognition rates of the proposed PRS algorithm are 95%, 94%, 93%, 91% and 90% respectively, while the recognition efficiency of the SRP algorithm is 81%, 80%, 78%, 77% and 74% respectively. It can be seen that PRS has excellent recognition performance and good robustness. Therefore, the PRS algorithm proposed in this paper meets the requirements of face recognition accuracy and stability. However, the research content is insufficient, and the special environment such as dark light and backlight is not considered, which needs further improvement in the future.

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