Face recognition method based on adaptive sine angle robust principal component analysis

Abstract

The invention discloses a face recognition method based on adaptive sine angle robust principal component analysis, and belongs to the technical field of face recognition, and the method comprises the steps: obtaining a face image, and carrying out the preprocessing of the face image; constructing a robust principal component analysis model based on an adaptive sine angle, and training the robust principal component analysis model by using the training set; solving an optimal projection matrix by using a non-greedy iterative algorithm; mapping the original face features to a discrimination space by using the optimal projection matrix; and performing face recognition by using a nearest neighbor classifier, and performing robustness evaluation on a recognition result. According to the method, the adaptive sine angle is added, abnormal values can be effectively suppressed in the face of noise data, the influence of the abnormal values on the projection direction is reduced, and the method plays a key role in improving robustness.

Description

Technical Field

[0001] The present invention relates to a face recognition method, specifically a face recognition method based on adaptive sine angle robust principal component analysis, belonging to the technical field of image processing. Background Art

[0002] With the rapid development of artificial intelligence technology, face recognition technology has gradually become an indispensable core means in many fields such as identity authentication, security monitoring, and financial payment. The efficient operation of this system depends on accurately extracting key features from the input image to ensure the accuracy of identity verification and individual recognition. However, the complexity and diversity inherent in image data, as well as various interferences that may be encountered during the acquisition, storage, and transmission processes, such as changes in lighting, differences in shooting angles, and occlusion problems, pose numerous challenges to face recognition. These factors not only weaken the visibility of facial features, resulting in feature distortion or information loss, but also significantly reduce the overall accuracy and robustness of the recognition system. To address these challenges, researchers are committed to developing more advanced algorithms and models, aiming to find an effective feature extraction method that can effectively handle noisy images, is efficient and adaptable, so as to improve the performance of face recognition technology in complex environments.

[0003] Principal component analysis (PCA) is a classical dimensionality reduction method based on the L2 norm. It reduces data redundancy by global mean centering, but due to its sensitivity to noise and the need to stretch a two-dimensional image into a one-dimensional vector, structural information is lost. For this reason, a series of improved methods have been proposed: L1-norm based principal component analysis (L1-PCA) enhances robustness by minimizing the reconstruction error, but has large computational storage requirements; L1-norm principal component analysis (PCA-L1) reduces storage consumption by maximizing variance, but has the defect of non-optimal criterion function.

[0004] In summary, there are still problems in the balance between the robustness and computational complexity of existing methods, resulting in possible performance fluctuations due to data complexity and noise interference in practical applications. Therefore, developing a more effective feature extraction method to suppress noise and improve robustness remains a current research hotspot and challenge. Summary of the Invention

[0005] Object of the Invention: Aiming at the above problems, the object of the present invention is to provide a face recognition method based on adaptive sine angle robust principal component analysis, which can effectively extract features even in the face of noisy data, improve the robustness of the model, and reduce the interference of noise in image processing.

[0006] Technical Solution: The face recognition method based on adaptive sine angle robust principal component analysis of the present invention includes the following steps:

[0007] Step 1: Obtain a face image, perform preprocessing, then construct a dataset and divide it into a training set and a test set according to a ratio;

[0008] Step 2: Construct a robust principal component analysis model based on the adaptive sine angle. With the goal of minimizing the sine angle, compare the determined adaptive sine angle with the sine angle of each input face image, and adjust the sine angle larger than the adaptive sine angle to the adaptive sine angle to construct an objective function, and use the training set to train the robust principal component analysis model; where the output term of the robust principal component analysis model is the optimal projection matrix;

[0009] Step 3: Use a non-greedy iterative algorithm to solve the optimal projection matrix;

[0010] Step 4: Map the original face features to the discriminant space using the optimal projection matrix;

[0011] Step 5: Use a nearest neighbor classifier for face recognition and conduct a robustness evaluation on the recognition results.

[0012] Further, the steps of obtaining a face image and performing preprocessing include:

[0013] Convert the face image into a two-dimensional image matrix, expand the two-dimensional image matrix into an augmented matrix, and use the augmented matrix as the input term of the robust principal component analysis model based on the adaptive sine angle.

[0014] Further, the expression of the objective function is:

[0015]

[0016] In the formula, X is the augmented matrix formed by splicing the original face images with noise, X i (j,:) is the j-th row vector of the i-th sub-matrix of the augmented matrix X, ‖‖2 represents the l 2,1 norm, W is the projection matrix, I d is the identity matrix, represents the transpose of the matrix, a is the adaptive sine angle, N represents the number of samples in the training set, and m represents the number of rows of each data matrix;

[0017] Transform the objective function, and after transformation, it is expressed as:

[0018]

[0019] Among them, the parameter A v is expressed as:

[0020]

[0021] In the formula, tr represents the trace of the matrix; Vi is a diagonal matrix, and the j-th diagonal element in this diagonal matrix is determined by the weight coefficient d ij where d ij has the following expression:

[0022]

[0023] In the formula, ε represents a minimum value.

[0024] Furthermore, the steps of using the non-greedy iterative algorithm to solve the optimal projection matrix include:

[0025] Step 31: Set the maximum number of iterations, initialize the projection matrix W as an orthogonal matrix, and calculate the weight coefficient d ij ;

[0026] Step 32: At the t-th iteration, fix the weight coefficient d ij (t-1) . At this time, the value of tr(A v ) has been determined, and the objective function is transformed into the following form:

[0027]

[0028] In the formula, the parameter G (t-1) = A v W (t-1) ,

[0029] Step 33: Perform singular value decomposition on the parameter G, which is expressed as:

[0030]

[0031] In the formula, the matrices U and V satisfy I n represents the n-order identity matrix, and I d represents the d-order identity matrix;

[0032] Step 34: Update the projection matrix W, and the expression is:

[0033]

[0034] In the formula, I n×d represents the truncated identity matrix of size n×d;

[0035] Step 35: Calculate the weight coefficient d ij (t) ;

[0036] Step 36: Determine the projection matrix W at the current iteration (t)Whether the convergence condition is satisfied. If not, update the iteration count \(t = t + 1\) and jump to step 33; otherwise, stop the iteration and obtain the optimal projection matrix.

[0037] Furthermore, the expression for the convergence condition is:

[0038] \(J(W (t-1) ) - J(W (t) )\leq\gamma\),

[0039] where \(J(\cdot)\) represents the objective function, \(t\) represents the current iteration count, \(W (t-1) is the projection matrix obtained in the \((t - 1)\)-th iteration, \(W (t) is the projection matrix obtained in the \(t\)-th iteration, and \(\gamma\) is the set threshold parameter.

[0040] Advantageous effects: Compared with the prior art, the significant advantages of the present invention are:

[0041] 1. The present invention adds an adaptive sine angle \(a\), so that when processing sample data with noise, for outliers, even if their deviation degree is very high, higher robustness can be obtained. Therefore, outliers can be effectively suppressed, and their influence on the projection direction can be reduced, which plays a key role in improving robustness;

[0042] 2. The present invention uses minimizing the sine angle, that is, minimizing the relative reconstruction error, as the objective function. Compared with other principal component analysis methods, such as L1-norm principal component analysis and R1-norm principal component analysis which use maximizing variance as the objective function, the present invention realizes the true purpose of the principal component analysis method;

[0043] 3. The present invention makes the time complexity relatively low by minimizing the relative reconstruction error, achieving a balance between efficiency and accuracy;

[0044] 4. Compared with the traditional principal component analysis method, the present invention continues the geometric structure of retaining data and the rotation invariance of the solution of the two-dimensional principal component analysis method. Description of the Drawings

[0045] Figure 1 is a flowchart of a face recognition method based on adaptive sine angle robust principal component analysis;

[0046] Figure 2 is a flow block diagram of a face recognition method based on adaptive sine angle robust principal component analysis;

[0047] Figure 3 is the recognition rate curve of the model under different feature dimensions in the Extended Yale B database;

[0048] Figure 4 is the recognition rate curve of the model under different feature dimensions in the AR database. Detailed implementation manner

[0049] In order to make the objectives, technical solutions and advantages of the present application clearer and more understandable, the present application will be further described in detail below with reference to the accompanying drawings and embodiments.

[0050] Combined with Figures 1 to 2 , the face recognition method based on adaptive sine angle robust principal component analysis described in this embodiment specifically includes the following steps:

[0051] Step 1: Obtain a face image and perform preprocessing, then construct a data set, and divide it into a training set and a test set according to a ratio.

[0052] Further, the steps of obtaining a face image and performing preprocessing include:

[0053] Convert the face image into a two-dimensional image matrix, expand the two-dimensional image matrix into an augmented matrix, and use the augmented matrix as an input item of the robust principal component analysis model based on the adaptive sine angle.

[0054] Inject controllable noise into the original face image to simulate interference in a real scene, convert each noisy image into its two-dimensional image matrix to retain the spatial structure information of the data, and horizontally splice all two-dimensional image matrices to construct an augmented matrix. Then, construct the preprocessed face image data into a data set, and the data set can be divided into a training set and a test set according to a ratio of 6:4 or other ratios. The training set is used to find the optimal projection matrix.

[0055] Step 2: Construct a robust principal component analysis model based on the adaptive sine angle, with the goal of minimizing the sine angle. Compare the determined adaptive sine angle with the sine angle of each input face image, and adjust the sine angle larger than the adaptive sine angle to the adaptive sine angle to construct an objective function, and use the training set to train the robust principal component analysis model; the output item of the robust principal component analysis model is the optimal projection matrix.

[0056] Construct a robust principal component analysis model (AS2DPCA) based on the adaptive sine angle a, with the goal of minimizing the sine angle. At the same time, replace the sine angle larger than the adaptive sine angle in the sample with the adaptive sine angle to ensure good robustness and reduce the influence of outliers, so as to construct an objective function.

[0057] The adaptive sine angle a specifies the number of outliers to be processed. Therefore, the adaptive sine angle a can effectively suppress outliers when facing noisy data, reduce its influence on the projection direction, and plays a key role in improving robustness. To improve universality, a is set as:

[0058] a = h × N

[0059] Among them, N is the number of training samples, and h is the adaptive sine rate. Thus, determining h means determining a. In actual situations, since the types and magnitudes of noise and the distribution of the application dataset are unknown, the specific number of outliers cannot be standardized. Therefore, a method based on knowledge and experience is used to determine the adaptive sine angle a.

[0060] Furthermore, the expression of the objective function is as follows:

[0061]

[0062] In the formula, X is the augmented matrix formed by splicing the original face images with noise, and X i (j, :) is the j-th row vector of the i-th sub-matrix of the augmented matrix X, and ‖‖2 represents the l 2,1 norm, W is the projection matrix, and I d is the identity matrix. represents the transpose of the matrix, a is the adaptive sine angle, N represents the number of samples in the training set, and m represents the number of rows of each data matrix;

[0063] The objective function is transformed, and the objective function can be represented by the following equivalent formula:

[0064]

[0065] In the formula, λa is a constant. Since it is inevitable in actual situations a minimum value ε is added to it. The definitions of d ij and A v are as follows:

[0066]

[0067] In the formula, V i is a diagonal matrix, and its j-th diagonal element is determined by d ij .

[0068] Then the transformed objective function is expressed as:

[0069]

[0070] Since the formula contains two unknown variables W and d ij , and there is a relationship between them, a fast non-greedy iterative algorithm is used to solve the projection matrix W.

[0071] Combined with Figure 2 , step 3, use the non-greedy iterative algorithm to solve the optimal projection matrix.

[0072] Furthermore, the steps of using the non - greedy iterative algorithm to solve the optimal projection matrix include:

[0073] Step 31, set the maximum number of iterations, initialize the projection matrix W as an orthogonal matrix, and calculate the weight coefficient d through the projection matrix W ij ;

[0074] Step 32, at the t - th iteration, fix the weight coefficient d ij (t-1) , at this time, the value of tr(A v ) has been determined, then the objective function is transformed into the following form:

[0075]

[0076] In the formula, the parameter G (t-1) = A v W (t-1) ,

[0077] Step 33, perform singular value decomposition (SVD) on the parameter G, expressed as:

[0078]

[0079] In the formula, the matrices U and V exist I n represents the n - order identity matrix, I d represents the d - order identity matrix;

[0080] Step 34, update the projection matrix W, the expression is:

[0081]

[0082] In the formula, I n×d represents the truncated identity matrix of size n×d;

[0083] Step 35, calculate the weight coefficient d at the current iteration ij (t) ;

[0084] Step 36, determine whether the projection matrix W at the current iteration (t) satisfies the convergence condition. If not, update the iteration number t = t + 1, and jump to Step 33; otherwise, stop the iteration to obtain the optimal projection matrix.

[0085] Furthermore, the expression of the convergence condition is:

[0086] J(W (t-1) ) - J(W (t) ) ≤ γ,

[0087] where \(J(\cdot)\) represents the objective function, \(t\) represents the current iteration number, and \(W\) (t-1) is the projection matrix obtained in the \((t - 1)\)-th iteration, and \(W\) (t) is the projection matrix obtained in the \(t\)-th iteration, and \(\gamma\) is the set threshold parameter.

[0088] Step 4: Map the original face features to the discriminant space using the optimal projection matrix.

[0089] Specifically, perform a standard matrix multiplication on the face image matrix to be processed and the optimal projection matrix obtained above to obtain a low-dimensional feature matrix containing the main feature information of the face.

[0090] Step 5: Use the nearest neighbor classifier for face recognition and evaluate the robustness of the recognition result.

[0091] The core of this step is to project the test image into the same low-dimensional feature space as the training image, and then by calculating the distance between features, find the most similar training sample and assign its label to the test sample to complete face recognition. At the same time, by repeating this recognition process on the test data containing various actual interferences and observing the change in the average recognition accuracy, the ability of the algorithm to resist interference and work stably is measured.

[0092] In an example, according to experience, \(h = 0.08\) is adopted to evaluate the performance of the present invention. The present invention aims to verify the performance of the face recognition method described in the present invention through experimental tests on two datasets, Extended Yale B and AR, and compare and evaluate it with models such as two-dimensional principal component analysis (2DPCA), L1-norm two-dimensional principal component analysis (2DPCA_L1), angular two-dimensional principal component analysis (Angle2DPCA), and optimal mean two-dimensional principal component analysis (OMF-2DPCA). For the Extended Yale B dataset, 50% of the image samples are randomly selected, and salt-and-pepper noise with a density randomly fluctuating in the range of 2% to 20% is applied to their pixels.

[0093] For the AR dataset, 50% of the image samples are randomly selected, and random noise conforming to a Gaussian distribution is added to their pixels, and the noise intensity covers 2% - 20% of the total number of pixels. Arbitrarily select 60% of the images as the training set, and the remaining 40% as the test set.

[0094] The comparison results are shown in Tables 1 to 3. Table 1 shows the recognition rates at different feature dimensions in the Extended Yale B face database, and Table 2 shows the average recognition accuracies in the Extended Yale B face database. It can be seen from Tables 1 and 2 that the average recognition accuracy of the face recognition method described in the present invention in the Extended Yale B dataset is better than that of other models. At the same time, at the optimal projection dimension, the average recognition accuracy is significantly better than that of other models. This shows the strong robustness of the method described in the present invention in the face recognition task for dealing with illumination changes and the ability to extract highly discriminative features, making it exhibit better performance than other comparison methods on challenging datasets.

[0095] Table 1

[0096]

[0097]

[0098] Table 2

[0099]

[0100] Table 3 shows the recognition rates at different feature dimensions in the AR face database, and Table 4 shows the average recognition accuracies in the AR face database. It can be seen from Tables 3 and 4 that the average recognition accuracy of the method described in the present invention in the AR dataset is better than that of other models. At the same time, at the optimal projection dimension, the average recognition accuracy is significantly better than that of other models. This shows that the present invention is not only robust to illumination, but also has significant advantages in dealing with practical problems such as expression changes and facial occlusions, demonstrating its wide applicability and making it potentially more competitive than other comparison models in simulating complex real-world scenarios.

[0101] Table 3

[0102]

[0103]

[0104] Table 4

[0105]

[0106] Combined with Figure 3 and Figure 4It can be seen that the average recognition accuracy of the method described in the present invention in the Extended Yale B dataset and the AR dataset is better than that of other models in each dimension. This is attributed to the structure of the adaptive sine angle a and the minimization of the relative reconstruction error in the present invention, which improves the effectiveness of the projection and enhances the recognition robustness. At the same time, when the number of selected feature vectors reaches a certain amount, the average recognition accuracy of the method described in the present invention basically tends to be stable, indicating that the algorithm can efficiently extract the core discriminant information in the data and allows for near-optimal performance to be achieved at a lower dimension.

Claims

1. A face recognition method based on adaptive sine angle robust principal component analysis, characterized in that, It includes the following steps: Step 1: Obtain a face image and perform preprocessing, then construct a dataset and divide it into a training set and a test set according to a ratio; Step 2: Construct a robust principal component analysis model based on an adaptive sine angle. With the goal of minimizing the sine angle, compare the determined adaptive sine angle with the sine angle of each input face image, adjust the sine angle larger than the adaptive sine angle to the adaptive sine angle to construct an objective function, and use the training set to train the robust principal component analysis model; where the output term of the robust principal component analysis model is the optimal projection matrix; Step 3: Use a non-greedy iterative algorithm to solve the optimal projection matrix; Step 4: Use the optimal projection matrix to map the original face features to the discriminant space; Step 5: Use a nearest neighbor classifier for face recognition and perform a robustness evaluation on the recognition result.

2. The face recognition method based on adaptive sine angle robust principal component analysis according to claim 1, wherein The steps of obtaining a face image and performing preprocessing include: Convert the face image into a two-dimensional image matrix, expand the two-dimensional image matrix into an augmented matrix, and use the augmented matrix as the input term of the robust principal component analysis model based on the adaptive sine angle.

3. The face recognition method based on adaptive sine angle robust principal component analysis according to claim 2, wherein, The expression of the objective function is: where X is the augmented matrix formed by stitching together the original face images with noise, X i (j, :) is the j-th row vector of the i-th sub-matrix of the augmented matrix X, and ‖‖2 represents the l 2,1 norm, W is the projection matrix, I d is the identity matrix, T represents the transpose of the matrix, a is the adaptive sine angle, N represents the number of samples in the training set, and m represents the number of rows in each data matrix; Transform the objective function, and after transformation, it is expressed as: Among them, parameter A v has the following expression: where tr represents the trace of a matrix; V i is a diagonal matrix, and the j-th diagonal element in this diagonal matrix is determined by the weight coefficient d ij ; the expression of d ij is: In the formula, ε represents a minimum value.

4. The face recognition method based on adaptive sine angle robust principal component analysis according to claim 3, wherein The steps of using a non-greedy iterative algorithm to solve the optimal projection matrix include: Step 31, set the maximum number of iterations, initialize the projection matrix W as an orthogonal matrix, and calculate the weight coefficient d ij ; Step 32, at the t-th iteration, fix the weight coefficient d ij (t-1) , at this time, the value of tr(A v ) has been determined, and the objective function is transformed into the following form: In the formula, the parameter G (t-1) = A v W (t-1) , Step 33: Perform a singular value decomposition on the parameter G, expressed as: G (t-1) = U (t-1) Λ (t-1) V (t-1)T , wherein, for matrices U and V, there is U T U = UU T = I n , V T V = VV T = I d , I n denotes the n-order identity matrix, and I d denotes the d-order identity matrix; Step 34: Update the projection matrix W, and the expression is: W (t) = U (t-1) I n×d V (t-1)T , where I n×d represents a truncated identity matrix of size n×d; Step 35, calculate the weight coefficient d at the current iteration number ij (t) ; Step 36, determine the projection matrix W at the current iteration count (t) whether it meets the convergence condition. If not, update the iteration count t = t + 1, and jump to Step 33; otherwise, stop the iteration to obtain the optimal projection matrix.

5. The face recognition method based on adaptive sine angle robust principal component analysis according to claim 4, wherein The expression of the convergence condition is: J(W (t-1) ) - J(W (t) ) ≤ γ, where J(·) represents the objective function, t represents the current iteration number, and W (t-1) is the projection matrix obtained in the (t - 1)-th iteration, and W (t) is the projection matrix obtained in the t-th iteration, and γ is the set threshold parameter.

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