A method and system for facial image reconstruction based on principal component analysis

Abstract

The present invention discloses a method and system for facial image reconstruction based on principal component analysis. First, the purity corresponding to each sample pixel is calculated based on the principal component space and the complement space; the purity corresponding to each sample pixel is used to update the initialization projection matrix; whether the convergence condition is met is determined; if the convergence condition is met, the dimension of the sample image to be tested is reduced and the face is reconstructed according to the updated initialization projection matrix to obtain a facial image; if the convergence condition is not met, the purity corresponding to each sample pixel is recalculated. The present invention combines the separability information of the complement space and the principal component space with the Purity index, so that the robustness of the "distance" between adjacent data classes is improved when extracting the principal component, and the independence of the data classes is enhanced, thereby improving the accuracy of facial reconstruction.

Description

Technical Field

[0001] The present invention relates to the technical field of facial image reconstruction, and in particular to a facial image reconstruction method and system based on principal component analysis. Background Art

[0002] In today's era of huge and complex data, we are faced with a large amount of data every day, and the dimensions of scientific data are likely to exceed thousands, such as digital images and videos, gene expression and DNA data, documents and financial time series. Therefore, data analysis of such data sets is affected by the dimensionality. The dimensionality reduction (subspace learning) algorithm becomes the key to solving the problem, projecting the original high-dimensional feature space into a low-dimensional space, thereby well preserving important statistical properties.

[0003] Among these methods, unsupervised dimensionality reduction methods are more effective in practical applications because the cost of obtaining labeled data is high and there is often no prior knowledge about new scientific problems. Therefore, unsupervised dimensionality reduction has become a research focus. Among unsupervised dimensionality reduction, principal component analysis (PCA) is currently the most widely used method, ranging from exploratory data analysis and classification (such as image retrieval and face recognition) to various modern applications (such as video analysis recommendation system design and understanding social network dynamics). The goal of PCA is to find the principal components composed of orthogonal basis vectors, and most of the variability of the data set is located on this orthogonal basis vector, projecting the data in the high-dimensional space into a low-dimensional space, where the data has the smallest reconstruction error in the least squares sense.

[0004] When a clean data matrix is ​​given, PCA can be easily implemented by performing a singular value decomposition (SVD) on the data matrix. The same problem becomes more intractable if the data is corrupted by a few outliers. The reason is that PCA's objective function based on the squared L2 norm is sensitive to outliers. Nowadays, outliers are becoming more and more common because a large number of cheap sensors are often used to acquire data. They occur due to various reasons, such as node or sensor failures, foreground occlusions of video sequences, or anomalies or other abnormal behaviors on some nodes of the network, so PCA may not achieve optimal performance.

[0005] In recent years, with the development of robust modeling techniques based on different norm loss functions, many robust principal component analysis methods based on different loss functions have been proposed, such as PCA-L1, HQ-PCA, R1-PCA, RPCA-OM, Angle PCA, etc. However, the above methods have the problem of poor robustness. Therefore, face reconstruction based on the above methods will inevitably have the problem of low face reconstruction accuracy. Summary of the invention

[0006] The purpose of the present invention is to provide a method and system for reconstructing a face image based on principal component analysis, so as to improve the accuracy of face reconstruction.

[0007] To achieve the above object, the present invention provides a method for reconstructing a face image based on principal component analysis, the method comprising:

[0008] Step S1: obtaining multiple original images;

[0009] Step S2: preprocessing each of the original images to obtain a sample image;

[0010] Step S3: extracting sample pixel points corresponding to each sample image to obtain a sample matrix;

[0011] Step S4: Utilization Calculate the purity corresponding to each sample pixel point; where W represents the initialization projection matrix, X represents the sample matrix, and p i Represents the i-th sample pixel x i The corresponding purity, ‖W T X|| is used to describe the variation caused by the signal, referred to as the principal component space, ‖x i -WW T x i || is used to describe the variation caused by noise, referred to as complementary space;

[0012] Step S5: Calculate the exponential improvement purity corresponding to each sample pixel point according to the purity corresponding to multiple sample pixel points

[0013] Step S6: Calculation The eigenvalues ​​of and the eigenvectors corresponding to each eigenvalue; where C represents the diagonal element The diagonal matrix of Indicates that multiple indexes improve purity The diagonal elements are composed of 1, which represents the unit column vector, (d i ) t Represents multiple vectors d i The diagonal elements of

[0014] Step S7: Select the eigenvectors corresponding to the first K largest eigenvalues ​​to update the initialization projection matrix W; K is a positive integer greater than or equal to 1;

[0015] Step S8: Determine whether the convergence condition is met; if the convergence condition is met, output the updated initialization projection matrix and execute "Step S9"; if the convergence condition is not met, return to "Step S4";

[0016] Step S9: Perform dimensionality reduction and face reconstruction on the sample image to be tested according to the updated initialization projection matrix to obtain a face image.

[0017] Optionally, the convergence condition includes:

[0018] The number of iterations reaches the set number;

[0019] Or the difference ΔJ of the target value J obtained from two adjacent iterations is less than the set threshold.

[0020] Optionally, the purity of each sample pixel point is calculated based on the purity of the sample pixel points. Specifically include:

[0021] Calculate the normalized relative purity of the total sample points according to the purity corresponding to multiple sample pixel points;

[0022] Calculate the exponential improvement purity corresponding to each sample pixel point according to the normalized relative purity of the total sample points and the purity of each sample pixel point

[0023] Optionally, the normalized relative purity of the total sample points is calculated according to the purity corresponding to the multiple sample pixel points, and the specific formula is:

[0024]

[0025] Among them, P represents the normalized relative purity of the total sample points, p i Indicates the purity corresponding to the i-th sample pixel, and n is the number of sample pixels.

[0026] Optionally, the exponential improvement purity corresponding to each sample pixel point is calculated according to the normalized relative purity of the total sample points and the purity of each sample pixel point. The specific formula is:

[0027]

[0028] Among them, P represents the normalized relative purity of the total sample points, p i Indicates the purity corresponding to the i-th sample pixel.

[0029] Optionally, performing dimensionality reduction and face reconstruction on the sample image to be tested according to the updated initialization projection matrix to obtain the face image specifically includes:

[0030] Obtain a sample image to be tested;

[0031] Cut the sample image to be tested to obtain a sample vector Q to be tested;

[0032] according to The dimension of the sample vector Q to be tested is reduced to obtain a low-dimensional space image matrix Y; wherein, is the updated initialization projection matrix;

[0033] The face is reconstructed according to the low-dimensional space image matrix Y to obtain a face image.

[0034] The present invention also discloses a facial image reconstruction system based on principal component analysis, the system comprising:

[0035] An acquisition module, used for acquiring multiple original images;

[0036] A preprocessing module, used for preprocessing each of the original images to obtain a sample image;

[0037] An extraction module, used to extract sample pixel points corresponding to each of the sample images to obtain a sample matrix;

[0038] Purity calculation module, used to utilize Calculate the purity corresponding to each sample pixel point; where W represents the initialization projection matrix, X represents the sample matrix, and p i Represents the i-th sample pixel x i The corresponding purity, ‖W T X‖ is used to describe the variation caused by the signal, referred to as the principal component space, ||x i -WW T x i ‖ is used to describe the variation caused by noise, referred to as complementary space;

[0039] The exponential improvement purity calculation module is used to calculate the exponential improvement purity corresponding to each sample pixel point according to the purity corresponding to multiple sample pixel points.

[0040] Eigenvector calculation module, used to calculate The eigenvalues ​​of and the eigenvectors corresponding to each eigenvalue; where C represents the diagonal element The diagonal matrix of Indicates that multiple indexes improve purity The diagonal elements are composed of 1, which represents the unit column vector, (d i ) t Represents multiple vectors d i The diagonal elements of

[0041] A selection module is used to select the eigenvectors corresponding to the first K largest eigenvalues ​​to update the initialization projection matrix W; K is a positive integer greater than or equal to 1;

[0042] The judgment module is used to judge whether the convergence condition is met; if the convergence condition is met, the updated initialization projection matrix is ​​output and the "dimensionality reduction and face reconstruction module" is executed; if the convergence condition is not met, the "purity calculation module" is returned;

[0043] The dimension reduction and face reconstruction module is used to perform dimension reduction and face reconstruction on the test sample image according to the updated initialization projection matrix to obtain a face image.

[0044] Optionally, the convergence condition includes:

[0045] The number of iterations reaches the set number;

[0046] Or the difference ΔJ of the target value J obtained from two adjacent iterations is less than the set threshold.

[0047] Optionally, the index improvement purity calculation module specifically includes:

[0048] A total sample point normalized relative purity calculation unit, used to calculate the total sample point normalized relative purity according to the purities corresponding to a plurality of sample pixel points;

[0049] An exponential improvement purity calculation unit is used to calculate the exponential improvement purity corresponding to each sample pixel point according to the normalized relative purity of the total sample points and the purity of each sample pixel point.

[0050] Optionally, the normalized relative purity of the total sample points is calculated according to the purity corresponding to the multiple sample pixel points, and the specific formula is:

[0051]

[0052] Among them, P represents the normalized relative purity of the total sample points, p i Indicates the purity corresponding to the i-th sample pixel, and n is the number of sample pixels.

[0053] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0054] The present invention discloses a method and system for facial image reconstruction based on principal component analysis, which replaces the distance measurement from data points to prototypes with the separability information of the principal component space and its complementary space, improves the influence of data points with higher reliability, and weakens the influence of data points with lower reliability; in addition, the present invention combines the separability information of the complementary space and the principal component space with the Purity index, so that when extracting the principal component, the robustness of the "distance" between adjacent data classes is improved, and the independence of the data classes is enhanced, thereby improving the accuracy of facial reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0056] Figure 1 This is a flow chart of the method for facial image reconstruction based on principal component analysis of the present invention;

[0057] Figure 2 This is a structural diagram of the face image reconstruction system based on principal component analysis of the present invention;

[0058] Figure 3 This is a graph showing the clustering recognition accuracy and projection dimension change when adding black and white noise blocks to the ORL dataset;

[0059] Figure 4 This is a curve chart showing the change in recognition accuracy and projection dimension for the FERET dataset;

[0060] Figure 5 This is the effect of face reconstruction by adding black and white noise blocks to the AT&T dataset. DETAILED DESCRIPTION

[0061] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0062] The purpose of the present invention is to provide a method and system for reconstructing a face image based on principal component analysis, so as to improve the accuracy of face reconstruction.

[0063] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0064] Example 1

[0065] like Figure 1 As shown, the present invention discloses a method for reconstructing a face image based on principal component analysis, the method comprising:

[0066] Step S1: Acquire multiple original images.

[0067] Step S2: pre-processing each of the original images to obtain a sample image.

[0068] Step S3: extracting sample pixel points corresponding to each of the sample images to obtain a sample matrix.

[0069] Step S4: Utilization Calculate the purity corresponding to each sample pixel point; where W represents the initialization projection matrix, X represents the sample matrix, and p i Represents the i-th sample pixel x i The corresponding purity, ‖W T X|| is used to describe the variation caused by the signal, referred to as the principal component space, ||x i -WW T x i || is used to describe the variation caused by noise, referred to as complementary space.

[0070] Step S5: Calculate the exponential improvement purity corresponding to each sample pixel point according to the purity corresponding to multiple sample pixel points

[0071] Step S6: Calculation The eigenvalues ​​of and the eigenvectors corresponding to each eigenvalue; where C represents the diagonal element The diagonal matrix of Indicates that multiple indexes improve purity The diagonal elements are composed of 1, which represents the unit column vector, (d i ) t Represents multiple vectors d i The diagonal elements.

[0072] Step S7: Select the eigenvectors corresponding to the first K largest eigenvalues ​​to update the initialization projection matrix W; K is a positive integer greater than or equal to 1.

[0073] Step S8: Determine whether the convergence condition is met; if the convergence condition is met, output the updated initialization projection matrix and execute "Step S9"; if the convergence condition is not met, return to "Step S4".

[0074] Step S9: Perform dimensionality reduction and face reconstruction on the sample image to be tested according to the updated initialization projection matrix to obtain a face image.

[0075] The following is a detailed analysis of each step:

[0076] Step S2: preprocessing each of the original images to obtain a sample image, specifically including:

[0077] Step S21: Decentralize each of the original images. Decenter the original image.

[0078] Step S22: Add noise to the original image after the centralization process to obtain a sample image. In order to verify the robustness of the system, the present invention adds noise to the above decentralized original image. During the process of adding noise, the position of the noise block is random, and the ratio of occluded noise pixels to image pixels is between 0.05-0.1. Optional noise includes salt and pepper noise and occluded noise blocks.

[0079] Step S3: extract the sample pixels corresponding to each sample image to obtain a sample matrix. m represents the number of sample features, and n represents the number of sample points. X=(x1,x2,…x n ), where x i Represents the i-th sample pixel; each pixel includes m sample features.

[0080] Step S4: Utilization Calculate the purity corresponding to each of the sample pixels; where W represents the initialization projection matrix, which is an arbitrary orthogonal matrix, m is the number of sample features, d is the dimension after projection, X represents the sample matrix, p i Represents the i-th sample pixel x i The corresponding purity, ||W T X|| is used to describe the variation caused by the signal, referred to as the principal component space, ‖x i -WW T x i || is used to describe the variation caused by noise, referred to as complementary space.

[0081] The principal component space of the present invention can be understood as a feature with large information content and usefulness; the complementary space can be understood as a noise or useless feature; the present invention replaces the distance measurement from the data point to the prototype with the separability information of the principal component space and its complementary space, which can improve the influence of data points with higher reliability and weaken the influence of data points with lower reliability.

[0082] Step S5: Calculate the exponential improvement purity corresponding to each sample pixel point according to the purity corresponding to multiple sample pixel points Specifically include:

[0083] Step S51: Calculate the normalized relative purity of the total sample points according to the purity corresponding to multiple sample pixel points. The specific formula is:

[0084]

[0085] Among them, P represents the normalized relative purity of the total sample points, p i Indicates the purity corresponding to the i-th sample pixel, and n is the number of sample pixels.

[0086] The larger the normalized difference of the present invention, the smaller the pixel x i The higher the Purity of the sample point relative to the total.

[0087] Step S52: Calculate the exponential improvement purity corresponding to each sample pixel point according to the normalized relative purity of the total sample points and the purity of each sample pixel point. The specific formula is:

[0088]

[0089] in, represents the exponential improvement purity corresponding to the i-th sample pixel, P represents the normalized relative purity of the total sample points, p i Indicates the purity corresponding to the i-th sample pixel.

[0090] In order to enhance the influence of pixel purity, the present invention defines “exponential enhancement of Purity” as the pixel x i Relative to the total about P and p i Function where p i Represents pixel x i The smaller the normalized relative purity, the higher the "exponential improvement purity". This exponential improvement is to increase the difference between useful features and useless features.

[0091] Step S6: Calculation The eigenvalues ​​of and the eigenvectors corresponding to each eigenvalue; where C represents the diagonal element The diagonal matrix of Indicates that multiple indexes improve purity The diagonal elements are composed of 1, which represents the unit column vector, (d i ) t Represents multiple vectors d i The diagonal elements.

[0092] Calculate the vector d i The specific formula is:

[0093]

[0094] Among them, P t Represents diagonal element The diagonal matrix of W represents the initialization projection matrix, X represents the sample matrix, Represents the i-th sample pixel x i The corresponding exponential improvement purity, p represents the norm dimension, 1 represents the unit column vector, and b represents the mean vector.

[0095] Step S7: Select the eigenvectors corresponding to the first K largest eigenvalues ​​to update the initial projection matrix W; specifically, when the number of sample features m is greater than the number of sample points n, use The SVD of can effectively solve this problem. If the number of sample features m is less than or equal to the number of sample points n, then it does not need to be considered.

[0096] Step S8: Determine whether the convergence condition is met; if the convergence condition is met, output the updated initialization projection matrix Then execute "step S9"; if the convergence condition is not met, return to "step S4". The convergence condition in the present invention includes: the number of iterations reaches the set number; or the difference ΔJ of the target value J obtained by two adjacent iterations is less than the set threshold.

[0097] The specific formula for calculating the target value J is:

[0098]

[0099] in, represents the exponential improvement purity, W represents the initialization projection matrix, x i represents the i-th sample pixel, b represents the mean vector, and p represents the norm dimension.

[0100] Step S9: Initialize the projection matrix according to the update Perform dimensionality reduction and face reconstruction on the test sample image to obtain a face image, specifically including:

[0101] Step S91: Acquire a sample image to be tested.

[0102] Step S92: cutting the sample image to be tested to obtain a sample vector Q to be tested.

[0103] Step S93: According to The dimension of the sample vector Q to be tested is reduced to obtain a low-dimensional space image matrix Y; wherein, The low-dimensional spatial image matrix Y of the present invention contains a large number of key features in the face image, such as eyes, nose, mouth, etc. In the process of dimensionality reduction, irrelevant information and noise have been removed. By visualizing these key information features, the reconstructed face image can be obtained.

[0104] Step S94: Reconstruct the face according to the low-dimensional space image matrix Y to obtain a face image.

[0105] The present invention further comprises S10: utilizing The clustering recognition accuracy of multiple reconstructed face images; where l i represents the i-th real face image, c irepresents the face image obtained by reconstructing the i-th face, N represents the total number of real face images, map(·) represents the function that maps each cluster index to the optimal class label, δ(·) represents the δ function, and ACC represents the accuracy of cluster recognition.

[0106] For the face recognition process, the clustering results of the images were further compared using the k-means classifier, where the accuracy of cluster recognition l i represents the real number label of the ith instance (also known as the ith real face image), and c i is the corresponding cluster index (the face image obtained by reconstructing the i-th face). map(·) represents the function that maps each cluster index to the best class label. δ(·) represents the δ function, that is, when the two input parameters l i and c i If they are the same, the value is 1, otherwise it is 0. The larger the ACC value is, the higher the cluster recognition accuracy is.

[0107] The present invention introduces the Purity index into the extraction of principal components and establishes a reconstruction error minimization model based on the separability information of the principal component space and its complementary space of the sampling points (i.e. ), and combines the L2,p modulus and optimal mean methods to further reduce the impact of outliers on the model.

[0108] The present invention introduces the Purity index in clustering into the extraction of principal components, so that PCA is no longer overly "sensitive" to the "distance" between adjacent data classes, thereby improving the robustness of PCA to the "distance" between adjacent data classes. At the same time, the robustness of the model is further improved by combining the L2,p modulus and the method of removing the optimal mean.

[0109] Example 2

[0110] like Figure 2 As shown, the present invention also discloses a face image reconstruction system based on principal component analysis, the system comprising:

[0111] The acquisition module 201 is used to acquire multiple original images.

[0112] The preprocessing module 202 is used to preprocess each of the original images to obtain a sample image.

[0113] The extraction module 203 is used to extract the sample pixel points corresponding to each of the sample images to obtain a sample matrix.

[0114] Purity calculation module 204, used to use Calculate the purity corresponding to each sample pixel point; where W represents the initialization projection matrix, X represents the sample matrix, and p iRepresents the i-th sample pixel x i The corresponding purity, ||W T X|| is used to describe the variation caused by the signal, referred to as the principal component space, ||x i -WW T x i || is used to describe the variation caused by noise, referred to as complementary space.

[0115] The exponential improvement purity calculation module 205 is used to calculate the exponential improvement purity corresponding to each sample pixel point according to the purity corresponding to multiple sample pixel points.

[0116] The feature vector calculation module 206 is used to calculate The eigenvalues ​​of and the eigenvectors corresponding to each eigenvalue; where C represents the diagonal element The diagonal matrix of Indicates that multiple indexes improve purity The diagonal elements are composed of 1, which represents the unit column vector, (d i ) t Represents multiple vectors d i The diagonal elements.

[0117] The selection module 207 is used to select the eigenvectors corresponding to the first K largest eigenvalues ​​to update the initialization projection matrix W; K is a positive integer greater than or equal to 1.

[0118] The judgment module 208 is used to judge whether the convergence condition is met; if the convergence condition is met, the updated initialization projection matrix is ​​output and the "dimensionality reduction and face reconstruction module" is executed; if the convergence condition is not met, the "purity calculation module" is returned.

[0119] The dimension reduction and face reconstruction module 209 is used to perform dimension reduction and face reconstruction on the sample image to be tested according to the updated initialization projection matrix to obtain a face image.

[0120] Preferably, the index improvement purity calculation module 205 specifically includes:

[0121] The total sample point normalized relative purity calculation unit is used to calculate the total sample point normalized relative purity according to the purities corresponding to a plurality of sample pixel points.

[0122] An exponential improvement purity calculation unit is used to calculate the exponential improvement purity corresponding to each sample pixel point according to the normalized relative purity of the total sample points and the purity of each sample pixel point.

[0123] The same parts as those in Example 1 will not be described in detail here.

[0124] Example 3

[0125] Taking the AT&T face image as an example, we first split the sample image into multiple face images of 32×32 pixels, so that each sample image is cut into vectors That is, all the pixels of a sample image are arranged in a row to form a sample vector, and the sample image corresponds to the sample vector one by one. Then it is decentralized and the projection matrix is ​​initialized. Choose any orthogonal matrix, d is the dimension after projection, and m is the dimension of the sample vector, 1024. Then according to the formula Calculate the Purity corresponding to each pixel. Where ||W T X|| is used to describe the variation caused by the signal; ||x i -WW T x i || is used to describe the variation caused by noise. At the same time, the larger the normalized difference, the smaller the pixel x i The higher the Purity of the sample point relative to the total number. Calculate the normalized relative Purity of the total sample points; in order to enhance the influence of pixel purity, calculate the "exponential improvement Purity" Then calculate P t It is a diagonal element The diagonal matrix of Then calculate C, which is the diagonal element. The diagonal matrix of When m>n, we can use The SVD of effectively solves this problem. Finally, take The eigenvectors corresponding to the first K eigenvalues ​​are used as the final dimension reduction matrix. In this embodiment, after each iteration, the updated initialization projection matrix is ​​obtained, and the target value is calculated. Until the difference between the target values ​​J obtained from two consecutive calculations is less than the set threshold (for example, ΔJ ≤ 10 -5 ), the iteration is stopped. In another embodiment, the iteration can be stopped when the number of iterations reaches a set number. Then the projection matrix obtained in the last iteration is recorded as the target projection matrix, and finally the target projection matrix is ​​used to perform dimensionality reduction processing on the face image to be reduced. In this embodiment, the clustering results of the image are further compared by the k-means classifier.

[0126] In order to verify the effectiveness and correctness of the method proposed in this invention, this method is compared with the classic PCA algorithm and several typical robust PCA algorithms in recent years (such as RPCA-AN, RPCA-OM and Angle PCA). The comparison results are as follows:

[0127] 1) Clustering experiment results on ORL dataset

[0128] Before conducting the face image reconstruction experiment, all samples were normalized to a mean of 0. K-means clustering was used for measurement. To eliminate random effects, the experimental method selected the position of the noise block randomly, and the ratio of noise pixels to image pixels was 0.10. The comparison results are shown in Figure 3 As shown. Figure 3 It can be found that the dimensionality reduction performance of the method disclosed in the present invention in different dimensions is generally better than other PCA algorithms. In particular, when p=0.5, the best recognition accuracy can be obtained.

[0129] 2) Clustering experimental results on the FERET dataset

[0130] Before conducting the face image reconstruction experiment, all samples were normalized to a mean of 0. K-means clustering was also used for measurement. No noise was added in this set of experiments. The comparison results are shown in Figure 2. Figure 4 As shown. Figure 4 It can be found that the dimensionality reduction performance of the method disclosed in the present invention in different dimensions is generally better than other PCA algorithms. Similarly, when p=0.5, the best recognition accuracy can be obtained.

[0131] Analysis: In the robust PCA algorithm, Angle PCA and Purity algorithms simultaneously consider the separability information of the principal component space and its complementary space. In most cases, the Purity method is superior to Angle PCA. Because the method disclosed in the present invention combines separability information with the Purity index, it improves the robustness of the "distance" between adjacent data classes when extracting principal components and enhances the independence of data classes. However, due to the nonlinear rapid decay characteristics, Angle PCA has poor ability to describe the global structural characteristics of the data, which makes the Angle PCA algorithm very easy to fall into a local optimal state, especially when it is interfered by noise. This feature makes Angle PCA less stable. Since Purity uses the L2,p norm as the distance metric, it is robust and rotationally invariant to outliers, can effectively eliminate the interference of a small number of outliers, and can eventually converge to the optimal solution and maintain a high clustering accuracy.

[0132] The effect of face reconstruction by adding black and white noise blocks to the AT&T dataset:

[0133] In order to visually observe the effect after reconstructing the masking noise map using the feature space, we conduct face image reconstruction experiments in the AT&T face database. Figure 5 The effects of four algorithms on noisy faces after face reconstruction are given. The number of features extracted in the experiment is 30. Figure 5It can be seen that the reconstruction effect of the classic PCA algorithm on the original image is very unsatisfactory, because the reconstruction performance of the PCA algorithm based on the L2,2 norm is easily affected by noise points, resulting in poor reconstruction effect. The two algorithms RPCA-AN and RPCA-OM can restore the facial contour more clearly, but the restoration effect of the occluded part of the noise block needs to be improved, and the traces of the occluded noise block are retained. The algorithm proposed in this paper can better eliminate the influence of the noise block in the dimensionality reduction process and has a strong ability to extract the overall structural features of the picture. When p = 0.5, the reconstruction error effect is weakened, which can further reduce the influence of the noise value on the optimal solution and improve the influence of the data point on the optimal solution. Therefore, a clearer facial contour can be obtained in image reconstruction, especially the recovery of the covered part is clearer.

[0134] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0135] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for facial image reconstruction based on principal component analysis, characterized in that: The method comprises: Step S1: obtaining multiple original images; Step S2: preprocessing each of the original images to obtain a sample image; Step S3: extracting sample pixel points corresponding to each sample image to obtain a sample matrix; Step S4: Utilization Calculate the purity corresponding to each sample pixel point; where W represents the initialization projection matrix, X represents the sample matrix, and p i Represents the i-th sample pixel x i The corresponding purity, ‖W T X‖ is used to describe the variation caused by the signal, referred to as the principal component space, ||x i -WW T x i || is used to describe the variation caused by noise, referred to as complementary space; Step S5: Calculate the exponential improvement purity corresponding to each sample pixel point according to the purity corresponding to multiple sample pixel points Step S6: Calculation The eigenvalues ​​of and the eigenvectors corresponding to each eigenvalue; where C represents the diagonal element The diagonal matrix of Indicates that multiple indexes improve purity The diagonal elements are composed of 1, which represents the unit column vector, (d i ) t Represents multiple vectors d i The diagonal elements of Step S7: Select the eigenvectors corresponding to the first K largest eigenvalues ​​to update the initialization projection matrix W; K is a positive integer greater than or equal to 1; Step S8: Determine whether the convergence condition is met; if the convergence condition is met, output the updated initialization projection matrix and execute "step S9"; if the convergence condition is not met, return to "step S4"; Step S9: Perform dimensionality reduction and face reconstruction on the sample image to be tested according to the updated initialization projection matrix to obtain a face image.

2. The method for facial image reconstruction based on principal component analysis according to claim 1, characterized in that: The convergence conditions include: The number of iterations reaches the set number; Or the difference ΔJ of the target value J obtained from two adjacent iterations is less than the set threshold.

3. The method for facial image reconstruction based on principal component analysis according to claim 1, characterized in that: The purity is increased by calculating the index corresponding to each sample pixel point according to the purity corresponding to the plurality of sample pixel points. Specifically include: Calculate the normalized relative purity of the total sample points according to the purity corresponding to multiple sample pixel points; Calculate the exponential improvement purity corresponding to each sample pixel point according to the normalized relative purity of the total sample points and the purity of each sample pixel point 4. The method for facial image reconstruction based on principal component analysis according to claim 3, characterized in that: The normalized relative purity of the total sample points is calculated according to the purity corresponding to the multiple sample pixels. The specific formula is: Among them, P represents the normalized relative purity of the total sample points, p i Indicates the purity corresponding to the i-th sample pixel, and n is the number of sample pixels.

5. The method for facial image reconstruction based on principal component analysis according to claim 3, characterized in that: The exponential improvement purity corresponding to each sample pixel point is calculated according to the normalized relative purity of the total sample points and the purity of each sample pixel point. The specific formula is: Among them, P represents the normalized relative purity of the total sample points, p i Indicates the purity corresponding to the i-th sample pixel.

6. The method for facial image reconstruction based on principal component analysis according to claim 1, characterized in that: The step of performing dimensionality reduction and face reconstruction on the sample image to be tested according to the updated initialization projection matrix to obtain the face image specifically includes: Obtain a sample image to be tested; Cut the sample image to be tested to obtain a sample vector Q to be tested; according to The dimension of the sample vector Q to be tested is reduced to obtain a low-dimensional space image matrix Y; wherein, is the updated initialization projection matrix; The face is reconstructed according to the low-dimensional space image matrix Y to obtain a face image.

7. A face image reconstruction system based on principal component analysis, characterized in that: The system comprises: An acquisition module, used for acquiring multiple original images; A preprocessing module, used for preprocessing each of the original images to obtain a sample image; An extraction module, used to extract sample pixel points corresponding to each of the sample images to obtain a sample matrix; Purity calculation module, used to utilize Calculate the purity corresponding to each sample pixel point; where W represents the initialization projection matrix, X represents the sample matrix, and p i Represents the i-th sample pixel x i The corresponding purity, ‖W T X‖ is used to describe the variation caused by the signal, referred to as the principal component space, ||x i -WW T x i ‖ is used to describe the variation caused by noise, referred to as complementary space; The exponential improvement purity calculation module is used to calculate the exponential improvement purity corresponding to each sample pixel point according to the purity corresponding to multiple sample pixel points. Eigenvector calculation module, used to calculate The eigenvalues ​​of and the eigenvectors corresponding to each eigenvalue; where C represents the diagonal element The diagonal matrix of Indicates that multiple indexes improve purity The diagonal elements are composed of 1, which represents the unit column vector, (d i ) t Represents multiple vectors d i The diagonal elements of A selection module is used to select the eigenvectors corresponding to the first K largest eigenvalues ​​to update the initialization projection matrix W; K is a positive integer greater than or equal to 1; The judgment module is used to judge whether the convergence condition is met; if the convergence condition is met, the updated initialization projection matrix is ​​output and the "dimensionality reduction and face reconstruction module" is executed; if the convergence condition is not met, the "purity calculation module" is returned; The dimension reduction and face reconstruction module is used to perform dimension reduction and face reconstruction on the test sample image according to the updated initialization projection matrix to obtain a face image.

8. The face image reconstruction system based on principal component analysis according to claim 7, characterized in that: The convergence conditions include: The number of iterations reaches the set number; Or the difference ΔJ of the target value J obtained from two adjacent iterations is less than the set threshold.

9. The face image reconstruction system based on principal component analysis according to claim 7, characterized in that: The index improvement purity calculation module specifically includes: A total sample point normalized relative purity calculation unit, used to calculate the total sample point normalized relative purity according to the purities corresponding to a plurality of sample pixel points; An exponential improvement purity calculation unit is used to calculate the exponential improvement purity corresponding to each sample pixel point according to the normalized relative purity of the total sample points and the purity of each sample pixel point.

10. The face image reconstruction system based on principal component analysis according to claim 9, characterized in that: The normalized relative purity of the total sample points is calculated according to the purity corresponding to the multiple sample pixels. The specific formula is: Among them, P represents the normalized relative purity of the total sample points, p i Indicates the purity corresponding to the i-th sample pixel, and n is the number of sample pixels.

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