CN108681725A - A kind of weighting sparse representation face identification method - Google Patents

Abstract

The invention discloses a kind of weighting sparse representation face identification methods, specifically follow the steps below：Step 1, training facial image is inputted, dictionary matrix A is obtained；Step 2, Feature Dimension Reduction is carried out using Principal Component Analysis to dictionary matrix A and facial image y to be measured, and makes dictionary matrix A and facial image y to be measured that there is l into the normalized of ranks₂Norm；Step 3, training facial image weight w is calculated using gaussian kernel function_i,j；Step 4, the training facial image weight w being introduced into step 3_i,j, construction weighting training dictionary matrix A '；Step 5, sparse coefficient x is solved, obtains and reconstructs facial image y to be measured^*；Step 6, according to the reconstruct of step 5 facial image y to be measured^*, calculate the corresponding residual error per class people of facial image to be measured；Step 7, it exports：The classification of facial image y to be measured is judged by formula (15), realizes recognition of face.The method of the present invention improves face recognition algorithms in posture, expression etc. compared with the accuracy of identification and robustness under changing environment in major class.

Description

A Weighted Sparse Representation Method for Face Recognition

technical field

The invention belongs to the technical field of image processing and pattern recognition, and in particular relates to a face recognition method with weighted sparse representation.

Background technique

As one of the hot topics in the field of computer vision and pattern recognition, face recognition technology is widely used in ID card information systems, bank monitoring, customs entry-exit inspections, and criminal suspects due to its strong adaptability, high security, and intelligent interaction. It has potential application prospects in fields such as people chasing and fleeing, campus security, and access control systems.

A face recognition system usually includes three parts: face detection, feature extraction and recognition algorithm. Traditional face recognition technology research focuses on feature extraction and recognition algorithms, and some classic methods have been formed, such as principal component analysis, linear discriminant analysis, elastic matching, neural network and other methods. Many things in reality have the general characteristic of sparsity, and in the field of face recognition, if there are enough face image samples of each type, these face samples can be expanded into a face subspace, and the number of such face images Every image can be linearly represented or approximated by this subspace. Based on this idea, in 2009, Wright et al. believed that the sparsity of the image in the image mode not only exists within the image, but also exists between the image modes, and then proposed face recognition based on Sparse Representation Classification (SRC) method, using the linear correlation of similar face images, constructing all training samples into a super-complete dictionary and performing sparse reconstruction on test samples one by one, and finally classifying and discriminating according to the sparse reconstruction error. The problem of poor stickiness. Subsequently, a series of researches based on the SRC method have made great progress, representatively including the optimization strategy of the sparse reconstruction algorithm, the construction of the over-complete dictionary, and the combination of the SRC algorithm and other algorithms, etc. Although SRC has achieved excellent results in the field of face recognition and has attracted extensive research by scholars, there are still some technical difficulties. First of all, the collected face images are carried out in an uncontrollable natural environment, and often contain intra-class changes such as posture, illumination, and expression; in addition, the SRC algorithm is time-consuming and cannot meet the real-time requirements in practical applications. Based on this, how to efficiently obtain good recognition results in face recognition problems with large intra-class changes has become a concern of face recognition research.

Contents of the invention

The purpose of the present invention is to provide a weighted sparse representation face recognition method, which solves the problem of insufficient performance when the face image of the existing face recognition method is in a large category of changes such as posture and expression.

The technical solution adopted in the present invention is a method for face recognition with weighted sparse representation, which is characterized in that it is specifically carried out in accordance with the following steps:

Step 1, input the training face image to obtain the dictionary matrix A;

Step 2, adopt principal component analysis method to carry out feature dimensionality reduction to dictionary matrix A and human face image y to be tested, and carry out the normalization processing of column so that dictionary matrix A and human face image y to be tested have ₁₂ norm;

Step 3, using the Gaussian kernel function to calculate the distance or similarity between each training face image and the test face image y, that is, the training face image weight w _i,j ;

Step 4, introduce the training face image weight w _i,j in step 3, and construct the weighted training dictionary matrix A':

In formula (4), Represents the n _kth image of the kth class sample after weighting;

Step 5, solving the sparse coefficient to obtain the reconstructed face image to be tested;

Step 6, according to the reconstructed test face image y ^* obtained in step 5, calculate the residual error of each type of person corresponding to the test face image:

r _i (y)=||yy ^* || ₂ i=1,2,...,k (14);

Step 7, output: solve the category of the face image y to be tested, compare the category of the face image y to be tested with the category of the training face image, and when the two are consistent, realize face recognition;

The expression of the y category of the face image to be tested is:

identity(y) = _argmin ri(y) (15).

The present invention is also characterized in that,

In step 1, the dictionary matrix A is obtained according to the following steps:

Assume that there are k classes of training face images, and each class consists of n _i training face images, then there are A training face image;

Let the pixel of each face image be w×h, and accumulate the face images into a column vector v whose dimension is m=w*h, then v _i,j ∈ R ^m represents the jth A training face image, where m is the dimension of the feature vector;

All the column vectors of the i-th training face image can be combined into a sample set Then combine the sample sets A _i of k categories to get the dictionary matrix A:

A=[A ₁ , A ₂ , . . . , A _k ]∈R ^m×N (1).

In step 2, the dimensionality reduction processing method adopted is to process all the original training face images and test face images into 384-dimensional feature vectors.

In step 3, the training face image weight w _i,j is calculated by formula (2):

In formula (2), v _i,j represent the jth training face image of the i class, y represents the face image to be tested, and σ is the width parameter of the Gaussian kernel function, which is the width parameter of all training face images The average Euclidean distance between , namely:

In formula (3), M is the number of Euclidean distances between all samples.

In step 5, obtaining the reconstructed face image to be tested is specifically implemented according to the following steps:

Step 5.1, solving the l ₀ minimization problem:

In formula (5), x is a sparse coefficient;

Step 5.2, using the dual augmented Lagrangian multiplier method to solve equation (5), then the Lagrangian multiplier function corresponding to equation (5) is:

In formula (6), μ>0, μ is a constant and represents the compensation factor for transforming equality constraints into unconstrained problems, and γ is the obtained Lagrangian multiplier vector;

If γ ^* is a Lagrangian multiplier vector and satisfies the second-order sufficient condition of the optimization problem, then, when the compensation factor μ is large enough, the optimization problem of sparse coefficients can be solved by formula (7), namely:

It can be seen from formula (7) that to solve the sparse coefficient x, it is necessary to determine the values of the Lagrangian multiplier vector γ ^* and the compensation factor μ, and then calculate the values of x and γ at the same time through an iterative method, namely:

In formula (8), {μ _l } is a positive monotonically increasing sequence, and l represents the number of iterations.

In step 5.3, in order to accurately reconstruct the face image y to be tested, the ALM algorithm is applied to the dual problem, that is, the DALM algorithm, then formula (5) is transformed into formula (9):

In formula (9), the value range of the sparse coefficient x is Then the problem in the Lagrange function form of formula (9) can be expressed as:

In formula (10), β is a constant greater than zero and is the compensation factor for converting constraints into equations, and z is the sparse coefficient obtained during the reconstruction process;

Step 5.4, using the step-by-step iterative update method to solve the initialization problem x, the dual problem variables y ^* and z, let x=x _l , y ^* =y _l , and from this result, update z _l to z _l+1 , namely:

In formula (11), for projection to For the above operator, if it is determined that x=x _l , y ^* =y _l , then y ^* can be calculated by the following formula, namely:

βAA ^T y ^* ＝βAz _l+1 -(Ax _l -y) (12)

Then, the DALM algorithm can be expressed as:

Calculate the reconstructed face image y ^* to be tested by formula (13).

The beneficial effect of the present invention is,

(1) A kind of weighted sparse representation face recognition method of the present invention, the sparse representation classification algorithm WSRC_DALM that combines weighted training dictionary and DALM algorithm, this weighted training dictionary is used for describing all training face images and the human face image to be tested Differences under larger intra-category changes, thereby improving the recognition accuracy and robustness of face recognition algorithms in environments with large intra-category changes such as poses and expressions;

(2) A weighted sparse representation face recognition method of the present invention, the DALM algorithm adopted can effectively reduce the time complexity of the WSRC algorithm, and realize accurate reconstruction of test samples, and obtain robust recognition effect.

Description of drawings

Fig. 1 is the flow chart of a kind of weighted sparse representation face recognition method of the present invention;

Fig. 2 is a partial face image of the FEI face database in an embodiment of a weighted sparse representation face recognition method of the present invention.

Detailed ways

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

A kind of weighted sparse expression face recognition method of the present invention, specifically carry out according to the following steps:

Step 1, input the training face image to obtain the dictionary matrix A:

Assume that there are k classes of training face images, and each class consists of n _i training face images, then there are A training face image;

Let the pixel of each face image be w×h (w is the width, h is the height), and accumulate the face images into a column vector v whose dimension is m=w*h, then v _i,j ∈ R ^m represents the j-th training face image of the i-th category, where m is the dimension of the feature vector;

All the column vectors of the i-th training face image can be combined into a sample set Then combine the sample sets A _i of k categories to get the dictionary matrix A:

A＝[A ₁ ,A ₂ ,...,A _k ]∈R ^m×N (1);

Step 2, use the principal component analysis method to perform feature dimensionality reduction on the dictionary matrix A and the face image y to be tested, and perform column normalization so that the dictionary matrix A and the face image y to be tested have _l2 norm; The dimensionality reduction processing method used is to process all the original training face images and test face images into 384-dimensional feature vectors; while the traditional WSRC algorithm mainly performs image scaling processing.

Step 3, use the Gaussian kernel function to calculate the distance between each training face image and the test face image y, that is, the training face image weight w _i,j :

In formula (2), v _i,j represent the jth training face image of the i class, y represents the face image to be tested, and σ is the width parameter of the Gaussian kernel function, which is the width parameter of all training face images The average Euclidean distance between , namely:

In formula (3), M is the number of Euclidean distances between all samples;

Step 4, introduce the training face image weight w _i,j in step 3, and construct the weighted training dictionary matrix A':

In formula (4), Represents the n _kth image of the kth class sample after weighting;

Step 5, solving the sparse coefficient to obtain the reconstructed face image to be tested;

Step 5.1, solving the l ₀ minimization problem:

In formula (5), x is a sparse coefficient;

In step 5.2, since the l ₁ norm problem is an NP-hard problem, it can usually be transformed into a convex problem of l ₁ norm, that is, the dual augmented Lagrange multiplier method is used to solve formula (5), then formula (5 ) corresponding to the Lagrange multiplier function is:

In formula (6), μ>0, μ is a constant and represents the compensation factor for transforming equality constraints into unconstrained problems, and γ is the obtained Lagrangian multiplier vector;

If γ ^* is a Lagrangian multiplier vector and satisfies the second-order sufficient condition of the optimization problem, then, when the compensation factor μ is large enough, the optimization problem of sparse coefficients can be solved by formula (7), namely:

It can be seen from formula (7) that to solve the sparse coefficient x, it is necessary to determine the values of the Lagrangian multiplier vector γ ^* and the compensation factor μ, and then calculate the values of x and γ at the same time through an iterative method, namely:

In formula (8), {μ _l } is a positive monotonically increasing sequence, l represents the number of iterations,

In step 5.3, in order to accurately reconstruct the face image y to be tested, the ALM algorithm is applied to the dual problem, that is, the DALM algorithm, then formula (5) is transformed into formula (9):

In formula (9), the value range of the sparse coefficient x is Then the problem in the Lagrange function form of formula (9) can be expressed as:

In formula (10), β is a constant greater than zero and is the compensation factor for converting constraints into equations, and z is the sparse coefficient obtained during the reconstruction process;

Step 5.4, using the step-by-step iterative update method to solve the initialization problem x, the dual problem variables y ^* and z, let x=x _l , y ^* =y _l , and from this result, update z _l to z _l+1 , namely:

In formula (11), for projection to For the above operator, if it is determined that x=x _l , y ^* =y _l , then y ^* can be calculated by the following formula, namely:

βAA ^T y ^* ＝βAz _l+1 -(Ax _l -y) (12)

Then, the DALM algorithm can be expressed as:

Equation (13) can accurately calculate the reconstructed face image y ^* to be tested, and can guarantee the convergence of the dual algorithm.

Step 6, according to the reconstructed test face image y ^* obtained in step 5, calculate the residual error of each type of person corresponding to the test face image:

r _i (y)=||yy ^* || ₂ i=1,2,...,k (14);

Step 7, output: Find the category of the face image y to be tested, compare the category of the face image y to be tested with the category of the training face image, and when the two are consistent, determine that the face image y to be tested belongs to category k Which type in the face image is trained to realize face recognition;

The expression of the y category of the face image to be tested is:

identity(y) = _argmin ri(y) (15).

The intra-class variation of face images refers to the differences in images presented by the same person under different viewing angles; the training dictionary (dictionary matrix) is a collection of face images describing all training samples under the posture interference factor, and each column of the matrix Both depict images of the same kind of people.

The size of the training face image of the same person is the same, and there is only a change in posture deflection, without the influence of factors such as illumination and occlusion.

The simulation situation and effect of the embodiment are as follows:

The face images used in the experiment of this embodiment come from the FEI face database, which contains 2800 color images of 200 people, where the images of each person cover changes in posture and illumination. In the embodiment of the present invention, 100 people are randomly selected from the FEI face database, and each person selects 11 images with different poses, and the size of each image is 480640.

As shown in Figure 2, the simulation experiment is to firstly process all the images in gray scale, and then randomly select 7 images of each person to construct the training dictionary matrix A, and the remaining images are used as the face images to be tested, and then use the PCA method to analyze the training dictionary matrix A. The matrix and test samples are dimensionally reduced to 384 dimensions, and then the weight of each training sample to the test sample is calculated to construct a weighted training dictionary matrix. Then according to the l1 norm minimization method (l1_ls method) of step 5 and step 6 (DALM method) to solve the sparse coefficient of the test image, finally by calculating the residual ri between the original test image y and the reconstructed test image y' (y) to determine the category. The software platform of this simulation experiment is MATLAB 7.0.

The experiments of the simulation embodiment compared the recognition effect and robustness between the improved weighted sparse representation face recognition method of the present invention and the classic weighted sparse representation method, and the experimental results are as shown in Table 1:

It can be seen from Table 1 that the improved weighted sparse representation face recognition method of the present invention can increase the recognition rate of the classic weighted sparse representation method by about 15%. promotion and application prospects.

The present invention is a weighted sparse representation face recognition method, a sparse representation classification algorithm WSRC_DALM combining the weighted training dictionary and the DALM algorithm, the weighted training dictionary is used to describe all training face images and the face images to be tested The differences under intra-class changes can improve the recognition accuracy and robustness of the face recognition algorithm in the context of large intra-class changes such as posture and expression; the DALM algorithm used can effectively reduce the time complexity of the WSRC algorithm, and Realize accurate reconstruction of test samples and obtain robust recognition results.

Claims (5)

1. A kind of weighted sparse representation face recognition method, is characterized in that, specifically carries out according to the following steps: Step 1, input the training face image to obtain the dictionary matrix A; Step 2, adopt principal component analysis method to carry out feature dimensionality reduction to dictionary matrix A and human face image y to be tested, and carry out the normalization processing of column so that dictionary matrix A and human face image y to be tested have ₁₂ norm; Step 3, using the Gaussian kernel function to calculate the distance between each training face image processed in step 2 and the face image y to be tested, that is, the training face image weight w _i,j ; Step 4, introduce the training face image weight w _i,j in step 3, and construct the weighted training dictionary matrix A': In formula (4), Represents the n _kth image of the kth class sample after weighting; Step 5, solve the sparse coefficient, and obtain the reconstructed face image to be tested; Step 6, according to the reconstructed test face image y ^* obtained in step 5, calculate the residual error of each type of person corresponding to the test face image: r _i (y)=||yy ^* || ₂ i=1,2,...,k (14); Step 7, output: solve the category of the face image y to be tested, compare the category of the face image y to be tested with the category of the training face image, and when the two are consistent, realize face recognition; The expression of the y category of the face image to be tested is: identity(y) = _argmin ri(y) (15). 2. a kind of weighted sparse representation face recognition method according to claim 1, is characterized in that, in step 1, obtains dictionary matrix A and specifically implements according to the following steps: Assume that there are k classes of training face images, and each class consists of n _i training face images, then there are A training face image; Let the pixel of each face image be w×h, and accumulate the face images into a column vector v whose dimension is m=w*h, then v _i,j ∈ R ^m represents the jth A training face image, where m is the dimension of the feature vector; Merge all column vectors of the i-th training face image into a sample set Then combine the sample sets A _i of k categories to obtain the dictionary matrix A: A=[A ₁ , A ₂ , . . . , A _k ]∈R ^m×N (1). 3. A kind of weighted sparse representation face recognition method according to claim 1, characterized in that, in step 2, the dimensionality reduction processing method adopted is to process all original training face images and the face images to be tested into a 384-dimensional feature vector. 4. a kind of weighted sparse representation face recognition method according to claim 1, is characterized in that, in step 3, training face image weight w _{i, j} is calculated by formula (2): In formula (2), v _i,j represent the jth training face image of the i class, y represents the face image to be tested, and σ is the width parameter of the Gaussian kernel function, which is the width parameter of all training face images The average Euclidean distance between , namely: In formula (3), M is the number of Euclidean distances between all samples. 5. A kind of weighted sparse representation human face recognition method according to claim 1, is characterized in that, in step 5, obtains and reconstructs the human face image to be tested and specifically implements according to the following steps: Step 5.1, solving the l ₀ minimization problem: In formula (5), x is a sparse coefficient; Step 5.2, using the dual augmented Lagrangian multiplier method to solve equation (5), then the Lagrangian multiplier function corresponding to equation (5) is: In formula (6), μ>0, μ is a constant and represents the compensation factor for transforming equality constraints into unconstrained problems, and γ is the obtained Lagrangian multiplier vector; If γ ^* is a Lagrangian multiplier vector and satisfies the second-order sufficient condition of the optimization problem, then, when the compensation factor μ is large enough, the sparse coefficient x optimization problem can be obtained by formula (7), namely: It can be seen from formula (7) that to solve the sparse coefficient x, it is necessary to determine the values of the Lagrangian multiplier vector γ ^* and the compensation factor μ, and then calculate the values of x and γ at the same time through an iterative method, namely: In formula (8), {μ _l } is a positive monotonically increasing sequence, l represents the number of iterations, In step 5.3, in order to accurately reconstruct the face image y to be tested, the ALM algorithm is applied to the dual problem, that is, the DALM algorithm, then formula (5) is transformed into formula (9): In formula (9), the value range of the sparse coefficient x is Then the problem in the Lagrange function form of formula (9) can be expressed as: In formula (10), β is a constant greater than zero and is the compensation factor for converting constraints into equations, and z is the sparse coefficient obtained during the reconstruction process; Step 5.4, using the step-by-step iterative update method to solve the initialization problem x, the dual problem variables y ^* and z, let x=x _l , y ^* =y _l , and from this result, update z _l to z _l+1 , namely: In formula (11), for projection to For the above operator, if it is determined that x=x _l , y ^* =y _l , then y ^* can be calculated by the following formula, namely: βAA ^T y ^* ＝βAz _l+1 -(Ax _l -y) (12) Then, the DALM algorithm can be expressed as: The reconstructed face image y ^* to be tested is obtained by solving formula (13).