CN106778522A - A kind of single sample face recognition method extracted based on Gabor characteristic with spatial alternation - Google Patents

Abstract

The invention discloses a single-sample face recognition method based on Gabor feature extraction and space transformation, which mainly solves the inability of the traditional face recognition method due to the fact that the intra-class scatter matrix is zero under the condition of only a single training sample image. application problem. This method uses Gabor wavelet to extract the spatial feature vector from the original single-sample image, then fuses the extracted spatial feature vector and the original spectral feature vector, uses the feature space transformation method to perform low-dimensional feature space transformation on the fusion feature matrix, and converts it to Transform into a low-dimensional subspace, and finally, use the nearest neighbor classifier to complete the identification. The method of the invention can accurately complete the recognition of a single-sample human face, improves the recognition precision and reduces the calculation cost. Compared with the prior art, the face recognition method proposed by the present invention is more effective and robust.

Description

A single-sample face recognition method based on Gabor feature extraction and spatial transformation

technical field

The invention belongs to the field of pattern recognition and image processing, and relates to the face recognition problem under the situation that the traditional face recognition method cannot be used for a single face image because the scatter matrix in the class is zero; specifically, it is a Gabor feature-based The single-sample face recognition method of extraction and spatial transformation can be used for video surveillance and identity recognition in single-sample situations.

Background technique

Face recognition technology is the most important type of biometric recognition technology. It is currently widely used in video surveillance, supervision and law enforcement, multimedia, process control, identification and other fields. So far, many researchers have achieved a lot of scientific research results in this area. However, for harsh or specific environments, it often poses a new challenge to the face recognition system. For example, law enforcement officers only have a facial image on the criminal's ID card, and at this time they can only use this image for monitoring Compared. For this scenario where there is only one face image, the face recognition problem will become very difficult, mainly because the intra-class scatter matrix in the commonly used classification model is zero, Fisher linear discriminant analysis, maximum divergence difference and other traditional methods will not be used directly. This situation is usually called the single training sample face recognition problem in an unconstrained environment. How to use surveillance to capture a single new face of a criminal under the conditions of poor lighting, large changes in facial posture, and large changes in expression is a big challenge to complete accurate automatic recognition. At present, the problem of face recognition for single training samples has not been well solved.

In recent years, some researchers at home and abroad have done some research on single-sample training images. Gao et al. proposed a Fisher linear discriminant analysis method based on singular value decomposition (SVD) for single-sample training images (Gao Q, Zhang L, ZhangD.Face recognition using FLDA with single training image per person[J].Applied Mathematics and Computation ,2008,205(2):726-734.), the method first decomposes a single image by SVD to obtain a set of base images, and then uses the original image and this set of base images to construct each new training image . At this point, the intra-class scatter matrix in the FLDA model can be obtained. Koc and Barkana et al proposed a method based on column rotation orthogonal triangular decomposition (QRCP) (Koc M, Barkana A.A new solution to one sample problemin face recognition using FLDA[J].Applied Mathematics and Computation,2011,217(24) :10368-10376.), this method uses the column rotation orthogonal triangular decomposition (QRCP) to process the single training sample image, and also obtains a set of base images, and then uses the obtained base images to construct an approximate image (the approximate image contains 97% of the energy of the original image), and finally use the obtained approximate image and the original image to form a new training image for each class, so as to obtain the intra-class scatter matrix in the FLDA model. Li et al. proposed another method to obtain the intra-class scatter matrix (Li L, Gao J, Ge H.A new face recognition method via semi-discrete decomposition for one sample problem[J]. Optik-International Journal for Light and Electron Optics, 2016,127(19):7408-7417.), this method uses semi-discrete decomposition (SDD) instead of SVD or QRCP, uses artificially set decomposition energy parameters to obtain approximate images, and also obtains the intra-class scatter matrix in the FLDA model.

Although both SVD-based and QRCP-based Fisher linear discriminant analysis methods can solve the face recognition problem of a single training sample, these two methods also have the following three shortcomings: (1) The reconstructed approximate image is not very satisfactory Or convinced; (2) In the method based on QRCP, no theoretical analysis and explanation is given, and the approximate image must contain at least 97% of the energy of the original image; in the method based on SVD, when the number of approximate images is greater than 4, the basic There is only one slight difference between the image and the original. (3) In the methods based on SVD and QRCP, the decomposition and storage of large-scale images are ignored.

In terms of recognition rate and recognition time, the method based on SDD is better than the method based on SVD and QRCP, and requires less storage space, but there are still three main defects in the method based on SDD: (1) the method stops The criterion needs human control; (2) The method based on SDD still uses Fisher's discriminant criterion, that is: the method still uses the intra-class scatter matrix and the inter-class scatter matrix to obtain effective discriminant information.

Contents of the invention

In view of the above-mentioned problems, the present invention proposes a single-sample face recognition method based on Gabor feature extraction and spatial transformation to solve the problem that the intra-class scatter matrix is zero in the single-sample image scenario. Due to the feature dimension of face recognition, it can also guarantee a certain recognition performance. Therefore, the accuracy and robustness of face recognition in practical applications are improved.

The key technique for realizing the present invention is: in the situation of a single training sample image, at first utilize Gabor wavelet to extract the spatial feature vector from the original single training sample image; then use the extracted spatial feature vector and the original spectral feature vector The fused feature matrix is obtained; and then the fused feature matrix is transformed into a low-dimensional feature space by using the feature space transformation method, and the fused feature matrix is transformed into a low-dimensional subspace. Finally, the nearest neighbor classifier is used for identification. The single-sample face recognition method based on Gabor feature extraction and spatial transformation not only greatly improves the recognition rate, but also reduces the computational complexity. Compared with the existing technology, this method is more effective and robust.

To achieve the above goals, the specific steps are as follows:

(1) Gabor wavelet is used to extract the spatial information of a single image.

(1.1) Construct Gabor filter function: the present invention adopts a two-dimensional Gabor filter to extract the spatial information of a single image, which is a Gaussian kernel function adjusted by a complex sine plane. is defined as:

where f is the central angular frequency of the complex sinusoidal plane wave, θ represents the normal parallel stripe direction of the Gabor function, φ is the phase, σ is the standard deviation, and γ is the spatial ratio used to specify the ellipticity supported by the Gabor function.

(1.2) Construct Gabor filter bank: Since the Gabor filter bank is made up of a group of Gabor filters with different frequencies and directions, in the present invention, we use the Gabor filter bank with five different scales and eight different directions , the following two formulas give a Gabor filter bank with five different scales and eight different directions:

(1.3) Gabor representation of facial image: For a facial image A(x,y), its Gabor representation can be obtained by convolution and Gabor filtering of the original image, namely:

Among them, G(x,y) represents the two-dimensional convolution result of Gabor filtering at different scales u and different directions v. And the size of G(x,y) is determined by the downsampling factor ξ, and the mean value and unit variance are zeroed to obtain a filter feature matrix Z _u,v ∈R ^m*n .

(1.4) Construct the Gabor direction block feature matrix: convert the filter feature matrix Z _{u, v} obtained in (1.3) into a one-dimensional column vector, and use Z ₀ to represent five different scales and eight The feature matrix of the Gabor direction block in different directions is as follows:

in, is the one-dimensional representation of Z _u,v at scale i, and Z ₀ ∈ R ^{(m *n)×40} is the Gabor direction block feature matrix obtained from the convolution result G(x,y).

2. Fusion of spatial information extracted by Gabor wavelet and spectral information of the original image itself.

The Gabor direction block feature matrix obtained from step 1 is Z ₀ ∈ R ^(m*n)×40 . On the other hand, since a single training sample image itself contains very important spectral information, the Gabor space feature vector and spectral feature The vector Y ₀ ∈ R ^{(m *n)×41} is fused, and the fusion feature matrix F∈R ^(m*n)×41 can be obtained:

where _σ1 and _σ2 are the standard deviations _{of Z0} and Y0, respectively, which can be obtained by calculating the square root of the variance of the eigenvectors.

3. Feature space transformation based on fusion feature matrix.

(3.1) Establish fusion feature optimization model

(3.2) Perform feature space transformation to obtain transformation matrix

4. Construct the projected feature vector

For the test feature vector f∈R ^n×1 , the projected feature vector can be obtained by the following linear transformation

Obviously, the above computational complexity is significantly reduced.

5. After obtaining the projected feature vector, use the nearest neighbor classifier for identification.

The inventive method has the following advantages:

(1) overcome the difficult problem that single training sample encounters: because the intraclass scatter matrix in the single training sample model is zero, so traditional Fisher's criterion fails, and the method of the present invention reconstructs intraclass scatter through Gabor filtering and feature space transformation matrix.

(2) The present invention can make full use of the spatial information of the original image and its own spectral information. At the same time, Gabor-based spatial feature information is more robust than the spectral feature information of the image itself, and can avoid local distortions caused by changes in expression, pose, and illumination. The recognition rate and recognition time are greatly improved, and the calculation cost is reduced. Compared with the prior art, the face recognition method proposed by the present invention is more effective and robust.

Description of drawings

The flowchart of Fig. 1 method of the present invention

Figure 2 The real part of Gabor filtering at 5 different scales and 8 different directions

Figure 3 Convolution results of 2 Gabor filters for a single face image

Figure 4. Five different face images from each dataset

Figure 5 The recognition rate of the four methods under different projections (ORL face database)

Figure 6 The recognition rate of the four methods under different projections (Yale face database)

Figure 7 The recognition rate of the four methods under different projections (FERET face database)

detailed description

The invention is a single-sample face recognition method based on Gabor feature extraction and space transformation. Referring to Fig. 1, the specific implementation steps of the present invention include the following.

Step 1. Use Gabor wavelet to extract the spatial information of a single image.

(1.1) Construct Gabor filter function: the present invention adopts a two-dimensional Gabor filter to extract the spatial information of a single image, which is a Gaussian kernel function adjusted by a complex sine plane. is defined as:

where f is the central angular frequency of the complex sinusoidal plane wave, θ represents the normal parallel stripe direction of the Gabor function, φ is the phase, σ is the standard deviation, and γ is the spatial ratio used to specify the ellipticity supported by the Gabor function.

(1.2) Construct Gabor filter bank: Since the Gabor filter bank is made up of a group of Gabor filters with different frequencies and directions, in the present invention, we use the Gabor filter bank with five different scales and eight different directions , the following two formulas give a Gabor filter bank with five different scales and eight different directions:

(1.3) Gabor representation of facial image: For a facial image A(x,y), its Gabor representation can be obtained by convolution and Gabor filtering of the original image, namely:

Among them, G(x,y) represents the two-dimensional convolution result of Gabor filtering at different scales u and different directions v. And the size of G(x,y) is determined by the downsampling factor ξ, and the mean value and unit variance are zeroed to obtain a filter feature matrix Z _u,v ∈R ^m*n .

(1.4) Construct the Gabor direction block feature matrix: convert the filter feature matrix Z _{u, v} obtained in (1.3) into a one-dimensional column vector, and use Z ₀ to represent five different scales and eight The feature matrix of the Gabor direction block in different directions is as follows:

in, is the one-dimensional representation of Z _u,v at scale i, and Z ₀ ∈ R ^{(m *n)×40} is the Gabor direction block feature matrix obtained from the convolution result G(x,y).

Step 2. Fusion of spatial feature information extracted from Gabor features and spectral information of the original image.

Since the single sample image itself contains very important spectral information, the Gabor space feature vector and spectral feature vector Y ₀ ∈ R ^(m*n)×41 are fused to obtain the fusion feature matrix F ∈ R ^{(m*n) ×41} :

where _σ1 and _σ2 are the standard deviations _{of Z0} and Y0, respectively, which can be obtained by calculating the square root of the variance of the eigenvectors.

Step 3. Perform feature space transformation on the fusion feature matrix F.

(3.1) Establish fusion feature optimization model

In order to be able to distinguish each class in all training images, it is desirable that the differences from the same class are as small as possible, and conversely, the differences between sample images from different classes are as large as possible. Inspired by the idea of Fisher's criterion, we established the following fusion feature optimization model:

Our goal is to use the feature space transformation to project the fusion feature matrix into a low-dimensional feature subspace, and find an optimal linear transformation matrix that can maximize the separation between classes.

(3.2) Perform feature space transformation to obtain transformation matrix W ₂ .

(3.2a) Construction of Gabor inter-class scatter matrix and Gabor intra-class scatter matrix.

Assuming that n-dimensional training samples are obtained from the fusion feature matrix, c is the number of classes, and n _i (i=1,2,...,c) is the number of training samples of the i-th class, so Gabor inter-class scatter matrix and Gabor The intra-class scatter matrix is defined as follows:

in, is the j-th fused feature vector from the i-th class, f _i is the mean vector of the i-th class, and f ₀ is the mean vector of all training samples.

We simultaneously maximize and minimize The transformation matrix W can be obtained. Its optimization model is as follows:

But when the matrix in the above formula and matrix When singular, the above criterion does not hold. In this case, matrix factorization as well as feature space transformation usually play an important role. In the feature space transformation, since our goal is to maximize the difference between different categories, we should discard , because it contains useless information; while the Important information about the null space.

(3.2b) Project Gabor inter-class scatter matrix and Gabor intra-class scatter matrix to s ₁ -dimensional subspace and obtain transformation W ₁ .

In this step, first consider the The singular value decomposition (SVD) of

Block U _b into blocks, in therefore,

Thus, a formula of the following form is obtained:

in, is a column-orthogonal matrix, is a diagonal matrix with non-increasing and positive diagonal elements. In practical applications, the matrix The singularity will lead to the reduction of discriminative ability. Therefore, its zero eigenvalues and corresponding eigenvectors should be discarded. Based on the above considerations, first, using the transform Transform the original data into s ₁ -dimensional space. So it gets transformed

(3.2c) Perform relevant transformations in the s ₁ -dimensional transformation space to obtain transformation W ₂ .

Transformation has been obtained in step (3.2b) In the resulting transformed space, the between-class scatter matrix and the intraclass scatter matrix become respectively:

in, So the original n×n dimensional inter-class scatter matrix and intra-class scatter matrix are reduced to s ₁ ×s ₁ dimension.

Now, we consider The eigenvalue decomposition of :

in is an orthogonal matrix, is a diagonal matrix. So there are:

In most application areas, rank is greater than The rank of , and ∑ _w is non-singular because:

So have:

Therefore, the optimal transformation matrix It can be obtained by the following formula:

In fact, the above optimization problem It can be transformed into the following eigenvalue problem to solve:

The solution to the above eigenproblem can be obtained by solving the generalized eigenvalues. Assume that λ ₁ , λ ₂ , ..., λ _t are the t largest eigenvalues arranged in descending order of the eigenvalue problem, and w ₁ , w ₂ , ..., w _t are the corresponding eigenvectors.

In order to solve the problem Two steps are mainly considered: the first step is to maximize the inter-class scatter matrix through singular value decomposition (SVD), and the second step is to solve the generalized eigenvalue problem. The key issue in the first step is to deal with the following optimization problems:

We know: is a column-orthogonal matrix, is a diagonal matrix with non-increasing and positive diagonal elements. Therefore, it can be obtained that U _b1 is the solution of the above problem.

Additionally, pseudoinverses are often used to solve singular matrices. The pseudo-inverse of a matrix can be computed by singular value decomposition (SVD). A natural extension to using the pseudoinverse is to exploit the eigendecomposition matrix or (to fulfill). More specifically, let M=U∑V ^T be the singular value decomposition of M, where U and V are column-orthogonal matrices, and ∑ is a diagonal matrix with positive diagonal elements, then the pseudo-inverse of M is M ⁺ = V∑ ^-1 U ^T . Based on the above discussion, we get The optimal transformation matrix for

Thus, based on the above transformation and argumentation, we conclude that in the transformed s ₁ -dimensional subspace, is an optimal transformation matrix.

Step 4. Construct projected feature vectors

For a face test image I∈RM ^×N , the Gabor-based spatial feature matrix can be given by the formula obtained, and by the formula The fusion feature matrix can be obtained. Therefore, the Gabor-oriented block feature matrix of a new face test image by the formula as well as available.

Step 5. Finally, use the nearest neighbor classifier for identification.

Based on the above description, for a facial image A(x, y), the spatial feature information is extracted by Gabor wavelet, and then fused with the spectral information of the original image, and then the feature space is transformed, and the transformed s ₁ -dimensional subspace , we get the optimal transformation matrix And get the projected eigenvector Then use the nearest neighbor classifier for identification. The nearest neighbor classifier (NNc) is a non-parametric method classifier, its main idea is: Suppose the training sample set is X={(x ₁ ,l ₁ ),(x ₂ ,l ₂ ),…,(x _n ,l _n )}, where l _i ,i=1,2,…,n are class labels, if there is a minimum distance between the test sample x and the k samples x ₁ ,…,x _k of the training sample, then the test sample x belongs to class l _i (i=1,2,...,k).

Suppose F ^test is the test image, according to the formula Gabor direction block feature matrix x ^test can be obtained. It can be seen from the following formula that F ^test belongs to the i-th category:

in,

The effects of the present invention can be further illustrated by the following simulation experiments.

1. Simulation conditions and parameters

Examples of the present invention are directed at ORL, Yale and FERET face databases. The ORL database contains 400 face images of 112×92 size for 40 people, 10 for each person. Since these images were taken at different times, they have variations in pose, angle, scale, expression and glasses etc. Figure 4(a) presents 5 different face images of this dataset. In this experiment, 1 image of each person is used for training, and the remaining 9 images are used for testing; the Yale face database contains 165 images from 15 people, and each person has 11 images. These images change according to facial expressions and lighting conditions, such as: happy, sad, surprised, indifferent, wearing glasses, etc. Figure 4(b) presents 5 different facial images of this dataset. In the experiment, the size of each image is set to 100×100, 1 image of each person is used for training, and the remaining images are used for testing; the FERET face database was initiated by the US Department of Defense through the DARPA project. This dataset contains 14051 facial grayscale images from 1199 different people with poses, facial expressions, etc. Figure 4(c) presents 5 different face images of this dataset. In the experiment, we select 5 different images of 15 people, a total of 75 facial images, and resize the images to 80×80. We conducted 50 experiments on the above three face databases and compared them with the existing methods, namely Fisher's linear discriminant analysis method based on SVD on a single face image, Fisher's linear discriminant analysis method based on QRCP and based on Fisher's linear discriminant analysis method for SDD. Figure 2 shows Gabor filter banks with 5 different scales and 8 different directions. Figure 3 shows the convolution results of 2 Gabor filters on a single face image.

2. Simulation content and result analysis

In the simulation test, the method of the present invention is compared with the traditional Fisher linear discriminant analysis method based on SVD, the Fisher linear discriminant analysis method based on QRCP and the Fisher linear discriminant analysis method based on SDD, and the experiment is carried out on three data sets.

experiment one:

Experiment 1 was implemented on the ORL face database according to the above five steps. The experimental results on the recognition rate are shown in Figure 5. From Figure 5, we can see that among the four methods, the maximum recognition rate of the proposed method is 76.67 %, are higher than other methods (the maximum recognition rate of Fisher's linear discriminant analysis method based on SVD is 56.67%, the maximum recognition rate of Fisher's linear discriminant analysis method based on QRCP is 68.89%, the maximum recognition rate of Fisher's linear discriminant analysis method based on SDD The recognition rate is 71.94%). Compared with the other three methods, our proposed method has the largest recognition rate and achieves the best recognition performance. Obviously, the robustness of the proposed method is due to the utilization of Gabor direction feature blocks and fusion of feature space transformations.

Experiment 2:

The second experiment was implemented on the Yale face database according to the above five steps. Figure 6 shows the relationship between the recognition rate of the four methods and the variation of the projection vector. From Figure 6, we can draw the following conclusions: the proposed method varies with As the number of projection vectors increases, the recognition rate increases gradually, and the recognition performance gradually increases. The maximum recognition rates of Fisher's linear discriminant analysis method based on SVD, Fisher's linear discriminant analysis method based on QRCP, Fisher's linear discriminant analysis method based on SDD and the proposed method are 24.00%, 38.67%, 45.33% and 64.67%, respectively. From the perspective of recognition rate, the proposed method is optimal. The Fisher linear discriminant analysis method based on SDD and the Fisher linear discriminant analysis method based on QRCP are suboptimal. The Fisher linear discriminant analysis method based on SVD method has the best recognition performance. is the worst, this Figure 6 can fully illustrate the above point of view

Experiment three:

Experiment 3 was implemented on the FERET face database according to the above five steps. The SVD-based Fisher linear discriminant analysis method, the QRCP-based Fisher linear discriminant analysis method, the SDD-based Fisher linear discriminant analysis method, and the relationship between the recognition rate and the projection vector of the proposed method are shown in Figure 7. It can be clearly seen from Figure 7 that the recognition performance of the proposed method is higher than that of the other three methods, and the recognition rate gradually increases with the increase of the number of projection vectors, which shows a good recognition performance. The best recognition rates of Fisher's linear discriminant analysis method based on SVD, Fisher's linear discriminant analysis method based on QRCP, Fisher's linear discriminant analysis method based on SDD and the proposed method are: 88.83%, 86.67%, 93.33% and 96.67%, respectively.

The above three experiments show that the single-sample face recognition method based on Gabor feature extraction and spatial transformation of the present invention is robust to local distortions caused by changes in expression, posture and illumination due to Gabor feature blocks in actual face recognition. Therefore, it has better recognition results. Table 1 shows the maximum recognition rate (rr, %) and recognition time (t, s) of the four methods on three different data sets. #1, #2, and #3 represent the ORL, Yale, and FERET datasets, respectively.

Table 1 The maximum recognition rate (rr, %) and recognition time (t, s) of the four methods on different data sets.

It can be seen from Table 1 that the recognition rate of the proposed method is higher than that of the other three methods (namely: Fisher's linear discriminant analysis method based on SVD, Fisher's linear discriminant analysis method based on QRCP, and Fisher's linear discriminant analysis method based on SDD). The recognition rate is also far less than the other three methods in terms of recognition time. In other words, in all the above experiments, the running time of the proposed method on the ORL, Yale and FERET datasets is about 22.28, 98.08 and 52.60 times faster than the SDD-based method, respectively.

As can be clearly seen from the experimental result figure, the recognition rate of the inventive method is obviously higher than the Fisher's linear discriminant analysis method based on SVD, the Fisher's linear discriminant analysis method based on QRCP and the Fisher's linear discriminant analysis method based on SDD, and the average recognition time significantly lower than the other three algorithms. This temporal difference is mainly caused by image vectorization. It can be seen that the face recognition method of the present invention is a very effective and robust single-sample face recognition method.

Claims (3)

1. A single-sample face recognition method based on Gabor feature extraction and spatial transformation comprises the following steps:

(1) extracting spatial information of a single image by using a Gabor wavelet:

(1.1) constructing a Gabor filter function: the invention adopts two-dimensional Gabor filtering to extract the spatial information of a single image, which is a Gaussian kernel function adjusted by a complex sinusoidal plane; is defined as:

wherein f is the central angular frequency of the complex sinusoidal plane wave, θ represents the normal parallel stripe direction of the Gabor function, φ is the phase, σ is the standard deviation, γ is the spatial ratio for specifying the supporting ellipse of the Gabor function;

(1.2) constructing a Gabor filter bank: since the Gabor filter bank is composed of a group of Gabor filters with different frequencies and directions, in the present invention, we use Gabor filter banks with five different scales and eight different directions, and the following two formulas give a Gabor filter bank with five different scales and eight different directions:

(1.3) Gabor representation of face image: for a face image a (x, y), its Gabor representation can be obtained by convolution of the original image and Gabor filtering, i.e.:

wherein G (x, y) represents the two-dimensional convolution result of Gabor filtering in different scales u and different directions v, and the size of G (x, y) is determined by a down-sampling factor ξ, and the zero mean and unit variance are carried out on the G (x, y) to obtain a filtering feature matrix Z_u,v∈R^m*n；

(1.4) constructing a Gabor direction block feature matrix: filtering characteristic matrix Z obtained in (1.3)_u,vConversion into one-dimensional column vector, using Z₀The Gabor direction block feature matrix representing five different scales and eight different directions of the face image a (x, y) is as follows:

wherein,is Z_u,vOne-dimensional representation at the scale i, Z₀∈R^(m*n)×40Is a Gabor direction block feature matrix obtained from the convolution result G (x, y);

(2) and fusing spatial information extracted by Gabor wavelet and spectral information of the original image: obtaining a Gabor direction block feature matrix Z from the step (1)₀∈R^(m*n)×40On the other hand, since a single training sample image itself contains very important spectral information, the Gabor spatial feature vector and the spectral feature vector Y are combined₀∈R^(m*n)×41Performing fusion to obtain a fusion feature matrix F ∈ R^(m*n)×41：

Wherein σ₁And σ₂Are each Z₀And Y₀The standard deviation of (a), which can be obtained by calculating the square root of the variance of the feature vector;

(3) feature space transformation based on the fusion feature matrix:

(3.1) establishing a fusion characteristic optimization model

(3.2) performing feature space transformation to obtain a transformation matrix

(4) Constructing a projection feature vector;

(5) after the projected feature vectors are obtained, the nearest neighbor classifier is used for identification.

2. The single-sample face recognition method based on Gabor feature extraction and spatial transformation according to claim 1; the method is characterized in that: the specific process of the feature space transformation framework in the step (3.2) is as follows:

(3.2a) defining Gabor inter-class spreading matrices and intra-class spreading matrices:

suppose that n-dimensional training samples are obtained from the fused feature matrix, c is the number of classes, n_i(i ═ 1,2, …, c) is the number of training samples of class i, and then the inter-Gabor scattering matrix and the intra-Gabor scattering matrix are defined as follows:

wherein,is the jth fused feature vector, f, from class i_iIs the mean vector of class i, f₀Is the mean vector of all training samples;

(3.2b) transforming the inter-class and intra-class scatter matrices to s₁In the space of dimensions and obtaining a transformation W₁：

First considerSingular Value Decomposition (SVD)

Will U_bThe block-shaped materials are divided into blocks,whereinTherefore, the temperature of the molten metal is controlled,

thus, the formulaCan be converted into the following forms:

wherein,is a matrix of orthogonal columns,is a diagonal matrix with non-increasing and positive diagonal elements; in practical application, the matrixThe singularity of (a) may cause a reduction in discrimination ability; therefore, its zero eigenvalue and corresponding eigenvector should be discarded; based on the above considerations, we utilize transformationsTransforming the original data to s₁In the space of the dimension;

(3.2c) at s₁Performing a correlated transformation in a transformation space of dimensions to obtain a final transformation W₂：

In the obtained s₁Inter-class scatter matrices in dimension transform spaceThe following steps are changed:

intra-class scatter matrixThe following steps are changed:

wherein,

now, we considerDecomposition of characteristic values of (2):

whereinIs an orthogonal matrix in which the matrix is orthogonal,is a diagonal matrix; thus, there are:

in most of the fields of application,is greater thanAnd ∑, and_wis non-exotic, due to:

therefore, there are:

thus, the optimal transformation matrixCan be obtained by the following formula:

3. the single-sample face recognition method based on Gabor feature extraction and spatial transformation according to claim 1; the method is characterized in that:

the specific method for constructing the projection feature vector in the step (4) comprises the following steps:

for test feature vector f ∈ R^n×1The projected feature vector can be obtained by linear transformation as follows

It is apparent that the computational complexity is significantly reduced, and the face test image I ∈ R^M×NThe Gabor-based spatial feature matrix can be formulated fromIs obtained and expressed byCan be fusedA feature matrix; thus, a new Gabor directional block feature matrix for the face test imageThis can be obtained from the following equation:

then x is the Gabor directional block feature matrix we need, here denoted as