Single-sample face recognition based on mirror singular value decomposition

Since the 1990s, face recognition technology has become one of the hot research topics in the fields of computer vision, pattern recognition and information technology. On this basis, effective recognition methods such as principal component analysis (PCA) [1,2], two-dimensional principal component analysis (2DPCA) [3], two-dimensional principal component analysis (2DPCA) [4] and linear discriminant analysis (LDA) [5] have been proposed. However, the existing recognition methods for frontal face images can only achieve good recognition results when there are a sufficient number of representative face image samples. However, in some special occasions, such as law enforcement, customs passport verification and ID card verification, only one image can be obtained for each category (person). At this time, only these limited number of images can be used to train the face recognition system. If the above-mentioned methods are used to process such a face recognition system with a limited number of training samples, the recognition rate will drop significantly, or even become unsuitable. Reference [6] first uses singular value decomposition on the original face image, then uses several larger singular values ​​obtained by decomposition to approximately reconstruct the original face image, and uses the reconstructed face image and the original image as training samples, thereby expanding the number of original training samples. Then, the 2DPCA method is used to extract features from the sample set with the added training samples. This method can achieve good recognition results. However, due to the changes in posture and expression of face images, the greater the change, the greater the recognition error of the algorithm. Based on this, this paper proposes a mirror singular value decomposition method based on image mirroring and singular value decomposition. This method first performs a mirror transformation on the face image, then performs singular value decomposition on the original face image and the mirror image respectively, and then uses several larger singular values ​​to reconstruct the original face image respectively. These reconstructed images, original images and mirror images are used as training samples, and the (2D)2PCA method is used to extract features from them. Finally, the classification method based on the minimum Euclidean distance is used to classify and recognize the sample set. Since the rotation and other posture changes of the face image are taken into account, the experimental results on the ORL face database show that this method has better recognition performance than the method in reference [6].
1 Idea and implementation of the method
1.1 Generation of mirror face images
Adding mirror images can partially eliminate the impact of head rotation on face recognition, and the face image is basically symmetrical [7]. At this time, we can consider mirroring the original face image A with its vertical center axis according to formula (1), thereby expanding the number of original training face images.
A1=A×M (1)
Where M is a square matrix with anti-diagonal elements as 1 and other elements as 0.
1.2 Face representation based on singular value decomposition

1.3 Feature extraction based on (2D)2PCA

During training, each training face image Ak (k=1,2,…,M) is projected onto Z and X respectively to obtain the projection feature matrix Ck (k=1,2,…,M) of the training sample; at the same time, during testing, for any test face image A, first use formula (5) to obtain the feature matrix C, and then use the nearest neighbor classifier based on the minimum Euclidean distance to classify and recognize the test face image. The structural flow chart of the algorithm in this paper is shown in Figure 1.

2 Experimental results and analysis
2.1 Face database used in the experiment
The face database used in this experiment is the ORL face database, which consists of 40 people, each of whom consists of 10 256 grayscale frontal face images of size 112×92. These images were taken at different times, different lighting, different expressions and different postures. Figure 2 shows some standard face images and their mirror images in the ORL face database.

2.2 Experimental methods and results
In order to compare the recognition effects of various methods, this paper conducts 10 groups of experiments on the ORL face database, including the single-sample PCA algorithm, the SVD+PCA algorithm, the SVD+2DPCA algorithm proposed in reference [6], the SVD+(2D)2PCA algorithm, and the method proposed in this paper. That is, the 1st, 2nd, 3rd, ..., 10th images of each person, a total of 40 face images, are used as training samples, and the remaining 360 images are used as test samples for classification and recognition, and then the average recognition rate is taken. The test results are shown in Table 1. In the following (2D)2PCA method, the row dimension reduction dimension is 10, that is, only the column dimension is changed.

Different feature extraction methods do have a certain impact on the improvement of system recognition rate. In order to verify that the improvement of recognition rate of the proposed method does not only depend on the choice of (2D)2PCA feature extraction method, but is due to the increase of mirror face image samples, the single sample PCA algorithm, SVD+PCA algorithm, SVD+2DPCA algorithm, SVD+(2D)2PCA algorithm and the proposed algorithm are respectively used on the ORL face database. The 1st, 2nd, 3rd, ..., 10th images of each person are used as training face images, and the remaining 360 images are used as test samples. The average recognition rate of 10 groups of experiments under the same feature vector dimension is taken as the final recognition rate. The test results are shown in Figure 3.

At the same time, in order to compare the stability of the reference methods and the proposed method under different numbers of test samples [9], the following test experiment was conducted: the 1st, 2nd, 3rd, ..., 10th images of each person were taken as training samples in the ORL face database, and 10 groups of experiments were conducted. At the same time, in each group of experiments, the first 2, 3rd, ..., 9 images other than the training samples were taken as test samples, and the average recognition rate of each group of experiments was calculated. The experimental results are shown in Figure 4.

2.3 Experimental results analysis
As can be seen from Table 1, under different training sample conditions, the recognition effect of the proposed method is significantly higher than that of the other methods proposed in the references. This is mainly because the addition of mirror information can reduce the impact of posture changes on face recognition. From the experimental data in Figure 3, it can also be seen that when the feature dimension increases, the recognition effects of the SVD+2DPCA and SVD+(2D)2PCA methods are similar, but neither is as good as the proposed method. Moreover, from the comparison curve between the SVD+(2D)2PCA method and the proposed method, it can be seen that the improvement of the recognition rate of the proposed method mainly depends on the addition of mirror information of the face image, rather than just the selection of the (2D)2PCA feature extraction method. As can be seen from Figure 4, with the increase in the number of test samples, the recognition rate of the PCA method is lower and its stability is weaker. Compared with the SVD+2DPCA and SVD+(2D)2PCA methods, the proposed method not only ensures a higher recognition rate than other methods, but also shows strong stability.
By adding mirror images to the original face images to expand the number of training face samples, a new method based on mirror singular value decomposition is proposed. Experiments show that compared with other single-sample face recognition methods, the method proposed in this paper has a higher recognition rate, overcomes the influence of changes in face posture on the recognition results to a certain extent, and achieves better recognition results. However, the recognition rate of existing methods based on single-sample face recognition is generally not high, and the proposal of effective algorithms needs further research.
References
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