1.

INTRODUCTION

Similarity Distance Measurement is a major research area in machine learning and computer vision. In recent years, computer vision tasks have become the hottest topic of technological development in today’s society. Traditional Similarity Distance Measurement is mainly studied for the distance metric between image feature vectors to find a discriminate and robust metric model to measure the similarity between two samples. However, traditional similarity distance measurement methods usually design a metric model based on the feature vector of one-shot image, using the label information of the data to learn a metric subspace so that the distance of sample pair with same label is as small as possible and the distance of sample pair with different label is as large as possible. Compared with the tasks of image matching and recognition in traditional computer vision, these problems application scenarios are more complex, and the targets in the images have serious misalignment problems, which leads to extremely unstable image features and brings a great challenge to the similarity distance metric of images.

2.

RELATED WORK

Person re-identification is a hot topic and attracts a large number of researchers study on this topic^1-5. Person re-recognition is very complex and the target’s appearance is affected by various factors, including camera angle, gait, background, lighting, etc. Existing models is of poor identification accuracy on test data⁴. Thus, person re-identification task is very challenging. The researchers utilized various methods to improve the identification accuracy of existing methods.

For metric learning based method, researchers target metric learning algorithms by learning a robust and discriminative metric model. Weinberger et al.⁶ designed a metric learning algorithm based on the k-nearest-neighbor to learn a Mahalanobis distance. This method learns a metric model that draws closer the k-nearest neighbor samples with the same label, while expanding the distance of sample pair with different labels. Davis et al.⁷ build an optimization model by establishing two Gaussian distributed differential relative entropy functions to learn a novel distance model for pedestrian image similarity measurement. Guillaumin et al.⁸ modelled logistic discrimination based metric method such that the similarity of positive pair based on this metric model are smaller than that of negative pair. Zheng et al.⁹, on the other hand, established a projection subspace learning method for relative distance comparison and probabilized the model. The model learns a metric subspace by maximizing the probability that the positive samples and the negative samples are correctly recognized. Koestinger et al.¹⁰, on the other hand, use the idea of hypothesis testing to establish a likelihood ratio model based on the distribution probabilities of positive and negative samples to learn a Mahalanobis distance. Moreover, Liao et al.¹¹, learn a projection subspace based on a quadratic discriminant analysis based on a sample pair difference vector space. In addition, the KISSME algorithm is used to learn a distance function for the projected samples. Zhao et al.¹² introduced the kernelization approach and proposed a kernelized stochastic KISS algorithm, which enhances the Gaussian distribution characteristics of the training data by kernelizing the original features of training samples. While, these metric learning algorithms have poor generalization ability and low accuracy of testing results.

In recent years, the deep learning methods have been wildly applicated in computer vision tasks and achieved very good results. Li et al.¹³ established a person re-recognition network model (FPNN) based on ‘Siamese’ network structure, which is an early and very representative network for person re-recognition, but its recognition accuracy is very low. Ahmed et al.¹⁴ carried out an improvement on the FPNN person re-recognition network model for discriminative feature extraction. Ustinova et al.¹⁵ built a local feature-based network model using the characteristics of body structure. Liu et al.¹⁶ introduced adversarial generative network (GAN) and attention mechanism to build a network model with the ability to fight against small local interference. However, deep networks need a large amount of data for model training and has limited generalization ability among different surveillance networks, requiring a large amount of data labeled for each surveillance network for model optimization. Deep network-based person re-identification methods have major drawbacks in various detection, recognition and prediction applications.

3.

METRIC LEARNING METHOD FOR PERSON RE-IDENTIFICATION

In this problem, the similarity between pedestrian images is measured by learning a Mahalanobis distance model. Given two sample sets: A = {x₁,x₂,…,x_i,…,x_N}, where x_i, indicates the appearance feature of the sample of the i-th pedestrian under camera A; B = {z₁, z₂, ‧‧‧, z_j, ‧‧‧, z_N}, where z_j denotes indicates the appearance feature of the sample of the j-th pedestrian under camera B. The mathematical expression of the model is as follows

where M ≥ 0 is a positive semi-definite matrix. x_i, z_j represent the feature vectors of two samples from different camera view, respectively. Moreover, M is the metric matrix of distance model. In order to learn a discriminative metric subspace, Liao et al.¹¹ first learn a set of projection features and then learn a Mahalanobis distance by KISSME⁵ method.

where x_i – z_j represents the difference feature vectors. The model of XQDA11 method is established as follows:

According to the related properties of the Rayleigh Entropy, the largest value of the function in equation (3) above is the largest eigenvalue of matrix and the solution is corresponding eigenvector w₁. We use the first r eigenvectors to obtain a set of projection features by W = (w₁, w₂, ‧‧‧, w_r).

4.

IMPROVEMENT OF METRIC LEARNING ALGORITHM BASED ON SIMILAR SAMPLE CONSTRAINTS

In this task, there is a serious overfitting problem. The projection subspace realizes the separation of positive and negative samples by finding a series of feature transformation patterns. To overcome the over-fitting problem, we use the reference set information to establish a pairwise similarity distance metric learning model against over-fitting problem for complex scenes.

and , denote the sample sets under different camera views of the test data, respectively. Then, by using the metric model introduced above, we find the most similar k samples in the reference set for each individual. These k samples are used to calculate the mean difference feature vector to estimate the center of positive pairs’ difference vector:

where q_ij = 0 or 1. q_ij =1 denotes is similar sample of k nearest neighbors. q_ij =0 denotes is dissimilar sample. α_ij denotes the sample’s weight over , defined as follows:

Then, we calculate the center of the training data positive sample difference vector: .

The distribution constraint of positive samples’ difference feature vectors between test data and training data is defined as follow,

where S denotes the distance between distribution of positive sample pairs in the test data and in the training data. This distance is used to limit the distance between the identified pairs and the positive pairs.

Define C = B as a reference set, where B is the data collected under camera B in the training data. Then, the similarity distance between each individual in the test data and each sample in the reference set C is calculated. Samples from Reference set C and test instances from A′ will form negative sample pairs. We define the distance between the similar sample pairs in the reference set and the positive sample pairs as follows:

where is the similar sample pair difference vector distribution center of test individuals in the reference set. p_ij denotes the matching relationship between x_s and z_t. , z_j∈C. p_ij =1 denotes is a sample that is similar to less than (negative sample), and p_st =0 denotes (x_s,z_t) is a pair of similar samples of the k′ nearest neighbors. We use the metric model in Section 3 to calculate the similarity between samples of different camera views. The samples with the highest similarity are treated as similar samples.

where D′ indicates the distance from the center of similar sample pairs in the reference set to the center of the theoretical distribution of positive samples. The distance in equation (6) is introduced as a constraint to the learning of the projection subspace in the second part, so as to improve the generalization ability of the metric model to the test data. The mathematical expression of improved metric learning model is as introduced in equation (9):

The improved metric learning model is transformed to solve the following problem,

The improved metric model is obtained by solving the eigenvalue problem in equation (10). It is worth noting that during the computation, we train the metric model separately for each test individual. Because the test individuals are individual-specific, the characteristics of each test individual vary.

5.

EXPERIMENT

To validate the performance of our model, the identification rates on VIPeR³ dataset is summarized. For the evaluation of the accuracy of algorithms for this task, the widely used cumulative accuracy curve (CMC)⁵ is used to evaluate the performance of our model.

The identification results are compared to some first-class methods to further prove the improvement effect of our novel model. The results are displayed in Figure 1 and Table 1. The identification results of rank-1, 5, 10, and 20 are listed in Table 1. According to the results in this table, it can be clearly seen that the algorithm in this paper has achieved the best recognition accuracy on all indicators. Especially in the recognition accuracy of rank-1, compared to the best comparison model, OSNet, rank-1 accuracy is improved by 3.4%. The recognition accuracy of rank-1, rank-5, rank-10 and rank-20 is improved to 71.4%, 93.6%, 98.2% and 99.8%, respectively. Compared to the baseline comparison algorithm XQDA, the recognition accuracy of the rank-1 of our model is reised by 30.8%. The recognition accuracy improvement effect is very significant.

Figure 1.

Comparison of identification accuracy of different methods on VIPeR dataset.

Table 1.

Comparison results on VIPeR dataset.

6.

CONCLUSION

Overfitting is a common phenomenon that affects the accuracy of algorithms in machine learning tasks. We take person re-identification problem as the object and studies similarity measurement model against the overfitting problem. Person re-identification technology is based on the similarity measurement of pedestrian image pairs, which is more complicated than the traditional data point classification problem and cannot be constrained by the direct sample population distribution distance. In this paper, similar samples of individuals are tested to form pseudo positive pairs. The optimization of the metric model is guided by constraining the difference between the test individual’s positive pairs and the theoretical center of probability distribution. Finally, through extensive comparative experiments and parameter analysis, the effectiveness of our model is verified.