Research on Face Recognition Method by Autoassociative Memory Based on RNNs

1 Intelligent School of Technology and Engineering, Chongqing University of Science and Technology, 401331 Chongqing, China 2Key Laboratory of Machine Perception and Children’s Intelligence Development, Chongqing University of Education, 400067 Chongqing, China 3College of Safety Engineering, Chongqing University of Science and Technology, 401331 Chongqing, China 4China United Engineering Corporation Limited, 310052 Hangzhou, Zhejiang, China 5Chongqing Energy Investment Group Science and Technology Co., Ltd., 400061 Chongqing, China


Introduction
With the development of information and Internet, biometric technology has been rapidly developed for security, confidentiality, and convenience in Internet applications.Nowadays, many biometric technologies have been developed, such as fingerprint recognition, face recognition, and iris recognition [1,2].Among them, face recognition is one of the most widely used biometric technologies [3].However, these technologies may be still vulnerable to sophisticated hacker attacks.N. Ratha et al. [4,5] summed up eight basic threats that plague biometric-based authentication systems.One of vulnerabilities (Threat 6) is that it is possible to modify templates in the biological database or insert templates from unauthorized users into the biological database [6].Biometric templates are a set of stored biometric features comparable directly to probe biometric features [7].
In recent years, substantial research has been conducted to improve operation security in view of the above threats, especially the protection of biometric template database for Threat 6. Biometric template protection schemes have been divided into Cancelable Biometrics (CBs), Biometrics Cryptosystems (BCs) and Biometrics in the Encrypted Domain (BED) [8].CBs are to use noninvertible transformation to convert the original biometric data into intentionally distorted information [9].In [10], it proposed a new method for the design of alignment free cancelable fingerprint templates using local minutia structures formed by zoned minutia pairs.A novel cancelable biometric template generation algorithm using Gaussian random vectors and one way modulus hashing was proposed in [11].In BCs, a key is either bound (key binding schemes) or extracted (key generation schemes) from biometric data [8].The key binding schemes can be classified as fuzzy vault schemes [12] and the fuzzy commitment schemes [13].Regarding key generation schemes, a number of discretized fingerprint descriptors and appropriate error correcting codes were used to propose an effective biometric cryptosystem construction for biometric template protection Complexity in [14].However, as in the case of CBs, CBs usually present a performance degradation with respect to the systems relying on unprotected data [8].From this secure multiparty computation and homomorphic cryptosystems were used to carry out BED [15].At present, current approaches to BED are based on garbled circuits [16] and homomorphic encryption [15], but these schemes are much more complex than the representations used in the aforementioned articles [17].
Although these schemes achieved some success, they do not completely eliminating the risk of hacker attacking and tampering the templates.There is no doubt that the existence of the template database is a hidden danger to public security [8].In order to tackle this problem, a new face recognition method by associative memory (AM) is proposed in this paper.Although we focus on face recognition throughout this paper, our study can be extended to other biometric authentication methods.
Associative memories (AMs) are brain-style devices designed to store a set of patterns as stable equilibria such that the stored patterns can be reliably retrieved with the initial probes containing sufficient information about the patterns [18].AMs can be divided into Autoassociative Memory (AAM) and Hetero-Associative Memory (HAM) [18].When the input  and the output  are identical,  is said to be memorized with  in the AAM, whereas  is said to be memorized with  in the HAM.In recent years, AMs, especially the AMs based recurrent neural networks (RNNs), have been widely studied.For example, in [19], a synthesis procedure for designing associative memories based on discrete-time recurrent neural networks (DTRNNs) was presented and the global convergence of the DTRNNs was guaranteed via the stability analysis.In order to get some broad conditions for design cloning templates of RNNs, some new methods about associative memories based on RNNs with time delay are given in [20].Meanwhile, in the research process of AM based on RNNs, the stability of RNNs plays a decisive role in the realization of associative memory.In [21][22][23], the stability of RNNs is studied systematically.Besides, the RNNs were also widely used in many fields [24,25].However, if we want to better realize associative memory among facial features, the constraints of the current AM based RNNs are still relatively conservative.Therefore, it is necessary to use stability analysis to slack the constraints and apply them to face recognition.
Based on the aforementioned discussion, the main contributions of this paper are listed as follows: (1) To protect the face features database fundamentally, a new face recognition method by AAM based on RNNs is proposed without establishing face feature database, in which the face features are transformed into the parameters of the AAM model.
(2) An AAM model based on RNNs with a tunable slope activation function is proposed, which is different from the work of [20,21] that only discusses on Autoassociative Memory at the fixed slope activation function.
(3) The constraints of AAM model parameters are relaxed by our theories.It provides a theoretical basis for ensuring the effectiveness of face recognition.
The rest of this paper is organized as follows.The overview of the proposed method is elaborated in Section 2. In Section 3, we propose an AAM model based on RNNs, then the stability of the model is analyzed in detail, and its design procedure is given.In Section 4, a face AAM recognition method is established.Two experiments are presented in Section 5. Finally, conclusions are drawn in Section 6.

Overview of the Method
In order to solve a problem of hacker attacking and tampering the templates, a face recognition method by AAM based on RNNs is proposed in absence of the biometric database, as shown in Figure 1.
The common method of face recognition is usually to compare the facial features collected on site with those in the face database one by one, and then to determine whether if it has access right based on their similarity.In contrast, the method proposed in this paper is not to establish a face database, but to set up some special kind of relationship between facial features of authorized users.This relationship is stored in the model parameters after AAM training.Therefore, the relationship is unique because model parameters will vary with the authorized users.
For example, there are four users, respectively are A, B, C, and D. If the users A, B, and C have access right, and the user D has no access right, the model parameters  1 can be obtained by AAM training of the facial features of users A, B, and C, where the user C can achieve AAM, while the user D cannot.Similarly, if the users A, B, and D have access right, and the user C has no access right, the model parameters  2 can be obtained by associative memory training of the facial features of users A, B, and D, where the user D can achieve AAM, while the user C cannot.Obviously, the model parameters  1 and  2 are completely different due to due to the uniqueness of each user's facial features.Therefore, it could realize face recognition without establishing the face database, where facial features of authorized users are converted to model parameters.The specific face recognition method is as follows.
At the registration stage, under the condition that the face features of the authorized users are extracted, AAM model parameters are obtained by AAM training where its input and output are coming from facial features from the extracted authorized users.Therefore, the special relationship between authorized users' facial features has been stored in the AAM model parameters due to the uniqueness of each user's facial features.
At the recognition stage, when a user accesses the face recognition system, the user's facial features are first obtained through a feature extractor and then are entered into the trained AAM model to get its output features.Whether the visitor can access is determined by its similarity between the input features and the output features.
In the face identification, authorized users can successfully pass identification detection because of the special relationship (AAM model parameters), whereas unauthorized users cannot.

Technical Solutions
The face recognition method proposed in this paper is implement through AAM based on RNNs.Therefore, this section first proposes an AAM model based on RNNs for face recognition system, where a tunable slope activation function is given.Meanwhile, in order to slack the constraint conditions of the model, its stability is proved and analyzed by 2 Theorems and 2 corollaries.Finally, in order to guarantee the implementation of the associative memory function of face recognition method, the associative memory process of AAM model based on RNNs is discussed and its design procedure is given.

Stability Analysis.
On the basis of the new tunable slope activation function mentioned above, it is necessary for the AAM model to attain stability under different slope factors.The stability constraints that the model needs to satisfy are given through the following theorems and corollaries.Theorem 2. In ( 5), choose 0 <     ≤ 1/ℎ.
Remark 5.The proof of Theorem 4 is similar to that of Theorem 2.
On the basis of the above theorems, if we choose  > 1, we can draw the following corollaries.Corollary 6.From Theorem 2, let 0 <     ≤ /ℎ.
(II) When   = (/  −   ℎ), (5) converges to a stable state, and its value is smaller than −ℎ.Remark 8. From the above two corollaries, one can draw a conclusion that the constraints, parameters of the model in [19,20] needing to meet, are conservative compared with the constraints proposed in this paper.In other words, the constraints of the model parameters proposed in this paper are relatively slack.

Associative Memory.
Next, we will discuss associative memory process of AAM model based on RNNs by use of the above theories.
The parameters of the AAM model can be obtained by the aforementioned associative memory parameters' acquisition process.Therefore, under the known associative memory parameters, the associative memory process is described as follows.
Next, we give the design procedure of AAM based on RNNs by use of above the associative memory parameters' acquisition process and associative memory process.See Procedure 1.
Synthesize the AAM model with the connection weight matrixes A, B, and C and bias vector D. From the above procedure, an AAM model can be obtained.Get   () ,   () ,  () from  ()  ; 23: end for 24: Get coefficient matrix B, C, and bias vector D by use of   () ,   () ,  () from  ()  ; Procedure 1

The Face Recognition Method
In this section, according to the stability analysis and the procedure of AAM model based on RNNs in Section 3, the face recognition method by AAM model is established.As shown in Figure 2, the method can be divided into three parts, namely, image preprocessing, model training, and face image recognition.
Step Step 3 (image recognition).During the recognition process, if someone wants to access a face recognition system, the person's face image will be obtained.By image preprocessing method in Step 1, the corresponding binary input matrix  can be obtained.If binary input matrix  is input into the established AAM model, the corresponding binary output matrix  will be gotten by AAM.Subtract output  from input  and you have the matrix  =  − .The number  of zero elements in the matrix  can be calculated, and then a ratio  = (/)×100% is obtained.Under the circumstance that the matching threshold , 0 ≤  ≤ 1 is set, the ratio , 0 ≤  ≤ 1 is compared with the set match threshold .If the ratio  ≥ , it shows that this identification is successful; otherwise, it shows that this identification is a failure.
Remark 14.In the Step 1, the number of neurons of RNNs grows as more selected face images are added.The relationship between the number of neurons and the number of selected face images should satisfy the inequality: 2  ≥ , where  is the number of neurons of RNNs and  is the number of selected face images.

Experiments and Summary of Findings
In this section, recognition performance indicators are listed first.On that basis, Experiment 1 is simulated to test the feasibility of the proposed face recognition method, and Experiment 2 is simulated to evaluate the performance of the proposed face recognition method.Finally, according to the results of two experiments, some findings can be summarized 5.1.Recognition Performance Indicator.In this section, the false acceptance rate (FAR) is used to evaluate the performance of the proposed face recognition method.The specific formula of FAR is as follows: where NFA and TNT stand for the number of false acceptance and the total number of tests, respectively.From (13), we can get that lower number of FAR equate to better performance of the proposed face recognition method.The initial conditions of the established AAM model are . ., ), respectively.Binary matrixes  1 ,  2 , . . .,  20 as the input and output of the model appear as ( 1 ,  1 ), ( 2 ,  2 ), . . ., ( 20 ,  20 ), respectively.According to the AAM model training method of the Step 2 in Section 4, model template parameters can be obtained   () ,   () ,  () ,  ∈ (1, 2, ⋅ ⋅ ⋅ 891).
A binary matrix transformed by a face image that has been trained before by AAM, is used as input to the established AAM model, then the corresponding binary output matrix can be obtained by AAM:

𝛼 =
Subtract output  from input  and you have the matrix  =  − .The number of zero elements in the matrix  is  = 891 by calculation, and then the consistent percentage  = (/) × 100% = [/(33 × 27)] × 100% = 100% can be obtained.If the threshold is defined as  = 0.95, we can see that  = 100% > .Therefore, the visitor is considered to have access.
The result of experiment shows that the proposed face recognition method by AAM based on RNNs can realize biological recognition, and its feasibility is verified.
Randomly selecting a face image which is from unregistered people, such as shown in the Figure 4(b), a face image named s5 3.bmp in the ORL database.Then, the image s5 3.bmp is transformed into a binary matrix  through the transformation of image dimension and image binarization like the processing steps in the registration phase.The binary matrix  is used as input to the established AAM model, and then the corresponding binary output matrix  can be obtained.The matrix ℓ is obtained by matrix  minus matrix , and then the number of zero elements in the matrix  = 95.
The consistent percentage  = (/)×100% = [95/(33×27)]× 100% = 87.96%can be obtained.If the threshold is defined as  = 0.95, we can see that  = 87.96%< .Therefore, the visitor is considered to have no access.According to the above acquired AAM model and mentioned face recognition steps, 240 face images of 24 unregistered people randomly selected from the ORL database are used as input to the established AAM model, respectively.By calculation, the false accept number is 2. Therefore, NFA = 2 and TNT = 240.Finally, according to (13), we can get that the FAR of the established facial recognition method is The results of experiment show that if the image of an unauthorized user who is not registered before is used as input to AAM, the corresponding AAM effect is not good enough.It can be concluded that the proposed face recognition method can achieve certain face recognition effects with good performance.

Summary of Findings.
In general, our findings can be summarized as follows: (1) In the absence of a face database, the method of AAM based on RNNs can realize face recognition.That is, the AAM model based on can replace the face database to achieve the face recognition effect.Thus, the intrusion and tampering of face database are indirectly avoided.

Conclusion
In the paper, an AAM model based on RNNs is proposed to implement faces recognition in the absence of a face database.The stability of the model is studied in detail, and a design procedure of AAM is given.Based on the proposed AAM model and the procedure of AAM, a face AAM recognition method is established.Two experiments are given to verify the proposed face recognition method.
From the examples in Section 5, we know that the proposed face recognition method by AAM based on RNNs is feasible.

Figure 1 :
Figure 1: Flowcharts of the face recognition method by AAM based on RNNs.

ComplexityFaceFigure 2 :
Figure 2: Process of the face recognition method by AM based on RNNs.

Figure 3 :
Figure 3: Dimensions adjusted face images through the size adjustment function of the Microsoft office 2010 software.

Figure 4 :
Figure 4: The face images selected from the database.