Two-Factor Face Authentication: Topographic Independent Component Analysis (TICA) and Multispace Random Projection (MRP)

Lee Gin Chong Faculty of Engineering and Technology

Multimedia University Melaka, Malaysia

e-mail: gclee@mmu.edu.my

Loo Chu Kiong Faculty of Information Science and Technology

Multimedia University Melaka, Malaysia

e-mail: ckloo@mmu.edu.my

Chockalingam Letchumanan Faculty of Information Science and Technology

Multimedia University Melaka, Malaysia

e-mail: chockalingam@mmu.edu.my

Abstract—A two-factor face authentication method is presented by using Topographic Independent Component Analysis (TICA) as feature extractor in conjunction with Multispace Random Projection (MRP). Instead of using face alone to access the system, a permissible access requires a pair of genuine face and valid token in authentication mechanism. The formulation is revocable but not reversible and makes replacement effortlessly, hence, offers security reinforcement. Evaluations on TICA as feature extractor before and after MRP have been conducted in the forms of ROC curve, FAR, FRR and scores distribution. The performance of the system has been evaluated under a number of scenarios (normal, stolen token, and stolen face) using Facial Recognition Technology face images.

Keywords-face authentication; TICA; MRP; FAR; FRR; ROC.

I. INTRODUCTION The development of identity authentication systems

based on biometric traits analysis is becoming widespread reality. Some of the biometric modalities include face, voice, fingerprint, iris, retina, palm print, gait, etc have been studied these last years [1]. Among all, face-based authentication has gained substantial interest as face is exclusive trait for specific individual, which offers a convenient and reliable way to protect from impostors access. Unlike some other traits (iris and fingerprint), facial image acquisition does not require special equipments, where various digital cameras can be used for image capturing. Apart from that, identity verification using facial images can be done effortlessly by common people whereas traits such as fingerprint and iris can be distinguished only by specialists and experts.

In face authentication, the identity of the user, for instance via physical tokens or secret passwords, a priori is known. The system has to verify whether the a priori user is a genuine or an impostor. In other words, it is a one-to-one matching process to compare a facial input image with a predefined template. However, working with rough images is

not efficient. Hence, as in most images processing problems, extracting discriminant features from the images is crucial in face authentication. Devoid of a proper mechanism, feasible discriminant features are hardly known a priori. PCA (Principle Component Analysis) [2] which is one of the pioneer methods often used for facial image feature extraction has been implemented for face authentication. Another feature extraction is based on LDA (Linear Discriminant Analysis) as in [3]. While, in [4], ICA (Independent Component Analysis) has been claimed to offer improved success rate compared to equivalent system using PCA in face authentication.

In this paper, TICA (Topographic Independent Component Analysis) [5] which is extended from typical ICA is proposed to implement feature extraction in face authentication. Similarly to PCA, LDA, and ICA, TICA is subspace analysis method [6]. Face authentication necessitates large-scale of facial images acquisition and storage of face data; which might stem serious security issues in terms of privacy and identity theft. Moreover, due to the essential permanence of face data, if a face is compromised, it is compromised forever. For this reason, cancelable face based on MRP (Multispace Random Projections) [7] is proposed and works cooperatively with TICA to resolve privacy invasion and non-revocable issues of face-based biometrics in identity authentication.

The outline of this paper is given as follows. Section II describes face authentication and its problems. Section III shows the implementation of TICA in feature extraction for face authentication. Section IV presents the formulation of cancelable face based on MRP. Section V shows the experimental results and the discussions. Conclusions are drawn in Section VI.

II. FACE AUTHENTICATION Face authentication is distinct from face recognition in

the sense that, in the former, the system knows the identity of a user in advance, for instance via physical tokens or secret passwords, and should verify whether the a priori user is a

2009 International Conference of Soft Computing and Pattern Recognition

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DOI 10.1109/SoCPaR.2009.153

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2009 International Conference of Soft Computing and Pattern Recognition

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DOI 10.1109/SoCPaR.2009.153

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client or an impostor; while in the latter, the system does not know the identity of the user and should determine which of the stored image reveals the identity of user [8] [9]. The former will be concentrated in this paper.

A. Overview of Face Authentication As depicted in Fig. 1, a typical face authentication

system involves four main mechanisms: Facial Data Acquisition, Feature Extraction, Template Matching and Decision making [10].

Face authentication process is begun with facial data acquisition from user via capturing devices, namely digital cameras. Face detection and face normalisation techniques are often applied on the captured images prior to feature extraction. Normalised facial data will then be processed in order to extract a feature set. The extracted feature set is compared with the predefined template using similarity measures such as Nearest Neighborhood Classification (NCC) to compute similarity score, s.

Lastly, binary decisions (reject or accept) will be determined based on the comparison, as in equation (1), between the similarity score with a preset threshold value, t , which is referred as Uniform Threshold (UT) method [11].

if s t≥ accept, otherwise reject (1)

B. Security and Privacy in Face Authentication A large scale of facial images acquisition and storage of

facial data are necessary in face authentication; which might stem serious security concerns in terms of identity theft and privacy invasion. Furthermore, due to the vital permanence of face data, if a face is compromised, it is compromised forever. Non-revocation poses typical face authentication system stumbles upon the durable intrusion due to its single factor basis authentication. For this reason, the notion of cancelable biometric [7] [12] [13] has been proposed to formulate multifactor authentication.

III. FEATURE EXTRACTION Feature extraction generally plays important role to

condense the original face data. Working in original high-dimensional data space has been shown in [3] is not efficient. Redundant information in original data might, up to certain extent, deteriorate the performance of face authentication. Therefore, the extraction of relevant, discriminant features from the original data is necessitated. Subsequent authentication processes are performed in the reduced dimension feature subspace. Fastidious preference of the features is crucial in face authentication. Subspace analysis is one of the most important and well-known approaches to implement feature extraction. PCA is one of the pioneer subspace analysis methods often used for face recognition [14] [15] [16] and face authentication [2]. Another is based on LDA as in [3]. While, in [4], ICA has been claimed to offer improved success rate compared to equivalent system using PCA in face authentication.

Figure 1. Typical Face Authentication System

A. Topographic Independent Component Analysis (TICA) In this work, we intend to investigate the performance of

TICA as feature extractor in face authentication. TICA is one of the variants of classic ICA proposed by Hyvärinen and Hoyer [5]. In a similar way as in classic ICA [17], TICA factorises observed data x as a linear transformation of r basis function B and combining coefficients s:

x Bs= (2)

where B = {b1,…, br} is invertible and s = {s1,…, sr}. Components si are assumed to be non-Gaussian and mutually independent in classic ICA. However, this assumption of independence has been relaxed in TICA. In other words, components that are close to each other within the scope of dependency defined by a neighborhood system as in [18] are assumed to be dependent; that is they are correlated in their energies within topography.

Basic properties of TICA include: 1) All the components si are uncorrelated. 2) Components si that are far from each other are independent, at least approximately. 3) Components si that are near to each other tend to be active (non-zero) simultaneously, i.e. energies are positively correlated.

TICA is defined using a likelihood function with the introduction of neighborhood function h(i, j) [5]. Given m observed data x(t), t=1,…, m, the log-likelihood function is estimated as

2

1 1 1

log ( | ) ( ( , ) , ( ) )m r r

it j i

p x w G h i j w x t= = =

= < >∑∑ ∑

log | det |m w+ (3)

where w =B-1 is the inverse filter and the scalar function G has a similar role as the log density function of the independent component si in classic ICA. Learning algorithm of TICA model can be achieved by maximizing Eq. (3) with

Data Acquisition

Feature Extraction

Template Matching

Decision Making

Human Faces

Accept or Reject

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respect to w which can be implemented using gradient descent algorithm as in [19].

B. The implementation of TICA in face authentication The objective here is to implement TICA to learn a set of

topographically ordered basis vectors, namely the face subspace. In ICA face authentication [4], face subspace is obtained from manual ordering of the source vectors. With the aid of neighborhood enforcement in TICA, ordering of basis vectors can be done effortlessly by setting the appropriate dimension and mode (“torus” or “standard”) of neighborhood matrix. A gallery of face images will then be compressed by projecting them onto the face subspace in order to obtain the fixed length features vectors or “templates”. During authentication process, a probe face image is matched to a stored template by projecting it onto the face subspace and hence similarity score will be computed. Decision making is performed by comparing the similarity score with a preset threshold value to verify if the face is authenticated.

IV. TWO-FACTOR FACE AUTHENTICATION TICA subspace basis vectors are reversible or allow

reconstruction of original image. By knowing the coefficient of a face in TICA model, the original face image can be simply reconstructed with considerable low error. It poses an enormous security hole for intruder to attack authentication system with a single factor (stolen face biometrics). It is noticeable that single factor authentication is no more secure to be employed in practical environment. As a result, the notion of cancelable biometrics has been introduced. One of the promising formulations is Multispace Random Projections (MRP) [7]. In this work, MRP is proposed in conjunction with the implementation of TICA in face authentication system to provide a more secure and trustable two-factor face authentication system.

A. Multispace Random Projections (MRP) MRP is a two-factor cancelable formulation which

reinforces the security level of the system by necessitating a valid token and a genuine biometrics data for a permissible access. Raw biometrics datum is first transformed into a fixed length feature vector x∈ℜn via a feature extractor. Next, the feature vector is projected onto a sequence of random spaces that were derived from a user-specific pseudorandom number (PRN). The resulting random projection (RP) vector is formulated as follows:

(1/ )v m Rx= (4)

where R∈ℜmn is a m x n random matrix, m≤ n, and n is the feature length. The mixing process is revocable but non-reversible which makes replacing biometrics as simple as replacing PRNs. The basic formulation in Eq. 4 can be extended to include G users to generate G different RP features, i.e., multiple random subspaces Rk which formulate a set of unique random projection vectors:

(1/ )k kv m R x= (5)

where k=1,…,G .

B. The implementation of MRP in face authentication The implementation of MRP in face authentication

consists of two phases namely feature extraction and multispace random projection. In feature extraction, TICA model is applied as a feature extractor to compress face image to a fixed length feature vector with length n as described in section III. In multispace random projection phase, the feature vector is further projected onto the derived random subspace to produce the random projection vector. By adapting MRP into typical face authentication system, a modified two factor authentication system is created as in Fig. 2. In addition to face biometrics data, user-specific PRNs are entered to the system to strengthen the security level. Template matching and decision making are performed on the random projection vectors, details as in [7].

V. EXPERIMENT RESULTS AND DISCUSSIONS These experiments were conducted on frontal face

images from the publicly available Face Recognition Technology (FERET) face database [20]. One face image for each 1000 persons was randomly chosen from dataset “fa” as training set. 500 clients and 500 impostors were selected from dataset “fb”. Each client and impostor group were further grouped into 250 validation set and 250 test set. Validation set and testing set were chosen to be independent to present objectives results.

Training set was used for TICA subspace learning. The validation set was selected to produce client and impostor access scores in order to evaluate system performance. Finally, the test set was used to simulate realistic authentication tests. Each of the face images was preprocessed using eye finding, geometrical normalization and illumination normalization [21] and was sized into 35x35 pixels.

Figure 2. Two-factor authentication system

Data Acquisition

Feature Extraction

Template Matching

Decision Making

Human Faces

Accept or Reject

MRP

PRNs

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The evaluations were performed for dimension of TICA subspace set at 100 and MRP at 100. Synergetic Neural Network (SNN) [22] was adapted in decision making to compute the access scores between a query face and template face. The lower the score is, the more similarity between them. A. Performance Evaluations a) Validation Set: The performance measures of face authentication can be done by plotting the False Accept Rate (FAR hereinafter) versus the False Rejection Rate (FRR hereinafter) with threshold value being an implicit parameter. Different pairs of FAR and FRR values can be computed by selecting different values of threshold values. Such a plot is known as Receive Operating Characteristic (ROC hereinafter) Curve. It indicates the performance of an authentication system. ROC curve closer to axes implies better performance. Moreover, equal error rate (ERR hereinafter) occurs when FAR = FRR provides alternative approach to observe the system performance and hence determine threshold setting. b) Test Set: To simulate realistic authentication performance, both FAR and FRR were determined using threshold value at ERR using test set.

For comparison purpose, we first implemented TICA alone (TICAonly hereinafter) and evaluated the authentication performance in terms of ROC and equal error rate (EER) empirically using validation set. Determine FAR and FRR using test set were followed. Thereafter, MRP was implemented cooperatively with TICA (TICAmrp hereinafter). However, TICAmrp is two-factor authentication model; we have evaluated the performance for both stolen face and stolen token scenarios.

Fig. 3 (a) shows the EER obtained from validation set on TICAonly. The error rate is 0.132. ROC curve of TICAonly in Fig. 3 (b) is relatively far from axes. On the contrary, the ERR for both stolen face scenario and stolen token scenario in TICAmrp is 0.064 and 0.076 respectively [Fig.4 (a) and 5 (a)]. In term of ROC curve, both scenarios showed a closer curve to axes [Fig.4 (b) and 5 (b)].

Frequency distribution of scores measure for TICAonly and TICAmrp are shown in Fig.6 (a) and 6 (b) respectively. Impostor scores for TICAonly distribute from approximately 0.83 to 0.99 whereas genuine user scores distribute from about 0.835 to 0.99. For TICAmrp, genuine user scores distribute from 0.89 to 0.98, impostor scores for stolen token distribute from 0.935 to 0.99 and impostor scores for stolen face distribute from 0.945 to 0.985. The overlapping area between genuine distribution and impostor distribution is relatively larger in TICAonly as compared to TICAmrp for both stolen token and stolen face scenarios. Moreover, TICAmrp exhibits more concentrative scores distribution in both genuine and impostor which might be due to the adaptation of MRP.

Table I. summarises the results obtained on testing set, both with the use of TICAonly and TICAmrp. For TICAmrp, threshold value at 0.9557 is the average value obtained at EER for both stolen token and stolen face scenarios. It is noticeable that error rate of TICAonly is larger than TICAmrp by about 55%.

Figure 3. Performance of TICAonly:

(a) EER = 0.132 (b) ROC curve

TABLE I. RESULTS FROM TEST SET

Algorithm Threshold FAR FRR (FAR+FRR)/2 TICAonly 0.9442 0.0920 0.1920 0.142 TICAmrp 0.9557 0.0880 0.0680 0.078

The experiment results imply that the performance of

TICAonly does not show a reliable authentication result. For TICAmrp, in addition to include stronger security due to non-reversible property of MRP feature vector, results shows TICAmrp has higher success rate in authentication. Therefore, MRP was not only adapted to reinforce the security but was used as a tool to improve performance. Original MRP provides the flexibility in controlling the mean and standard deviation of impostor distribution meanwhile maintain genuine distribution which can minimize the overlapping area, details is in [7]. In this work,

(a)

(b)

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SNN was adapted in score measure which might break the flexible control of impostor distribution. However, experiment results show that we have gained better authentication performance.

VI. CONCLUSION REMARKS The contributions of the paper are the following: First,

we have implemented TICA in conjunction with MRP to formulate two-factor face authentication as a step to improve the authentication system security due to its revocability. Second, we have empirically evaluated the performance of TICAmrp. Third, based on our findings, we have proved that

Figure 4. Performance of TICAmrp - Stolen Face Scenario:

(a) EER = 0.064 (b) ROC curve

TICAmrp shows a better authentication result than TICAonly. Even SNN was adapted in score measure which might break the flexible control of impostor distribution; however, we have gained consistent authentication performance. It creates avenue to investigate and to search for suitable classifier in decision making mechanism. Future work might further investigate the effects of large size facial data, different dimensions of TICA face space and MRP random space on the authentication consistency. In addition, future attempts might replace the visible face images with thermal infrared images.

Figure 5. Performance of TICAmrp - Stolen Token Scenario:

(a) EER = 0.076 (b) ROC curve

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Figure 6. Frequency Distribution: (a) TICAonly (b) TICAmrp - Stolen Face Scenario and Stolen Token Scenario

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