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Future Generation Computer Systems 28 (2012) 218–231

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Future Generation Computer Systems

journal homepage: www.elsevier.com/locate/fgcs

A secure biometric discretization scheme for face template protection

Hyunggu Lee, Andrew Beng Jin Teoh, Ho Gi Jung, Jaihie Kim ∗

School of Electrical and Electronic Engineering, Yonsei University, Biometrics Engineering Research Center (BERC), Republic of Korea

a r t i c l e i n f o

Article history:Received 26 May 2010Received in revised form30 September 2010Accepted 3 November 2010Available online 30 November 2010

Keywords:Biometrics discretizationDynamic bit allocationHelper data

a b s t r a c t

In this paper, a dynamic biometric discretization scheme based on Linnartz and Tuyls’s quantization indexmodulation scheme (LT-QIM) [Linnartz and Tuyls, 2003] is proposed. LT-QIM extracts one bit per featureelement and takes care of the intra-class variation of the biometric features. Nevertheless, LT-QIM doesnot consider statistical distinctiveness between users, and thus lacks the capability of preserving thediscriminative power of the original biometric features. We put forward a generalized LT-QIM scheme insuch a way that it allocates multiple bits to each feature element according to a statistical distinctivenessmeasure of the feature. Hence, more bits are assigned to high distinctive features and fewer bits to lowdistinctive features. With provision for intra-class variation compensation and dynamic bit allocationby means of the statistical distinctiveness measure, the generalized scheme enhances the verificationperformance compared to the original scheme. Several comparative studies are conducted on two popularface data sets to justify the efficiency and feasibility of our proposed scheme. The security aspect is alsoconsidered by including a stolen-token scenario.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

With growing concerns regarding biometric security, a biomet-ric cryptosystem [1,2] was outlined to secure a cryptographic keyby using biometric features or by generating a cryptographic keydirectly from biometric features. In both cases, the biometric fea-tures need to be quantized into the binary bit strings using somesort of user-specific information, so-called helper data. With thishelper data, the cryptographic key is extracted from the user’s bio-metric features, which is expected to be consistent at all times forthe user.

Due to intrinsic intra-class variation of biometric features, itis difficult to obtain an identical biometric key from the sameuser. The helper data are crucial to compensate for the intra-class variation of biometric features in order to alleviate thisproblem [3]. The problem occurs in a scenario when the helperdata are compromised by an adversary while attempting torecover the genuine user’s biometric key, namely, the ‘stolen-tokenscenario’. In the stolen-token scenario, the discriminative power ofgenerated bit strings would be severely degenerated.

This paper extends the work of Linnartz and Tuyls’s static onebit discretization scheme based on quantization index modulation(LT-QIM) [4,5]. We put forward a novel dynamic discretizationscheme based on the former idea. LT-QIM is basically a key

∗ Corresponding author. Tel.: +82 2 2123 2869; fax: +82 2 362 5563.E-mail addresses: [email protected] (H. Lee), [email protected]

(A.B.J. Teoh), [email protected] (H.G. Jung), [email protected] (J. Kim).

0167-739X/$ – see front matter© 2010 Elsevier B.V. All rights reserved.doi:10.1016/j.future.2010.11.006

binding cryptosystem which secures a cryptographic key witha biometric feature. The LT-QIM generates one bit per featureelement of biometric data by using user-specific helper data. Withthe helper data, a more consistent bit value can be obtainedfrom each user’s biometric feature. However, the scheme onlycompensates for intra-class variation but largely ignores the inter-class distinctiveness of biometric features, which can directlyaffect verification performance. If a sole intra-class variationis considered, the bit string may not have good inter-classdistinctiveness, and vice versa. Therefore, consideration of bothintra-class variation compensation and inter-class distinctivenesssimultaneously would be desirable.

The proposed scheme evaluates the inter-class distinctivenessby means of a statistical measure to determine the length of theextracted bits per feature element and hence allocates more bitsto a more distinctive feature element and allocates fewer bits to aless distinctive feature element. Therefore, by compensating intra-class variation and varying the length of allocated bits accordingto a class-specific distinctiveness measure, the scheme generalizesthe idea in the LT-QIM.

Biometric discretization with user-specific helper data deliv-ers a highly discriminative bit string and thus an excellent veri-fication performance compared to the original biometric system.Nevertheless, under the stolen-token scenario, the overall perfor-mance reverts to rely solely on the discriminative power of theoriginal biometric features. In practice, under the stolen-token sce-nario, the performance of a discretized feature is worse than one ofthe original biometric features due to information loss during thediscretization process. In such cases, we notice a remarkably poor

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H. Lee et al. / Future Generation Computer Systems 28 (2012) 218–231 219

performance from the discretized feature compared to the perfor-mance of the original system. However, the proposed scheme doesnot show significant loss compared to the original biometric sys-tem, and the performance of the proposed scheme is better thanthat of the LT-QIM even under the stolen-token scenario.

To justify the feasibility of our proposed scheme, we conductedseveral extensive experiments by adopting face biometrics asour subject of study. Note that such experiments could also beconducted using other biometric modalities, as long as the relativebiometric features are of an ordered feature vector.

The organization of the paper is as follows: In Section 2, state-of-the-art biometric discretizations are presented. The proposedbiometric discretization scheme with QIM-based helper data anddynamic bit allocationwill be presented in Section 3. Experimentalresults of the proposed scheme will be demonstrated in Section 4,and the conclusions drawn from this paper are given in Section 5.

2. State-of-the-art biometric discretizations

Discussions regarding existing works on biometric discretiza-tion techniques are roughly grouped into static and dynamicspheres according to the mode of bit allocation per feature ele-ment. The static approach allocates a fixed length of bit to everyfeature element. On the other hand, the dynamic approach allo-cates a varying number of bits according to the statistical distinc-tiveness of the feature.

2.1. Static biometric discretization

Teoh et al. [6] proposed BioHash as a scheme of static biometricdiscretization. They transformed the original biometric featureusing a projection matrix before discretization. By using a pseudo-random number generator, the projection matrix is definedand user-specifically designated to each user. After transformingthe original biometric feature with the projection matrix, eachelement of the transformed feature is quantized into one bitaccording to the global mean value of the element. As an extendedwork, their scheme is improved by using the random multispacequantization technique with Fisher discriminant analysis as thefeature extraction scheme for the quantization [7].

Linnartz and Tuyls [4] proposed another static discretizationtechnique based on the LT-QIM [5]. During enrollment, the userregisters a secret bit S to compute helper dataW . Based onwhetherthe S bit is 0 or 1, W is calculated as the difference to be added tothe biometric template X so that it is fit with either the odd or evengrid quantum accordingly. The value ofW is defined as

W =

2n +

12

q − X if S = 1

2n −12

q − X if S = 0.

(1)

From Eq. (1), W is determined from X with n and q, where n is aninteger value which is chosen to make sure that −q < W < q andthe quantization step q is determined by amultiple of the standarddeviation σX of an individual user’s feature. The value of n isdiscarded andW is retained as helper data. During authentication,the test biometric is obtained as X and decrypted using W toarrive at S, which is a noisy representation of S. The S is set toeither 0 or 1 depending on whether the sum of X and W falls inthe odd or even quantum. LT-QIM assigns one bit per element ofthe feature regardless of its discriminative power. Therefore, theLT-QIM cannot maintain good inter-class discriminative powerunder the stolen-token scenario. In their work, the authors didnot show the feasibility of the LT-QIM by experiments with realbiometric data.

Tuyls et al. [8] proposed a static one-bit discretization schemewith user-specific selection of the reliable feature elements.For the quantization of a feature element, they used a simplethreshold-based binarization with the mean value of an element’sdistribution. Then, the more reliable components of the extractedbits are chosen for discretized biometric representation. Based onexperiments conducted on two fingerprint data sets, error ratesof about 4.5% and 4.2% were obtained [8]. As a similar approach,Kevenaar et al. [9] proposed another static discretization schemeusing helper data with reliable components selection based on anerror function, and they showed equal error rates of 2.5% and 0.5%for FERET and Caltech face databases [10,11].

2.2. Dynamic biometric discretization

Chen et al. proposed a dynamic discretization scheme based onlikelihood ratio and a detection rate optimization [12]. The authorsnamed their scheme ‘‘detection rate optimized bit allocation(DROBA)’’. Using the distribution of a genuine user’s feature, theglobal probability density function of the feature is segmentedto satisfy the condition that each quantization interval has thesame probability mass in the global distribution. The number ofsegmented regions is determined by a criterion on the detectionrate optimization of the user’s feature. Due to equal-probablequantization intervals, their scheme does not reveal where theoriginal feature value resides.

Teoh et al. [13] proposed another dynamic discretizationschemewhich uses user-specific 2N level bits allocation. Accordingto user-specific standard deviation, discriminative power of thefeature is determined by the number of allocated bits. By usingthe allocated number of bits, the overall range of the featuredistribution is segmented into equal-interval regions, and eachsegment is labeled with a binary reflected gray code (BRGC).The overall range for quantization is bounded by minimum andmaximum values of the feature. Their concept of dynamic bitsallocation using user-specific statistical property is similar to theproposed schemeof this paper. The 2N discretization schemeneedslower and upper bounds for bit length determination and bitsvalue extraction. However, the proposed scheme of this paperdoes not utilize such bound values; instead, every quantizationprocess is done under modulo operation with determined bitlength. In addition, the proposed scheme compensates intra-classvariation while preserving inter-class distinctiveness by usinguser-specifically defined bit length. More details on the proposedscheme will be elaborated in Section 3.

Bui et al. recently proposed [14] a dynamic bit allocationscheme based on the QIM idea. They determined the bit lengthof each feature element dynamically with greedy and reliabilitybased measures, and then vary the size of the quantizationstep according to the bit length of the allocation. In theirimplementation, if the bit length of each feature elementis changed, the corresponding intra-class variation and inter-class distinctiveness vary simultaneously. In addition, for givenfeature elements, the bit length allocation is bounded with apredetermined overall bit resource, and the allocation can bechanged when the length of the overall bit resource is changed.

In our scheme, the application of LT-QIM is simplified. Theintra-class variation and inter-class distinctiveness are consideredtogetherwith a bit length assignment scheme based on a statisticalmeasure. Bui’s scheme is different from ours in two main points.First, our scheme does not change the quantization step size;the quantization step is inherently defined by the statisticaldistribution of each user’s feature element to compensate intra-class variation. Second, our scheme fixes the bit length per featureelement by using the ratio between dispersion of intra-classvariation and overall dispersion of the features. The bit length of

220 H. Lee et al. / Future Generation Computer Systems 28 (2012) 218–231

Fig. 1. An overall block diagram of the proposed biometric discretization.

each feature element is user-specifically determined and reflectsthe inter-class distinctiveness of the feature element. In addition,Bui et al. did not consider the stolen-token scenario. The proposedscheme in this paper verifies its robustness under the stolen-tokenscenario.

3. Generalized helper data-based discretization inspired byquantization index modulation (QIM)

3.1. Notations

Suppose we have J users with I training samples per user.Given D feature elements extracted from each facial image i ∈ {1,2, . . . , I} of user j ∈ {1, 2, . . . , J}, all feature elements are assumedto be mutually uncorrelated. Note that a superscript d ∈ {1, 2,. . . ,D} is used to specify the dimension to which a variablebelongs. Throughout this paper, the notations are used as follows:• xdij: a user’s feature element in dth dimension, ith training

sample of jth user.• xdj : a registered instance of dth element from jth user, it can be

any of xdij or an averaged value of training set.• xdj : a query instance of dth element and jth user, obtained from

a query sample of biometric data.• N =

∑Jj=1 I = JI: total number of samples from the entire user

population.• md

=1N

∑Jj=1∑I

i=1 xdij: mean of dth element from the entire

user population.• md

j =1I

∑Ii=1 x

dij: mean of dth element for jth user.

• σ dglobal =

1N

∑Jj=1∑I

i=1

xdij − md

2: standard deviation of dthelement from entire user population.

• σ dj =

1I

∑Ii=1

xdij − md

j

2: standard deviation of dth elementfor jth user.

• Bdj : allocated bit length to user’s feature element of dth

dimension of jth user.• qdj = ασ d

j : quantization step size of dth element for jth user,where α is an experimentally determined constant.

• hdalign_j: alignment component responsible to align the regis-

tered feature xdj to the center of the nearest quantization seg-ment.

• hdj : the final helper data.

• outBitsdj : extracted bit string from xdj or xdj with hd

j , qdj , and Bd

j .In this paper the helper data are defined, for each dth element

of jth user, with hdj , q

dj , and Bd

j .

3.2. Overview

The progression of the proposed scheme is summarized inFig. 1. From the original features of the user’s biometric samples,the quantization step and the corresponding bit length are firstdetermined. With a user-specifically determined quantizationstep, an alignment component is generated to compensate forintra-class variation. Finally, the helper data are generated byperturbing the alignment component with a random numbergenerator which is seeded by the ID number of the user. This isto bind the randomly generated key value to the biometric featurewith the perturbed helper data.

The proposed scheme consists of the following steps:

(1) Bits per feature element determination.(2) Alignment component generation.(3) Perturbation generation to the helper data.(4) Bit string decoding and mapping with a BRGC.

3.2.1. Bits per feature element determinationThe bit allocation per feature element depends on the ratio

between the dispersions of intra-class variation and the overallvariation of each feature element as follows:

Bdj = min

k

2k− L

and

L =total_widthd

qdj=

6σ dglobal

ασ dj

, k ∈ Z.(2)

For xdj , Bdj bits are allocated according to an intermediate value L.

In the Eq. (2), L denotes the ratio between the dispersions of intra-class variation and the overall variation of each feature element.total_widthd refers to the dispersion of Gaussian distribution for99% of users population, which is characterized by 6σ d

global. Thedispersion of intra-class variation qdj is expressed by a scaledstandard deviation of ασ d

j , and the scale factor α is experimentallydetermined. For determining the α, we tested the performance ofour proposed method for finite set of candidates (we tested 0.5,1, 1.5, 2, 2.5, 3) and chose the best parameter ‘2’, among them.Therefore, the α is set by 2 and 2σ d

j can include 68.2% of Gaussiandistribution of each user.

Accordingly, if qdj ≤ total_widthd and hence L is large, Bdj

increases. Otherwise, if qdj is similar to total_widthd, Bdj decreases.

In Fig. 2, a schematic diagram of bit length allocation isshown according to L in Eq. (2). Fig. 2(a) depicts 2-bit allocation


(a) Schematic diagram of 2-bit allocation case. (b) Schematic diagram of 1-bit allocation case.

Fig. 2. A schematic diagram of bits allocation according to the ratio between user’s quantization step and dispersion of the overall user population distribution.

for a chosen one-dimensional feature element of user A. Sincetotal_widthd is about four times larger than qdA, B

dA becomes 2. For

Fig. 2(b), the chosen feature element of A has total_widthd which isabout two times larger than qdA, and thus Bd

A is set to 1. In Fig. 2(a),distributions of other users, such as B and C will fall outside thedistribution of A, and the generated bit string of Awill be differentfrom the bit strings of B and C . As a result, the scheme assignsmore bits to a more distinctive feature. If Bd

A < 1, the feature willbe allocated by 1 bit. In such a case, there is not much differencebetween each user’s distribution and overall distribution, and thecompensation of intra-class variationmay not generate the uniquevalue of bits due to poor inter-class distinctiveness of the featuredistribution.

3.2.2. Alignment component generation to compensate intra-classvariation

In LT-QIM, two procedures are carried out to generate helperdata: one is intra-class variation compensation and the other is‘0’ or ‘1’ bit value assignment. These operations will be examinedbefore presenting our scheme.

The LT-QIM generates helper data to align registered featureelement xdj to the nearest even or odd grid quantum whichrepresent ‘0’ or ‘1’ bit region, respectively, as follows:

W dj =

2n +

12

qdj − xdj if Sdj = 1

2n −12

qdj − xdj

or

(2n − 1) +12qdj − xdj

if Sdj = 0

(3)

where n is an integer that satisfies −qdj < W dj < qdj . The quantiza-

tion step qdj of a user is determined by a multiple of the standarddeviation σ d

j . According to the assigned secrete value Sdj (‘0’ or ‘1’),the helper dataW d

j are generated.When a query element xdj is given, a binary bit is rendered along

withW dj as follows:

bitxdj ,W

dj

=

1, if 2nqdj ≤ xdj + W d

j < (2n + 1) qdj0, if (2n − 1) qdj ≤ xdj + W d

j < 2nqdj .(4)

Depending on the secret value Sdj given,W dj is used to align a query

element xdj into the center of the nearest ‘0’ or ‘1’ interval. Hence,variation within the quantization step for a user is compensated.

(a) Even centered interval. (b) Odd centered interval.

Fig. 3. An illustration of generated helper data of LT-QIM for the registered featureelement xdj .

In order to clarify these two procedures in LT-QIM, intra-classvariation compensation and ‘0’ or ‘1’ bit value assignment, theexistence of the registered element xdj can be restricted by twocases as follows:

(a) (2k − 0.5) qdj ≤ xdj < (2k + 0.5) qdj Even centered interval(b) (2k + 1 − 0.5) qdj ≤ xdj < (2k + 1 + 0.5) qdj Odd centered

interval

where k is an integer value. For both cases, the generated helperdata for xdj is depicted in Fig. 3. To better illustrate the relationbetween Sdj and its corresponding W d

j , 0W or 1W is used todifferentiate the helper data which renders Sdj = ‘0’ or Sdj = ‘1’,respectively.

The lower or upper bound of cases (a) and (b) is the center ofthe nearest ‘0’ or ‘1’ interval to xdj , and the generated helper data ofFig. 3 satisfy Eq. (3).

For case (a): (2k − 0.5) qdj ≤ xdj < (2k + 0.5) qdj , the generatedhelper data can be expressed as a difference between an upper orlower bound value and xdj as follows:

W jd =

(2k − 0.5) qdj − xdj =

0W if Sdj = 0

(2k + 0.5) qdj − xdj =1W if Sdj = 1.

Similarly, for case (b): (2k + 1 − 0.5) qdj ≤ xdj < (2k + 1+0.5) qdj , the generated helper data can be expressed as follows:

W jd =

(2k + 1 + 0.5) qdj − xdj =

0W if Sdj = 0

(2k + 1 − 0.5) qdj − xdj =1W if Sdj = 1.


As previously mentioned, the upper or lower bound of cases (a)and (b) is the center of the nearest ‘0’ or ‘1’ interval to xdj . Sinceboth ‘0’ and ‘1’ intervals alternate consecutively, there are manyother centers of ‘0’ or ‘1’ intervals. Among such centers, the upperand lower bounds are closer to xdj than the other centers. Therefore,one of the upper and lower bounds of cases (a) and (b) is indeed thecenter of the nearest quantization segment to xdj , as illustrated inFig. 3.

Whether a registered element xdj is placed in an ‘‘even centeredinterval’’ or an ‘‘odd centered interval’’, one of the 0W and1W represents the difference between the center of the nearestquantization segment to the registered element xdj and the xdj , asfollows:

Wnear =

(k + 0.5) qdj − xdj =

1W if k = even integer

(k + 0.5) qdj − xdj =0W if k = odd integer

where k = minn

(n + 0.5) qdj − xdj , n, k ∈ Z. (5)

We can observe a dependency between 0W and 1W from Eq. (3).The helper dataW d

j can be denoted with 0W and 1W as follows:

W dj =

2n +

12

qdj − xdj =

1W if Sdj = 12n −

12

qdj − xdj

or

(2n − 1) +12qdj − xdj

=

0W if Sdj = 0.

From the above, the difference of 0W and 1W satisfies: qdj =0W −1W. This result also holds for both cases (a) and (b) as

follows:For case (a), (2k − 0.5) qdj ≤ xdj < (2k + 0.5) qdj :0W −

1W =

(2k − 0.5) qdj − xdj−(2k + 0.5) qdj − xdj

=−qdj

= qdj .

For case (b), (2k + 1 − 0.5) qdj ≤ xdj < (2k + 1 + 0.5) qdj :0W −1W

=(2k + 1 + 0.5) qdj − xdj

−(2k + 1 − 0.5) qdj − xdj

=qdj = qdj .

The above results are summarized as follows.

(1) The one of the 0W and 1W representsWnear of Eq. (5).(2) The distance between two helper data 0W and 1W satisfies:

qdj =0W −

1W.

As a result, the following interpretation can be made for LT-QIM:The helper data Wnear are used to compensate the intra-classvariation of xdj by shifting xdj to the center of the nearest quan-tization segment, and the difference between helper data qdj =

|0W −

1W | generates variation of ‘0’ or ‘1’ bit value assignment.From the above observations, our scheme separates intra-class

variation compensation and bit value assignment. First, we gen-erate an alignment component hd

align_j by a difference between aregistered element xdj and the center of the nearest quantizationsegment. Then, by introducing random perturbation to the align-ment helper data hd

align_j, the final helper data hdj are generated. A

more detailed explanation of random perturbation will be givenin Section 3.3. In fact, the hd

align_j in Eq. (6) is the same to Wnear inEq. (5). However, wewill use hd

align_j as an alignment component forconsistency.

As the first part of generating the helper data, the schemecompensates the intra-class variation of a registered element xdjwith hd

align_j as follows:

hdalign_j =

(k + 0.5)qdj − xdj

where k = min

n

(n + 0.5)qdj − xdj and n ∈ Z. (6)

The compensation capability of hdalign_j for the intra-class variation

of a query input xdj with respect to xdj can be expressed with thetheorem below.

Theorem. With hdalign_j, a consistent bit string can be generated

from the intra-class variation of a query input xdj under a uniformquantization which has a quantization step size of qdj , if xdj satisfies:xdj − 0.5qdj

< xdj <

xdj + 0.5qdj

.

Proof of Theorem. According to Eq. (6), hdalign_j is meant to align

xdj to the center of the nearest quantization segment, and thesummation of xdj and hd

align_j can be expressed as follows:

hdalign_j + xdj =

(k + 0.5)qdj − xdj

+ xdj = (k + 0.5)qdj

where k = minn

(n + 0.5)qdj − xdj and n : integer.

xdj − 0.5qdj

< xdj <xdj + 0.5qdj

can be expressed as follows:

−0.5qdj <xdj − xdj

< 0.5qdj .

The summation of xdj and hdalign_j is h

dalign_j + xdj =

(k+ 0.5)qdj −

xdj+ xdj = (k + 0.5)qdj +

xdj − xdj

.

By putting together the above results, the summation of xdj andhdalign_j is bounded as follows:

kqdj < hdalign_j + xdj < (k + 1) qdj . �

3.2.3. Perturbation generation to the helper dataAs shown in Eqs. (3) and (4), the LT-QIM binds a ‘0’ or ‘1’ secret

value to each biometric feature element, and our scheme alsoprovides such a binding property by perturbing the helper data.The purpose of this secret value binding is to renew or reissue atemplate when an adversary has taken a template of a user.

Since the registered feature element, xdj has bit length Bdj , the

helper data are used to extract 2Bdj possible bit values from the fea-ture element by using a random number generator which is user-specifically seeded according to a discrete uniform distribution ofinteger numbers: U

−

2Bdj −1

− 1

, 2Bdj −1. The resultant helper

data are produced by perturbing hdalign_j as follows:

hdj =

hdalign_j + kqdj

mod

2Bdj qdj

,

where k ∈ U−

2Bdj −1

− 1

, 2Bdj −1. (7)

Even though the perturbation of the resultant helper can changethe generated bit string from the registered feature element, it cangenerate consistent bit string within the same quantization inter-val and different bit string between different quantization inter-vals. Therefore, the flip-around property of modulo operation inEq. (7) ensures that any helper data residing in overall dynamicrange 2Bdj qdj maintains the inter-class distinctiveness and intra-class invariance.

3.2.4. Bit string decoding and mapping with a BRGCThe progression from Sections 3.2.1–3.2.3 shows the process of

helper data generation. Note that the helper data of our scheme are


calculated element-wise.With the helper data, a final bit string canbe extracted from each feature element as follows:

Int_Val =

xdj + hd

j

qdj

mod

2B ,

outBitsdj = dec2gray(int_Val, B), where B = Bdj

(8)

where dec2gray(·, ·) is a function to convert an integer value to agray coded binary number. Under the stolen-token scenario, theproposed user-specific Bd

j bit offers inter-class distinctiveness, andeven if hd

j is changed with different random seed values, the inter-class distinctiveness can be preserved under modulo operation.A bit string outBitsdj is rendered by converting Int_Val from eachfeature element to BRGC, with a bit length of Bd

j .Finally, they are concatenated and truncated according to a

required bit length for the biometric discretizer. The concatenatedbit string can be expressed as follows:Bits_stringj

B_j×1 =

outBits1j outBits2j · · · outBitsDj

,

where B_j =

D−d=1

Bdj (9)

where each outBitsdj is a Bdj × 1 vector, and its concatenated vector

Bits_stringj is∑D

d=1 Bdj

× 1 vector. The truncation is done in

ascending order from lower to higher dimension.

3.3. Remarks on security aspect of our scheme

The biometric discretization scheme is expected not to revealany information about the final generated bit string and theoriginal biometric feature from the helper data.

As a remark on the security aspect of our scheme under thestolen-token scenario, the generated bit string is also assumed tobe compromised. This section will briefly examine the informationleakage issue under this context. A typical uniform quantizationscheme, which utilizes a threshold-based approach, such as 2N

discretization scheme [6] is also considered for comparison withour scheme which utilizes modulo operation.

A uniform quantization can be described as follows:

Int_Val =

maxd − mind

qdj

, if xdj ≥ maxd

xdj − mind

qdj

, if mind

≤ xdj < maxd

0, if xdj < mind

where mind= minimum value of dth element and

maxd = maximum value of dth element. (10)

Int_Val is a discretized value based on a uniformquantizer for inputxdj with quantization step qdj , and because it is bound to the originalfeature, it should be kept securely.

A uniform quantization can be modified by using the non-uniform size of the quantization steps qdj for each quantizationsegment of the feature element. Regardless of the non-uniform oruniform quantization steps, it is manifested that nt_Val is directlybound to the quantization segment where xdj exists. This is due tothe storing of the real value of the quantization bounds such asmind,maxd. From Int_Val and a uniform quantizer of Eq. (10), xdjcan be localized as follows:

Localization :

xdj ≥

maxd − mind

qdj

× qdj + mind

j

,

if Int_Val =

maxd − mind

qdj

Int_Val × qdj + mind

j

≤ xdj <

(Int_Val + 1) qdj + mind

j

,

if 0 < Int_Val <

maxd − mind

qdj

xdj <

mind

+ qdj, if Int_Val = 0.

(11)

For the boundary values of discretization such as Int_Val = 0,maxd −mind

qdj

, localization is not accurate due to discretization

around mind,maxd of Eq. (10). Nevertheless, Eq. (11) is a naturalconsequence due to a uniform quantization based on the thresholdvalues. Because Int_Val is discretized by the threshold values, it candirectly reflect which quantization interval it came from.

However, our scheme does not directly reveal the exact locationof xdj . According to Eq. (8), xdj can be localized as follows:

k × 2B+ Int_Val

qdj − hd

j

≤ xdj <

k × 2B

+ Int_Val + 1qdj − hd

j

,

where k is an arbitrary integer value, B = Bdj . (12)

Due to the infinite number of k values for Int_Valdj which satisfyEq. (8), the exact value of xdj cannot be uniquely localized evenif Int_Valdj and hd

j are compromised. Despite the dynamic rangeof the original feature can be constrained by the bound values,our scheme stores nothing concerning the bounds. Therefore, themodulo operation-based discretization in our scheme reveals lessinformation regarding the original feature than threshold value-based quantization.

4. Experiments

In order to verify the feasibility of our proposed scheme, thefollowing experiments have been investigated:A. Verification performance evaluation with independent user-

specific helper data assuming that user-specific helper data arekept securely.

B. Verification performance evaluation under the stolen-tokenscenario.

For experiment A, verification performance of the proposedscheme is evaluated when the user’s helper data are securelymanaged, and for experiment B, the validity of the proposedscheme is verified under the stolen-token scenario.

4.1. Data sets and preprocessing

The proposed scheme is tested using the extended YALEB [15]and PIE [16] databases. The extended YALEB database [15] isthe extended version of the YALEB database, which contains38 subjects, and for each subject 64 images are sampled withillumination variation but without pose variations. The extendedYALEB has many more subjects (38) than YALEB (10) and byusing the data set with more subjects, i.e. the extended YALEB,the measure of the verification performance can be more reliable.Some of the face images obtained from the extended YALEBdatabase are shown in Fig. 4.

The PIE database [16], which contains 68 subjects and 45 faceimages, is sampled per subject with different levels of illumination


Fig. 4. Examples of the illumination variation in images obtained from the extended YALEB face database.

Fig. 5. Examples of the illumination variation in images obtained from the PIE face database.

and without pose variation. Examples of images obtained from thePIE database are shown in Fig. 5.

4.2. Experimental settings

4.2.1. Face feature extractionFace features are extracted using appearance-based techniques

such as principle component analysis (PCA) [17] and eigenfeatureregularization and extraction (ERE) [18]. The PCA has been widelyadopted in many face recognition approaches, and ERE is arather recent technique which provides enhanced performance byregularizing eigen components of within scatter matrix. There isno restriction for the biometric feature extractor for our scheme,and in this paper, the proposed scheme is applied to the biometricfeatures obtained by using PCA and ERE.

4.2.2. Training and verification sets partitioningFor registration and testing purposes, facial images are

partitioned into a registration set and verification set. In theregistration phase, 15 samples are used to generate helper data.A user-specific quantization step qdj is determined and Bd

j of thediscretized feature element is chosen according to Eq. (2). Theextracted biometric feature elements of 15 training samples areaveraged. Then, a bit string is calculated from the averaged featureelement and concatenated according to Eq. (9). After truncatingthe concatenated bit string with the required bit length of thebiometric quantizer, the truncated bit string is registered toevaluate the verification performance of the proposed biometricdiscretization. For a fair performance comparison between theoriginal feature extractor and the proposed biometric discretizer,the original features of 15 training samples are averaged andregistered as a template for the baseline feature extractors, suchas PCA and ERE.

In the verification phase, another 15 samples of each user areused to verify the performance of the proposed scheme. Fromeach verification sample, a biometric feature is extracted andused to generate a bit string. The obtained bit string is comparedwith the registered one under Hamming distance metric. Forboth registration and verification, biometric image samples arerandomly selected from the face databases.

From the matching between bit strings of the same user,genuine distribution is calculated, and from thematching betweenthe bit strings of different users, imposter distribution is calculated.For a certain threshold of Hamming distancemetric, false rejectionrate (FRR) refers to that portion of genuine distributionwhich has alarger value than the threshold, and false accept rate (FAR) refers to

Fig. 6. Verification performance of the proposed scheme for the PCA feature on thePIE face database.

that portion of the imposter distribution which has a lower valuethan the threshold. When the FRR and FAR are the same, the valueof FAR or FRR refers to the equal error rate (EER). The verificationperformance of the proposed scheme is evaluated using EER.

The random sampling of training and verification sets isindependently repeated for five times, and the EER results areaveraged for the final representation in Figs. 6–9 and 12–15. Thestandard deviation value of the EER represented for above andbelow of the each curve by an error bar.

4.3. Verification performance evaluation with independent user-specific helper data

In this section, the performance of the proposed scheme iscompared with LT-QIM [4] and 2N discretization scheme [13].For each user, independently defined helper data are assignedand utilized under a verification scenario. Comparing it to thebaseline feature extractor, such as PCA and ERE, the proposedscheme provides improved performance as shown in Figs. 6–9. Inthe Figs. 6–9, the horizontal axis refers to the extracted bit lengthand utilized dimensions for the biometric discretization schemeand the baseline feature extractors, respectively.


Fig. 7. Verification performance of the proposed scheme for the ERE feature on thePIE face database.

Fig. 8. Verification performance of the proposed scheme for the PCA feature on theextended YALEB face database.

Due to dynamic bit allocation based on user-specific standarddeviation, the proposed scheme and 2N discretization are allocatedwith a similar number of bits per feature element, and they showsimilar performance for the extracted bit strings (more detailedcomparison will be given in Section 4.4). However, the LT-QIMshows a rather inferior performance compared to the proposedscheme. Due to the usage of independent user-specific helperdata, there is not much difference in imposter matching betweenthe proposed scheme and the LT-QIM. Therefore, the differencein verification performance comes from a difference in genuinedistributions.

Fig. 9. Verification performance of the proposed scheme for the ERE feature on theextended YALEB face database.

In Figs. 10 and 11, an advantage of the proposed schemeis shown with genuine and imposter distributions with an ex-tracted bit length of 192. With dynamic bit allocation according tothe user-specific statistical distinctiveness measure, the proposedscheme handles the intra-class variation more efficiently. There-fore, our scheme shows better performance than one of the LT-QIMfor the PCA and ERE features. In Fig. 10, from the PCA feature of PIE,our scheme and the LT-QIM show 2.3% and 13.2% EER, respectively.For the ERE feature of PIE, our scheme and the LT-QIM show 0.06%and 12.2% EER, respectively. From the PCA feature of YALEB, 4% and12.4%EER are shown for our schemeand the LT-QIM. Subsequently,for the ERE feature of Fig. 11, 0.05% and 8.8% EER are shown for ourscheme and LT-QIM.

In Figs. 6–9, the proposed scheme shows better performancewhen bit length increases. This result can be explained through thechanging of imposter distributionwith the increment of bit length.When using independently generated user-specific helper data,the obtained bit string of each user is uncorrelated. The distributionobtained by imposter matching of uncorrelated bit strings can bemodeled with a fractional binomial distribution [7,19]:

f (x) =B!

λ!(B − λ)!0.5λ(1 − 0.5)(B−λ) (13)

where B is the length of a bit string, x = λ/B, 0 ≤ x ≤ 1 is a ratioof λ Bernoulli trials among overall B Bernoulli trials. In this paper,each of λ Bernoulli trials are true with a probability of 0.5, and x isthe Hamming distance between two bit strings of different usersobtained using independently defined helper data. In this case, thebinomial distribution has the mean value of 0.5 and the standarddeviation of

√0.5(1 − 0.5)/B. If B is increasing, the imposter

distributionhas a fixedmeanvalue of 0.5 and its standarddeviationis decreasing. On the other hand, genuine distribution does notchange much with respect to B. Hence, when using independentlydefined helper data, the imposter and genuine distributions areseparated better for large B. This phenomenon was pointed out byTeoh et al. [7], and as a result, the performance of this explains theresults of Figs. 6–9.


. .

. .

Fig. 10. Genuine and imposter distributions of discretzied PCA and ERE features of the PIE face database.

Nevertheless, this does not hold for the stolen-token scenario,as the performance will regress. This will be examined in the nextsection.

4.4. Performance under stolen-token scenario

In this paper, when user-specifically defined helper data arecompromised (stolen-token scenario), the bit string of the genuineuser is guessed using the stolen helper data and biometric data ofthe remaining users. As shown in Figs. 12–15, the performance un-der stolen-token scenario is poorer than those shown in Figs. 6–9where the helper data are not compromised.

For the original PCA feature which has poor EER of more than40%, all biometric discretization schemes showbetter performancethan the PCA baseline. The PCA feature shows extreme intra-classvariationwhich is not clearly separable by the inter-class variation.However, the intra-class variation compensation of the quantizersseems to improve verification performance. Even though the intra-class variation is compensated for the genuine user, inter-classdistinctiveness does not provide an ideal distribution as shown inSection 4.3. This is evident when comparing Figs. 16 and 17 withFigs. 10 and 11.

For the ERE feature which has much a better EER indicator, thediscretization schemes show some degree of loss in their verifi-cation performance compared to the one with the ERE feature.However, the performance of our scheme does not deteriorate

much compared to the one with the ERE feature, and our schemeshows a better performance than that of the one with the LT-QIM.This is because LT-QIM does not consider inter-class distinctive-ness and simply represents each feature element in one-bit, whichleads to severe degradation in verification performance. On theother hand, our scheme allocates multiple bits according to theirdistinctiveness measure while compensating intra-class variationwith the helper data. The advantage of our scheme to the LT-QIMis shown in Figs. 16 and 17 where the extracted bit length is 192.

Our scheme and 2N discretization show a similar verificationperformance due to the usage of user-specific information todetermine the bit length of the discretized feature. Both schemesdetermine the quantization step of each user using standarddeviation of the user’s feature, and by using the quantization step,the bit length is determined. However, it should be noted that, fromFigs. 12–15, the performance of our scheme is consistently betterthan 2N discretization scheme for bit lengths smaller than 60.This is because the lower dimensions of the PCA and ERE featuresare more discriminative. For discriminative feature elements, ourscheme compensates for intra-class variation and improves theverification performance compared to one of the 2N discretizationschemes. However, for less discriminative features, the intra-classvariation compensation causes some loss in discriminative powerunder the stolen-token scenario.

The helper data compensate for the intra-class variation ofgenuine features according to the theorem of Section 3.2.2.


Fig. 11. Genuine and imposter distributions of discretzied PCA and ERE features of the extended YALEB face database.

Fig. 12. Verification performance of the proposed scheme for the PCA feature onthe PIE face database under stolen-token scenario.

Fig. 13. Verification performance of the proposed scheme for the ERE feature onthe PIE face database under stolen-token scenario.


Fig. 14. Verification performance of the proposed scheme for the PCA feature onthe extended YALEB face database under stolen-token scenario.

Fig. 15. Verification performance of the proposed scheme for the ERE feature onthe extended YALEB face database under stolen-token scenario.

Fig. 16. Genuine and imposter distributions of discretized PCA and ERE features under stolen-token scenario of the PIE face database.


. .

. .

Fig. 17. Genuine and imposter distributions of discretized PCA and ERE features under stolen-token scenario of the extended YALEB face database.

However, if the biometric feature is not discriminative, a queryfeature element of the imposter user could also satisfy the criterionof the theorem: (xdj − 0.5qdj ) < xdk < (xdj + 0.5qdj ) where xdj isthe registered genuine user’s feature element, and xdk is the queryfeature element of the imposter user, k = j.

In such cases, the imposter user can guess a similar bit stringto the genuine one, with the helper data of the genuine user.Therefore, if the short bit string is taken, our scheme outperforms2N discretization, but the performance gradually degraded whenincreasing the bit length.

In order to compare the intra-class variation of our scheme and2N discretization quantitatively, an indicator of normalized intra-class variation is introduced:

Normalized intra-class variation

=1

NIntra

J−j=1

I−i=1

NHDBits

xj, Bits

xij

,

where NIntra =

J−j=1

I−

i=1

1

,

xj = registered feature,xij = a query feature,J = overall number of users andI = images per user

(14)

where Bits (·) calculates the bit string from the biometric feature,and the extracted bit strings are comparedwith function NHD (·, ·)normalized Hamming metric.

The intra-class variation compensation is prominent for the EREfeature as shown in Figs. 18 and 19. However, the PCA feature doesnot signify any significant distinction in terms of normalized intra-class variation in both our scheme and 2N discretization. Due to theinherent low discriminative characteristic of the PCA features, thescheme fails to reduce the intra-class variation compared to the 2N

discretization scheme.

5. Conclusion

In this paper, a novel scheme for biometric discretization isproposed by generalizing LT-QIMbased on statistical bit allocation.The main contributions of this paper are summarized as follows.

(1) A robust biometric discretization scheme generalized from thescheme of Linnartz and Tuyls. The proposed scheme compen-sates intra-class variation using helper data inspired by LT-QIM. While compensating intra-class variation, the proposedscheme also represents inter-class distinctiveness by using dy-namic bit allocation with user-specific statistical property. Theproposed scheme provides consistent bit representation with-out much loss in discrimination power compared to one of theoriginal feature.


Fig. 18. Normalized intra-class variation for the proposed scheme and thediscretization of the PIE face database.

Fig. 19. Normalized intra-class variation for the proposed scheme and thediscretization of the extended YALEB face database.

(2) Experimentally proving the feasibility of the QIM-based quanti-zation. Ever since Linnartz and Tuyls introduced a QIM-basedbiometric discretization, the scheme has not been studiedthoroughly. In this paper, the feasibility of our scheme andLT-QIM is examined, even under the stolen-token scenario.

We observed that by adopting user-specific helper data, the verifi-cation performance is superior to the original baseline system. Theverification performance might be degraded unfavorably if user-specific helper data are compromised. However, under the stolen-token scenario, our scheme shows comparable performance to theoriginal baseline, and our scheme is much more robust than theLT-QIM scheme. Besides, the helper data in our scheme utilize par-tial information of the biometric data with modulo operation, andthe stored helper does not reveal the exact value of the original fea-ture. Therefore, our scheme is secure for biometric discretization.

Acknowledgement

This work was supported by the National Research Foundationof Korea (NRF) through the Biometrics Engineering Research Cen-ter (BERC) at Yonsei University. (No. R112002105080020(2010)).

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Hyunggu Lee received the B.S. degree in electronicengineering from Yonsei University, Seoul, Korea, in2003 and the M.S. degree in electronic engineeringfrom Yonsei University, Seoul, Korea, in 2005. He iscurrently working toward the Ph.D. degree in electricaland electronic engineering at Yonsei University. Hisresearch interests include biometrics, computer vision,and pattern recognition.

Andrew Beng Jin Teoh obtained his B.Eng. (Electronic) in1999 and Ph.D. degree in 2003 from National Universityof Malaysia. He is currently an assistant professor in EEDepartment, College Engineering of Yonsei University,South Korea. His research interest is in biometrics securityand pattern recognition. He had published around 150international journal and conference papers in his area.

http://www.vision.caltech.edu/html-files/


Ho Gi Jung received the B.E. M.E., and Ph.D. degreesin electronic engineering from Yonsei University, Seoul,Korea, in 1995, 1997, and 2008, respectively. He was withthe MANDO Corporation Global Research and Develop-ment Headquarters from 1997 to 2009. He developedenvironment recognition algorithms for intelligent park-ing assist systems (IPAS), collision warning and avoidance,and active pedestrian protection systems (APPS). SinceMay 2009, he has been with Yonsei University. His inter-ests are automotive vision, driver assistant systems (DAS),active safety vehicles (ASV), biometrics, and intelligent

surveillance. He is a member of IEEE, SAE, SPIE, IEEK, and KSAE.

Jaihie Kim received the B.S. degree in electronic engi-neering from Yonsei University, Seoul, Korea, in 1979,and the M.S. degree in data structures and the Ph.D.degree in artificial intelligence from CaseWestern ReserveUniversity, Cleveland, OH, in 1982 and 1984, respectively.Since 1984, he has been a professor in the School ofElectrical and Electronic Engineering, Yonsei University.He is currently the Director of the Biometric EngineeringResearch Center in Korea. His research areas includebiometrics, computer vision and pattern recognition. Pro-fessor Kim is currently the Chairman of Korean Biometric

Association.

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