A Channel Coding Approach for Human

8/8/2019 A Channel Coding Approach for Human

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428 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 4, NO. 3, SEPTEMBER 2009

A Channel Coding Approach for HumanAuthentication From Gait Sequences

Savvas Argyropoulos , Associate Member, IEEE, Dimitrios Tzovaras, Dimosthenis Ioannidis, andMichael G. Strintzis, Fellow, IEEE

AbstractHuman authentication using biometric traits hasbecome an increasingly important issue in a large range of ap-plications. In this paper, a novel channel coding approach forbiometric authentication based on distributed source codingprinciples is proposed. Biometric recognition is formulated as achannel coding problem with noisy side information at the decoderand error correcting codes are employed for user verification. Itis shown that the effective exploitation of the noise channel distri-bution in the decoding process improves performance. Moreover,the proposed method increases the security of the stored biometrictemplates. As a case study, the proposed framework is employedfor the development of a novel gait recognition system based on

the extraction of depth data from human silhouettes and a setof discriminative features. Specifically, gait sequences are repre-sented using the radial and the circular integration transformsand features based on weighted Krawtchouk moments. Analyticalmodels are derived for the effective modeling of the correlationchannel statistics based on these features and integrated in thesoft decoding process of the channel decoder. The experimentalresults demonstrate the validity of the proposed method overstate-of-the-art techniques for gait recognition.

Index TermsAuthentication, biometrics, channel coding, dis-tributed source coding, gait recognition, low-density parity check(LDPC) codes.

I. INTRODUCTION

HUMAN authentication has always been a field of primaryconcern in a variety of applications ranging from access

control in secure infrastructures to customizable smart-homeapplications. The existing solutions are mainly based on the useof secret words, called passwords, which must be entered bythe user when prompted or on the possession of identificationcards, called tokens. However, this type of identity establish-ment poses many limitations and induces high security risks.Specifically, passwords and tokens can be easily lost, stolen,forgotten, or shared. Moreover, passwords are usually easy toguess using social engineering and dictionary attacks while to-kens can be readily forged. Biometric recognition has emerged

Manuscript received March 08, 2008. First published June 30, 2009; currentversion publishedAugust 14, 2009. The associate editor coordinating the reviewof this manuscript and approving it for publication was Dr. Tieniu Tan.

S. Argyropoulos andM. G. Strintzisare with theDepartment of Electrical andComputer Engineering, Aristotle University of Thessaloniki, GR-54624 Hellas,Greece. They are also with the Informatics and Telematics Institute, Centrefor Research and Technology Hellas, Thermi-Thessaloniki, GR-57001 Hellas,Greece (e-mail: [email protected]; [email protected]).

D. Tzovaras and D. Ioannidis are with the Informatics and TelematicsInstitute, Centre for Research and Technology Hellas, Thermi-Thessa-loniki, GR-57001 Hellas, Greece (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIFS.2009.2025858

as a promising solution to the above issues during the last years.Biometrics refer to the unique physical or behavioral character-istics that describe the anatomy or behavior of individuals, e.g.,iris, fingerprint, voice, face, etc.

Gait recognition ([1], [2]) in particular has attracted much at-

tention during the last years as a very tempting approach forreal-time person authentication. The main advantage of gait as

a biometric modality is that it can be observed at-a-distance in

an unobtrusive manner and without the consent or cooperationof the subject. For this reason, it is very suitable for surveillance

applications or in environments where the application of otherbiometric traits is constrained. Present work on automatic gait

recognition has focused on the development of methods for the

extraction of meaningful features from the input gait sequences.

Static and dynamic body parameters of the human locomotion

are extracted to characterize the walking style of individuals.Subsequently, identity verification is considered as a classifi-

cation task and machine learning techniques are employed for

human recognition. The critical points in these approaches are

the extraction of unique, representative, and distinguishable fea-

tures and the effectiveness of the employed pattern recognition

methods.Furthermore, one of the major concerns in applications that

grant access based on a password, a token, or a biometric trait,is the protection of the original data to prevent malicious usefrom those who try to access them by fraudulent means. Inpassword-based systems, this problem has been investigated indepth and sophisticated encryption methods have been devel-oped [3]. Specifically, prior to storage to the physical medium(e.g., hard disk, USB token), cryptographic codes are applied tothe passwords and a hash code is generated with a one-to-onerelationship to the original password. The irreversibility of theemployed cryptographic codes renders the hash codes uselessto the potential attackers of the system since the original datacannot be revealed.

However, since the representation of biometric traits is notfixed over time, the existing solutions used in password-basedapplications to enhance security, such as cryptography, cannotbe applied. This is due to the fact that the existing cryptographicsolutions require the exact match of the prompted and the orig-inal signatures to grant access. Thus, novel encryption methodsneed to be developed to take into account the noise introducedin the representation of the biometric traits and account for theirinherent variability [4], [5].

In this paper, a novel framework for human authenticationin secure environments is developed and a channel coding ap-proach for biometric recognition based on distributed sourcecoding principles is proposed. First, the fundamental concepts

of distributed source coding are introduced and the problem of

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ARGYROPOULOS et al.: CHANNEL CODING APPROACH FOR HUMAN AUTHENTICATION FROM GAIT SEQUENCES 429

biometric recognition is formulated as the dual of data commu-nication over noisy channels. The main idea is that perturba-tions in the representation of the biometric features in differenttimes can be modeled by a (virtual) noise channel which cor-rupts the initial signal. The enrolment and authentication pro-cedures are considered as the encoding and decoding stages ofa communication system. Advanced channel coding techniquesare employed to increase the error correcting capabilities of thedecoder and channel statistics are exploited to enhance the per-formance of the biometric system.

As a case study, the proposed framework is employed for thedevelopment of a gait recognition system. Depth informationis utilized for enhanced silhouette segmentation and discrimi-native features are extracted for the representation of gait. Theuse of generalized Radon transforms and orthogonal momentsis employed. Then, the extracted features are integrated into thedistributed source coding framework and the parameters of thenoise channel are tuned based on these features. Finally, the pro-posed scheme is experimentally evaluated on a large database to

demonstrate its validity.

A. Related Work

Over the last years, several attempts have been made to ana-lyze gait signatures by extracting meaningful features from thesilhouette of the human body and using shape analysis. In [6],the width of the outer contour of the binary silhouette was usedas the basic feature and dynamic time warping was employedto match gait sequences. This work was extended in [7] wherehidden Markov models (HMMs) were employed to model thewalking style of individuals. Also, population HMMs were em-ployed in [8] to capture differences in stance shape between sub-

jects and very satisfactory results were reported. However, thatmethod used manually created human silhouettes for training.Moreover, an angular transform was applied in [9] to trans-form binary silhouettes into low-dimensional feature vectorsconsisting of average pixel distances from the center of the sil-houette. Additionally, linear time normalization was proposedto perform matching between test and reference gait cycles ofdifferent lengths [10]. In [11], the gait energy image techniquewas proposed to represent the human motion sequence with asingle image while preserving temporal information and sig-nificant improvements were demonstrated in comparison to thebaseline algorithm [12]. In a previous work [13], we have pro-posed the extraction of distinguishable features using the ra-

dial integration transform (RIT), the circular integration trans-form (CIT), and the weighted Krawtchouk moments [14]. TheRadon transform of binary silhouettes was also proposed in [15]in combination with linear discriminant analysis for gait recog-nition. Moreover, the use of moments for shape identificationhas received increased attention recently. Shutler et al. [16] pro-posed the use of Zernike velocity moments to describe and an-alyze the motion throughout a gait sequence.

Contrary to feature-based techniques, model-based methodstry to model efficiently the static and dynamic body parame-ters of the human locomotion. In [17], static parameters of thehuman body were extracted from the segmentation of the bodysilhouette into regions. In [18], seven ellipses were used to di-

vide the binary map of the walking subject. The features ex-tracted from these regions include the centroid, the aspect ratio

of major and minor axis of the ellipse, and the minor axis of eachellipse. In [19], the gait signature was generated using Fourierseries expansion of a signal corresponding to leg movements. Fi-nally, a full-body layered deformable model was introduced in[20] with 22 parameters describing the human body part shapes(widths and lengths) and dynamics (positions and orientations).

All the aforementioned techniques address the recognitionproblem as a classification task and employ statistical methodsor machine learning techniques to establish the identity ofindividuals. In this paper, an authentication scheme based onerror correcting codes and modeling of channel statistics isproposed. Channel codes have been previously used for thedevelopment of authentication schemes. In [21], a genericauthentication scheme based on channel codes was proposedto improve security and prevent unauthorized access in secureenvironments. Also, in [22], a channel coding scheme waspresented for secure biometric storage. Error correcting codeswere employed to tackle the perturbations in the representationof biometric signals and classification was based on the Ham-

ming distance between two biometric representations. Basedon this concept, the fuzzy commitment scheme was introducedto tolerate more variation in the biometric characteristics andprovide stronger security [23]. In this scheme, the user selectsat the enrolment a secret message . Then, the template consistsof the difference between the users biometric data andalong with an encrypted version of . At the authentication, thestored difference is added to the new biometric representation

and is decoded to the nearest codeword using errorcorrecting codes.

The fuzzy commitment scheme was extended in [24] where acryptographic framework, called fuzzy vault, was developed toprotect data in error-prone environments, such as biometric au-

thentication systems, and ReedSolomon (RS) codes were em-ployed. Similarly, a methodology based on channel codes andthe SlepianWolf theorem [25] for secure biometric storage waspresented in [26]. Specifically, low-density parity check(LDPC)codes were utilized for the development of an iris authenticationsystem and security of the biometric templates was quantified.Additionally, a fingerprint recognition system based on statis-tical modeling of the enrolled and the measured data was pre-sented in [27].

Furthermore, LDPC codes were also used for biometricauthentication in [28]. Similar to the fuzzy vault concept, thefuzzy commitment concept was introduced and the biometricauthentication problem was considered as a wire-tap problem.

A similar approach, but not in the context of biometric recog-nition, was presented in [29]. The multimedia authenticationproblem in the presence of noise was investigated, the theo-retical limits of the system were identified, and the tradeoffamong fidelity, robustness, and security was discussed. Thisapproach provides intuition for the proposed method in thispaper; the biometric recognition problem is considered as theanalogous of data transmission over a communication channel,which determines the efficiency of the system. Interestingly,the problem of coding distributed correlated sources has alsoattracted much interest in the field of video coding recently. Inthe seminal work of [30], the distributed source coding usingsyndromes scheme was proposed. Based on this work, the field

of distributed video coding [31] has emerged as a new trend invideo coding.


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The main contribution of this paper with regard to the ex-isting solutions is manifold. First of all, biometric recognitionis formulated as a problem of coding with side information.Based on the SlepianWolf theorem, the theoretical limits of thesystem are investigated and its security is quantified. Second, tothe best of our knowledge, this is the first method that incorpo-rates soft input values for channel decoding instead of makinga hard decision on the received input values. It is also shownthat the performance of the channel decoder relies on the effec-tive modeling of the dependency channel and the exploitation ofthe noise channel statistics. Furthermore, a novel gait recogni-tion system is developed based on the proposed channel codingframework. Based on a set of discriminative features extractedfrom the human silhouette, we develop a statistical model of thegait channel relating the enrolment to the probe signals andanalytic models are developed for authorized and unauthorizedtransactions. This practical implementation assists in corrobo-rating the merit of the proposed scheme and serves as a examplefor its application with other biometric signals.

II. OVERVIEW OF THE PROPOSED SYSTEM

A. Preliminaries

The goal of an error correcting code is to enable reliable trans-mission of a message over a noisy communication channel. Forthis reason, some redundant information is added to the mes-sage prior to transmission. Thus, even if some bits of the mes-sage are corrupted by noise, the decoder may successfully re-cover the original message. Especially, in block coding, the bi-nary information sequence is segmented into message blocks offixed length consisting of informa-tion digits. The encoder encodes the input message into a bi-

nary -tuple ( ) which is referred to as the codeword ofmessage . Apparently, there are codewords correspondingto each message and this set of codewords is called ablock code. A block code is called linear if and only if itscodewords form a -dimensional subspace of the vector spaceover the field GF (2). In other words, a binary block code is alinear code if and only if the modulo-2 sum of two codewordsis also a codeword. Since a linear code is a -dimen-sional subspace of the vector space of all the binary -tu-ples, it is possible to find linearly independent codewords,

in such that every vector in is a linearcombination of these codewords, that is

(1)

where is 0 or 1 for . If these linearly independentcodewords are rearranged as the rows of an matrix, thefollowing form is obtained:

(2)

where , for .Since the rows of matrix generate the linear code

, the matrix is called the generator matrix for . An

linear code is completely specified by the rows of the generatormatrix . Therefore, the encoder has to store the rows of the

matrix and to form a linear combination of these rows basedon the input message .

A desirable property for a linear block code is to possess thesystematic structure of the codewords. This means that the code-word is divided into two parts: (a) the message part and (b) theredundant checking part. The message part consists of the in-formation bits of the input message without any modificationand the redundant checking part consists of parity-checkbits, which are the linear sum of the information bits. Such codesare called as linear systematic block codes.

There is another useful matrix associated with every linearblock code. Indeed, for every matrix with independentrows, there exists an matrix with linearindependent rows such that any vector in the row space ofis orthogonal to the rows of . This matrix is called parity-check matrix of the code.

B. Proposed System

In biometric authentication systems, the user claims an iden-

tity and the measured biometric data (probe) are compared tothe corresponding templates of the claimed identity (gallery),which have been previously stored in the database, during theenrolment stage. The biometric classifier expert compares theextracted biometric features (biometric signature) of the probewith the gallery signature and the system must decide whetherthe user is a client (genuine transaction, class ) or an im-postor (unauthorized transaction, class ) based on a decisionrule. Thus, the problem of person authentication is a detectionproblem which can be analyzed by means of a binary hypothesistest. The first hypothesis accepts a certain candidateclaim for a client identity and the second hypothesisrejects this claim. Most biometric systems tackle this problem

using conventional pattern recognition and machine learningtechniques. In contrast, the proposed system relies on channelcodes for this decision and, in particular, on distributed sourcecoding principles, as illustrated in the following.

The SlepianWolf theorem addresses the problem of codingdistributed (not co-located) sources and decoding them jointly,as depicted in Fig. 1(a). If we consider two random sequences

and that are encoded using separate conventional entropyencoders and decoders, the achievable rates areand , where and are the entropiesof and , respectively. However, if the two sequences are jointly decoded, the achievable rate region according to theSlepianWolf theorem is defined by

(3)

(4)

(5)

where and are the conditional entropies andis the joint entropy of and . Thus, according to

(5), the SlepianWolf theorem states that separate encoding andjoint decoding of the two sequences can be as efficient as jointencoding.

The SlepianWolf theorem can be also applied in the problemof source coding with decoder side information [Fig. 1(b)].Specifically, if the sequence is correlated with the sequence

, which is available only at the decoder, but not at the encoder,the achievable rate for sequence is . Thus,


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Fig. 1. (a) Source coding of distributed sources and (b) source coding with sideinformation.

even though the encoder does not have access to the correlatedsequence , it can compress source as if were availableat the encoder. However, the SlepianWolf theorem does not

provide a practical implementation of the described system.Biometric authentication can be formulated as a sourcecoding with decoder side information problem if we considerthe gallery and the probe signals as the random variablesand , respectively. This representation is reasonable sincethe probe and the gallery signals are correlated and the probeis only available at the decoder (authentication) side. Thearchitecture of the proposed biometric authentication method isillustrated in Fig. 2. Let 1 be the original representation of thebiometric trait at the enrolment stage at time . In general, theprobe and gallery data are not identical even in the case of clienttransactions due to time-related modifications in the biometricpattern, its presentation, and the sensor which captures the

raw biometric data. The noise in the biometric signal can bemodeled by a (virtual) additive noise (or correlation) channelwhich induces noise . Thus, at the authentication stage, whichtakes place at time , the biometric system needs to detectwhether the input signal comes from a genuine oran impostor user.

This model is analogous to data communication over noisychannels and is similar to the notion that SlepianWolf codingprotects for transmission over the (virtual) noise channel.At the decoder, is regarded as if it were after transmis-sion over the noise channel and corrects it using error correctingcodes. Let the noise induced by the channel be denoted by ,then .

1Throughout thispaper, capital symbols denote stochastic sequencesand low-ercase symbols denote their respective realizations.

In the proposed system, the extracted biometric features areencoded using a SlepianWolf encoder at the enrolment stage.The biometric signature, which is stored in the database of thesystem, consists only of the parity bits of the generated code-word (or, equivalently, the parity bits ). In this way, access tothe parity bits cannot reveal information about the original bio-metric data and the privacy of templates is ensured. Security ofstored biometric data is analytically discussed in Section III-C.

At the authentication stage, the biometric signal comprisesthe systematic part of the bitstream and along with the parity bitsof the claimed identity, which are retrieved from the database,form a codeword which is decoded by the channel decoder. In-tuitively, the noise induced by the channel in case of genuinetransactions is small whereas the noise in impostor transac-tions is relatively large. Thus, the channel decoder can decodethe codeword only when the induced noise is small and the erroris within the correcting capabilities of the channel code. Other-wise, if the noise of the channel corrupts the signal, the resultingcodeword cannot be decoded and the transaction is rejected as

unauthorized. Thus, the problem reduces to the estimation of thenoise channel statistics and the exploitation of this a priori in-formation at the channel decoder. If the selected error correctingcode is suitable for error protection on this channel, the decoderwill decode errorlessly and the transaction is authenticated.

III. DISTRIBUTED SOURCE CODING FOR BIOMETRICAUTHENTICATION

The operation of a biometric system is divided in two stages,(a) the enrolment stage and (b) the authentication stage, whichare further analyzed below.

A. Enrolment Stage

Initially, at the enrolment stage, the biometric signature of anindividual is obtained. The extracted features form the vector

, thus . The feature vector must betransformed from the continuous to the discrete domain so that itcan be further processed by the channel encoder. This mappingcan be represented by a uniform quantizer with levels. Eachcomponent of is then mapped to an index in the set , throughthe function , where . Theresulting vector is fed to the SlepianWolf encoder,which performs the mapping , whereand outputs the codeword , .

In this work, the SlepianWolf encoder is implemented by

a systematic LDPC encoder [32]. LDPC codes were selecteddue to their excellent error detecting and correcting capabili-ties. They also provide near-capacity performance over a largerange of channels while simultaneously admitting implementaldecoders. An LDPC code is a linear block code of code-word length and information block length which is definedby a sparse parity matrix , where denotesthe parity bits produced by the encoder. The code rate is definedas . A code is a systematic code if every codeword con-sists of the original -bit information vector followed byparity-bits. In the proposed system, the joint bit-plane encodingscheme of [33] was employed to avoid encoding and storingthe bit-planes of the vector separately. Alternatively, LDPC

codes in a high-order Galois-field could be employed, but bi-nary LDPC codes were selected due to ease of implementation.


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Fig. 2. Architecture of the proposed authentication system based on SlepianWolf coding.

Subsequently, the systematic bits of the codeword arediscarded and only the parity bits , that is the parity bits

of the codeword , are stored to the biometric database. Thus,the biometric template of an enrolled user consists of the paritybits , and its size is .

B. Authentication Stage

At the authentication stage, a user claims an identity , a newsignature is extracted from the biometric features, and the vector

, , is constructed. The vector , whichforms the side information corresponding to , is fed to theLDPC decoder. The decoding functioncombines with the parity bits which are retrieved from thebiometric database and corresponds to the claimed identity .The decoder employs belief propagation [34], [35] to decode

the received codewords.If the errors introduced in the side information with regard

to the originally encoded signal are within the error correctingcapabilities of the channel decoder then the correct codeword isoutput after a number of iterations and the transaction is con-sidered as a client transaction. Thus, the output of the LDPCdecoder is the quantized vector . Note that the exactreconstruction of the quantized feature vector is re-quired, that is . Otherwise, if the decoder cannot decodethe codeword (which is indicated if the number of iterations in-creases over a specific number ) a special symbol isoutput and the transaction is considered as an impostor trans-action. Thus, the initial hypothesis on the user identity is givenby

Considering the above, the design of the system involvestwo critical parameters; the error correcting performance of thechannel code and the level of security of the parity bits . Onone hand, a channel code with low code rate exhibits high errorcorrecting capabilities, which results in the decoding of verynoisy signals. This means, that the channel decoder will be ableto decode the codeword even if the noise in the biometric signalhas been induced by impostors. Additionally, will consist of

many bits and will be more difficult to forge. On the other hand,channel codes of high code rate exhibit limited error-correcting

capabilities and reduce the security of the system since theparity bits produced by the channel encoder consist of a few

bits. Thus, the design of an effective biometric system based onthe channel codes involves the careful selection of the channelcode rate to achieve the optimal tradeoff between performanceand security.

Besides the code rate, the error correcting capabilities of thechannel decoder also depend on the information of the noisechannel and the relationship between the noise induced by thechannel and the side information. Accurate modeling of the dis-tribution of the noise channel may improve the knowledge of thechannel decoder by exploiting a priori information, as it will beanalyzed in Section V.

According to the SlepianWolf theorem (5), errorless de-coding of can be achieved if the rate for its representation

is bounded by [36]

(6)

where can b e calculated f rom and t he m appingof the function using the chain rule as follows:

(7)

From the above equations, it is obvious that the minimumrate is determined by the conditional entropy whichis in turn defined by the quantization function . In general,a finer quantizer yields a higher conditional entropyand, therefore, more parity bits. This increasesthe security of thestored biometric templates but at the same time increasesthe riskof rejecting a legitimate user. On the other hand, a coarser quan-tizer would introduce large quantization distortion which wouldincur large false acceptance errors. However, the selection ofthe optimal quantizer cannot be determined beforehand sincethe side information is not available at the encoder. Section VI

presents experimental results to illustrate how the quantizationprocess affects the performance of the authentication system.


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C. Biometric Template Security

Most biometric systems store biometric templates in the formof raw data, e.g., video sequences of walking sequences, pho-tographs of faces, etc. If these templates are compromised byattackers they can be used to impersonate legitimate users andgain access to facilities of the protected system. Other systems

store features extracted from the raw biometric data. Again, anattacker who accesses the stored data by fraudulent means canreconstruct the original raw biometric data, especially if the fea-ture extraction algorithm is known.

In general, security refers to how difficult it is for an adversaryto gain access to the stored biometric data of the users of thesystem and there are two quantities associated with it. The firstis the strength of the key which is stored to the databaseand refers to how difficult it is for an attacker to gain access toit. In [37], the min-entropy was suggested as a measure of thisquantity. The min-entropy of a random variable isdefined as [37]

(8)

In the proposed scheme, since the possible statesof the binary random variables are 0 and 1. Also, since min-entropy can be viewed as the worst-case entropy the strength ofthe key is actually larger in real applications. Otherwise stated,min-entropy provides a worst-case estimate of the predictabilityof the random variable . Moreover, the average min-entropy of

given is defined as

(9)

The second quantity refers to how difficult it is to guess theoriginal biometric data once the stored biometric templateis compromised2 and can be measured by the entropy loss. Theentropy loss is defined as

(10)

In [38], it is proven that the entropy loss can be convenientlybounded by the size of the biometric template, that is

. This result is in accordance with the information theoreticframework for security quantification presented in [39], wherethe size of the stored biometric template was used to quantifythe security of the system.

Following the conclusions of [38] and [39], in the proposedsystem, security is quantified by the number of bits that com-prise the biometric template, which is equal to the number ofthe parity bits. Since the main scope of this paper is to focus onthe effectiveness of the proposed scheme in terms of recogni-tion performance, the number of parity bits is primarilyselected so that the recognition rate performance is maximized.Once has been selected the security of the stored biometricsystem is analyzed. Further analysis of the security of the bio-metric templates remains a subject of future work.

2Note that we refer to the feature vector x instead of the raw biometric datab . This is because the biometric template protection scheme is usually applied

after the feature extraction algorithm has been determined. Thus, the difficultyin reconstructing raw data from the feature vector is not a design parameter ofthe security system.

Fig. 3. Application of (a) the RIT and (b) the CIT on a silhouette image.

IV. GAIT REPRESENTATION

It must be noted that the proposed biometric authenticationframework can be used with any biometric trait provided thata robust feature extraction method exists. As a case study, inthis paper, a gait recognition system is developed based on theproposed framework to illustrate its efficiency. The feature ex-

traction process of the gait sequences is briefly presented. Basedon these features, the parameters of the correlation channel willbe tuned in Section V.

Three feature-based techniques are used for the extraction ofmeaningful features from human silhouettes; the RIT, the CIT,and Krawtchouk moments. Since the exact description of thegait recognition system is out of the scope of this paper, only abrief discussion is provided for the sake of self-completeness.The interested readers are referred to [13] for additional detailson the features for gait representation.

The first step in human movement analysis is the extraction ofthe walking subjects silhouette from the input image sequence.In the proposed framework, 2.5-D information is available since

the gait sequence is captured by a stereoscopic camera. UsingDelaunay triangulation on the 2.5-D data, a 3-D triangulatedhull of the silhouette is generated and is further processed usingthe 3-D geodesic transform [40], thus generating the final nor-malized silhouettes and all the transformations are ap-plied to them.

A. Generalized Radon Transformations

The generalized Radon transforms are used due to their apti-tude to represent meaningful shape characteristics [41]. In par-ticular, the RIT transform of a function is defined as theintegral of along a line starting from the center of the sil-

houette which forms angle with the horizontal axis[Fig. 3(a)]. In our feature extraction method, the discrete formof the RIT transform is used, which computes the transform insteps of and is given by

(11)

where , and are the constant step sizesof the distance and angle , is the number of silhouettepixels that coincides with the line that has orientation and are

positioned between the center of the silhouette and the end ofthe silhouette in that direction, and .


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Fig. 4. Reconstruction of silhouette images using Krawtchouk momentsfor various moment order values (a) original silhouette, (b) ( N ; M ) =( W = 1 0 ; H = 4 ) ,(c) ( N ; M ) = ( W = 1 0 ; H = 1 6 ) ,(d) ( N ; M ) = ( W = 3 0 ; H = 2 ) ,and (e) ( N ; M ) = ( W = 1 5 ; H = 3 ) .

In a similar manner, the CIT is defined as the integral of afunction along a circle curve with centerand radius . Similar to the RIT transform, the discrete form ofthe CIT transform is used, as illustrated in Fig. 3(b), which isgiven by

(12)

where , and are the constant step sizes of the radius and angle variables, is the radius of the smallestcircle that encloses the binary silhouette image , and

.

B. Feature Extraction Using Orthogonal Discrete Transform

Based on Krawtchouk Moments

Besides the generalized Radon transforms, the use of a novelset of orthogonal moments is also proposed based on the dis-crete classical weighted Krawtchouk polynomials [14]. Thesemoments assure minimal information redundancy due to theirorthogonality and are used to extract local shape characteristics

of images. The weighted Krawtchouk moments of orderare estimated using the Krawtchouk polynomials for asilhouette image with intensity function as follows:

(13)

(14)

where , are the weighted Krawtchouk polynomials, and, represent the width and the height of the silhouette image,

respectively. Fig. 4 depicts a graphical representation of the re-constructed silhouette images using different orders of the width

and the height .

V. CORRELATION CHANNEL MODELING OF GAIT SEQUENCES

The architecture of the gait recognition system is depictedin Fig. 5. The RIT, CIT, and Krawtchouk feature vectors areextracted from the gait sequences, as described in Section IV,and are concatenated into the vector , which is quantized andencoded by the LDPC encoder. Subsequently, the parity bits

are stored to the database. This procedure is applied for everyframe of the gait sequence, thus the biometric template of a user

consists of templates, where is the number of frames in thegait sequence of that user. Additionally, for each user, a set ofindexes is stored to indicate the boundaries of gait cycles.3

At the authentication stage, the RIT, CIT, and Krawtchouktransformations are applied and the extracted feature vectorsare concatenated to form the vector . Again, this procedureis repeated for every frame in the gait sequence. Subsequently,the direct matching method is employed for template matching.This procedure has been described in detail in [13]. Next, theparity bits that correspond to these cycles are combined withthe side information and form the codeword , which is de-coded by the LDPC decoder. A transaction is considered legit-imate if the LDPC decoding succeeds for every frame of theindicated gait cycle.

The LDPC channel decoder employs belief propagation, aniterative algorithm based on a soft-decoding approach to retrievethe original codeword. The decoder tries to compute the a pos-teriori probability that a given bit in the generated codewordequals 0 given the received side information . Thus, the con-

fidence level of each bit in the codeword is defined by thelog-likelihood ratio (LLR) as

(15)

where denotes the th bit of the value . The critical pointin the operation of the described system is the efficient mod-eling of the dependency between the side information and theoriginal signal . Note that the correlation between andis modeled even though it is that is actually encoded. How-ever, since is the uniformly quantized version of , it willhave the same distribution with . The problem of modelingthe correlation channel of distributed sources has been also ad-

dressed in the context of distributed video coding [42]. Thenoise that is induced by the (virtual) dependency channel tothe measured biometric signal during the authentication stage isgiven by . In this work, the Cauchy distribution isemployed to model the probability distribution function of theresidual signal in genuine transactions and the uniform dis-tribution for the impostor transactions

genuine transactions

impostor transactions

where and are probability distribution parameters. Letbe the set of values that have the th bit equal to zero; then,

the probability that is equal to 0, in (15), is given by

(16)

The parameter is estimated by plotting the residual his-togram for the gait sequences and selecting the parameter thatbetter matches the actual curves. Fig. 6 illustrates the coeffi-cients of the feature vectors for the RIT, CIT, and Krawtchoukdescriptors at the enrolment stage and the authentication stagefor a genuine and an impostor user. The respective probabilitydistribution function of the residual signal for the genuine andimpostor users of the RIT feature vector is depicted in Fig. 7.

3The indexes are not protected since they do not provide critical informationabout the human gait sequence.


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Fig. 5. Architecture of the proposed gait authentication scheme.

Fig. 6. Graphical representation of the coefficients of the (a) RIT, (b) CIT, and (c) Krawtchouk feature vectors at the enrolment (blue line), a genuine user, and animpostor transaction.

These figures corroborate the selection of the proposed distri-bution models. The main reason for the selection of the spe-cific model is that the probe data during client transactions differslightly from the enrolled data, while the features from impostorsequences differ arbitrarily. Thus, the probability density func-tion of the residual signal exhibits a peak near zero and its tailsdegrade fast. It must be noted that the parameter of the prob-ability distribution model does not affect significantly the per-formance of the decoding algorithm. Specifically, as depicted in(15), the term appears both in the nomi-nator and the denominator. Thus, the LLR is insignificantly af-

fected which means that the impact of in the recognition ac-curacy is negligible. Nevertheless, the proposed values of thedistribution parameters were proven very reliable in the testeddata sets, as shown in Section VI.

VI. EXPERIMENTAL RESULTS

A. Database Description

The validity of the proposed method was evaluated on a large-scale proprietary database acquired within the course of theHUMABIO project [43]. The database was captured in an in-door environment and consists of people walking in a predefinedpath in a front-parallel view from the camera. The main course

of walking is around 6 m and the distance from the camera variesfrom 4 to 6 m. In addition, for eachsequence, the 3-D depth map

was captured using a stereo camera. This is the first database thathas depth data for assisted gait recognition. The database con-sists of 75 subjects. Four different experiments were recordedfor each subject: 1) the normal experiment, 2) the shoe ex-periment in which the users wear a different shoe type (slipper),3) the hat condition in which the users wear a hat, and 4) thebriefcase experiment in which the users carry a briefcase. Thenormal set was used as the gallery set and the other sets wereconsidered as the probe sets.

Experimental results are also reported on two large public gaitdatabases; the HUMAN ID Gait Challenge [12] and the CASIA

database [44]. The former database was captured in an outdoorenvironment and consists of 71 subjects. Seven experimentswere recorded using different recording views, shoe types, andsurfaces as described in Table I.

The CASIA database (dataset B) consists of 124 subjects.Only the sequences recorded at a 90 angle were considered.There are six sequences for each subject; four of them were con-sidered as gallery set and the remaining two were consideredas probe set. Moreover, three conditions are considered: 1) theNormal, 2) the Briefcase, where the subjects carry a brief-case or a bag, and 3) the Coat, where the subjects wear a coat.

B. Authentication Results

In an authentication scenario (or verification), the biometricsystem is used to grant access to individuals. Initially, a subject


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Fig.7. Probability distributionof the residual signal w for (a) a clientand(b)animpostor user for the RIT feature vector.

TABLE IEXPERIMENTAL CONDITIONS FOR GAIT RECOGNITION IN THE HUMAN ID

GAIT CHALLENGE DATABASE

claims his/her identity and the gait system compares the signa-ture with the stored one in the database. Then, based on the au-thentication procedure, the system establishes whether the iden-tity of the user is the claimed one. In this respect, authenticationresults in an one-to-one comparison and is quite different fromthe identification scenario, in which the system has to determinethe identity of users by comparing the measured data with all the

enrolled data in the database (one-to-many database).Regarding the features for the gait representation, the param-

eter was selected equal to 3 , as suggested in previous workon gait recognition [13]. Thus, the feature vector of the RITcomponent consists of coefficients. For the CITcomponent , which results in 72 coefficients. Finally,the Krawtchouk feature vector consists of 600 coefficient. As aresult, the concatenated feature vector that is fed to the LDPCencoder consists of coefficients. Forthe channel coding, a modified version of the RadfordNealpackage was used [45] and systematic channel codes of var-ious rates were produced. The LDPC decoder employs a beliefpropagation algorithm based on the soft decoding approach to

retrieve the original bits, as explained in Section V. In the fol-lowing, results are presented using rate operating characteristic

Fig. 8. FAR and FRR of the shoe experiment of the HUMABIO database asa function of the security bits.

(ROC) curves, which present the verification rate [or genuineacceptance rate (GAR)] versus the false acceptance rate (FAR).The false rejection rate (FRR) can be computed as .

Fig. 8 reports the performance results of the gait recognitionsystem for the shoe experiment as a function of the securityusing the proposed scheme for the protection of the templates.Thus, the horizontal axis represents the numbers of the paritybits, while the vertical axis represents the FAR and FRR. Specif-ically, if the code rate of the LDPC code is then the template

consists of bits. The more bits used for the

parity bits the more secure is the template since it is more dif-ficult to be broken. On the other hand, decreasing the size ofthe template increases the sensitivity of the system, which re-sults in more authentication failures of legitimate users. Thus,the recognition accuracy of the proposed system can be deter-mined by specifying the code rate . This is similar to the con-ventional approach that determines the operating points of theROC curve by varying the threshold that determines which sub-jects are granted access.

The proposed system was compared with a well-knownchannel coding method, the fuzzy commitment scheme, usingthe same feature vectors for gait representation. The results de-picted in Fig. 9 clearly indicate the superiority of the proposed

scheme over the fuzzy commitment scheme. The performancegain which is approximately 10% is mainly attributed to theuse of LDPC codes in the proposed scheme rather than RScodes which are used in the fuzzy commitment scheme andthe integration of soft input values for channel decoding byexploiting channel statistics. It must be also noted that theperformance gain is significant for all the experiments of thedatabase. This proves the superior performance of the proposedscheme as a biometric template protection method.

Furthermore, the proposed system was also compared withstate-of-the-art methods which perform authentication based onconventional pattern matching methods. The method presentedin [13] (RCK-G method) was selected for comparison since it

is the only method which performs classification in the HUM-ABIO database using depth data. The channel code rate is varied


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Fig. 9. ROC curves for the comparison of the proposed scheme with the fuzzycommitment (FC) scheme on the HUMABIO database.

Fig. 10. ROC curves for the comparison of the proposed scheme with thescheme of [13] in the hat, shoe, and briefcase experiments on theHUMABIO database.

to achieve different operating points which approximate the per-formance of [13]. The resulting ROC curves are illustrated inFig. 10. It can be easily observed that the proposed schemeachieves substantially better performance while at the same timeproviding security to the enrolled templates. The gain in recog-nition performance is approximately 1%3% in all the condi-tions. Thus, the proposed scheme increases the security of thebiometric templates while at the same time enhancing the per-formance of the system. The critical point for the effective per-formance of the system is mainly the effective modeling of the(virtual) noise channel as discussed in Section V. These resultsalso indicate that the performance of the proposed algorithm is

mainly attributed to the specific features vectors by employingthe proposed gait transforms.

Fig. 11. ROC curves for the comparison of the proposed scheme with (a) thescheme of [13] and (b) the baseline algorithm on the Human ID Gait ChallengeDatabase.

The proposed scheme was also tested on the outdoorHuman ID Gait Challenge database to demonstrate its validity.Fig. 11(a) illustrates the ROC curves of the proposed methodand the method of [13]. To make the figure more legible only theexperiments are depicted in the legend. Solid lines correspondto the proposed method whereas dashed lines correspond tothe method of [13]. It is again clear that the increased securityof the stored templates comes at no cost in the recognitionaccuracy. The proposed scheme is also tested with the baselinealgorithm [12] and the results are shown in Fig. 11(b). Again,solid lines correspond to the proposed method whereas dashedlines correspond to the Baseline algorithm. It is evident that

the performance gain varies between 10% and 30% for all theexperiments. The superior performance of the proposed schemecompared to the baseline algorithm is attributed to the syn-ergistic cooperation of the employed transformations for gaitrepresentation and the channel coding scheme. Nevertheless,the most important conclusion from this comparison is that theperformance of the proposed scheme is robust against noise onsilhouettes.

Furthermore, the system was tested on the CASIA databasewhich consists of more subjects. To the best of our knowledge,this is the first time that verification results are reported on thisdatabase. The ROC curves for the three experiments of the data-base are shown in Fig. 12. From this figure, it can be seen that for

the normal experiment, an equal error rate (EER) of 6% can beachieved, while for the two other experiments, the briefcase


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Fig. 12. Verification results of theproposed schemeusing theCASIAdatabase.

and the coat experiments, the EER becomes approximately20% and 30%, respectively. The reduction in recognition per-formance in these two experiments is logical since the probesequences contain significant noise with regard to the enrolledsequences.

Finally, the performance of the system with three differentparameter settings was evaluated on the HUMABIO database.More specifically, the parameter of the Cauchy distributionwas selected as , a different quantizer with

quantization levels was used, and different parameters wereused for the generation of the LDPC code. The main purposeof these experiments was to evaluate the effect of different pa-

rameter settings in recognition accuracy. The results of thesevarious parameter settings are illustrated in Fig. 13. For sakeof brevity, only the briefcase experiment is depicted but thesame remarks also hold for the other experiments. It is evidentthat the effect of the parameter in the recognition accuracy isnegligible which corroborates the statement in Section V. More-over, the use of another LDPC code results in almost identicalperformance. However, the selection of different quantizer de-teriorates significantly the recognition performance by 8% ap-proximately. For this reason, a quantizer with quantiza-tion levels was used for all the experiments.

VII. CONCLUSION

In this paper, a novel approach for the formation of thebiometric recognition problem as a distributed source codingproblem was introduced. A virtual dependency channel wasassumed to model the correlation between the biometric dataat the enrolment and the authentication stage. In this respect,biometric recognition is regarded as a problem of sourcecoding with side information at the decoder. As a case study,a framework for gait recognition was developed. Initially, theuse of depth data was employed to enhance the silhouettesegmentation algorithm and acquire more accurate features.Then, the features used for the representation of gait sequenceswere discussed in detail. Three quite discriminative featureswere extracted: RIT, CIT, and Krawtchouk. Subsequently, the

integration of these features in the distributed source codingframework was described and the tradeoff between security and

Fig. 13. ROCcurves of the proposed scheme using different parameter settingsfor the briefcase experiment on the HUMABIO database.

performance of the biometric system was analyzed. The exper-imental results validated the proposed method and demonstratethat the security of the stored templates can be increased onlyat a negligible penalty in performance. Future work shouldconcentrate on the quantification of security in a more rigorousway and the modeling of the virtual dependency channel withmore accurate models.

REFERENCES

[1] N. V. Boulgouris, D. Hatzinakos, and K. N. Plataniotis, Gait recogni-tion: A challenging signal processing technology for biometric identi-fication, IEEE Signal Process. Mag., vol. 22, no. 6, pp. 7890, Nov.

2005.[2] M. Nixon and J. Carter, Advances in automatic gait recognition, inIEEE Int. Conf. Automatic Face and Gesture Recognition, May 2004,pp. 139144.

[3] W. Stallings , Cryptography and Network Security: Principles andPractices. Upper Saddle River, NJ: Prentice-Hall, 2006.

[4] A. Jain, K. Nandakumar, and A. Nagar, Biometric template secu-rity, EURASIP J. Advances Signal Process., vol. 2008, no. Article ID579416, 2008.

[5] U. Uludag, S. Pankanti, S. Prabhakar, and A. Jain, Biometric cryp-tosystems: Issues and challenges, Proc. IEEE, vol. 92, no. 6, pp.948960, Jun. 2004.

[6] A. Kale, N. Cuntoor, A. N. Rajagopalan, B. Yegnanarayana, and R.Chellappa, Gait analysis for human identification, in Proc. 4th Int.Conf. Audio and Video Based Person Authentication, Guilford, U.K.,Jun. 2003, pp. 706714.

[7] A. Kale, A. Sundaresan, A. Rajagopalan, N. Cuntoor, A. Roy-Chowd-

hury, V. Kruger, and R. Chellappa, Identification of humans usinggait, IEEE Trans. Image Process., vol. 13, no. 9, pp. 11631173, Sep.2004.

[8] Z. Liu and S. Sarkar, Improved gait recognition by gait dynamics nor-malization, IEEE Trans. Pattern Anal. Mach. Intell., vol. 28, no. 6, pp.863876, Jun. 2006.

[9] N. V. Boulgouris, K. N. Plataniotis, and D. Hatzinakos, An angulartransformof gaitsequences for gaitassistedrecognition, in Proc. IEEE

Int. Conf. Image Processing, Singapore, Oct. 2004, pp. 857860.[10] N. V. Boulgouris, K. N. Plataniotis, and D. Hatzinakos, Gait recogni-

tion using linear time normalization, Pattern Recognit., vol. 39, no. 5,pp. 969979, May 2006.

[11] J. Han and B. Bhanu, Individual recognition using gait energy image, IEEE Trans. Pattern Anal. Mach. Intell., vol. 28, no. 2, pp. 316322,Feb. 2006.

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Dimosthenis Ioannidis was born in Larisa, Greece,in 1977. He received the Diploma degree in elec-trical engineering from the Electrical and ComputerEngineering department of the Aristotle Universityof Thessaloniki (AUTH), Thessaloniki, Greece, in2000, and the M.A. degree in advanced communica-tion systems and engineering from AUTH in 2005.

He is currently working as a Research Associate

with the Informatics and Telematics Institute of theCentre for Research and Technology Hellas, Thessa-loniki, Greece. His main research interests are in the

areas of biometrics, 3-D data processing, and web semantics.Mr. Ioannidis is a member of the Technical Chamber of Greece.

Michael G. Strintzis (S68M70SM79F03)received the Diploma in electrical engineering fromthe National Technical University of Athens, Athens,Greece, in 1967, and the M.A. and Ph.D. degreesin electrical engineering from Princeton University,Princeton, NJ, in 1969 and 1970, respectively.

He joined the Electrical Engineering Department,University of Pittsburgh, Pittsburgh, PA, where he

was an Assistant Professor from 1970 to 1976 andAssociate Professor from 1976 to 1980. Duringthat time, he worked in the area of stability of

multidimensional systems. Since 1980, he has been a Professor of Electricaland Computer Engineering at the Aristotle University of Thessaloniki, Thessa-loniki, Greece. He has worked in the areas of multidimensional imaging andvideo coding. Over the past ten years, he has authored many journal publi-cations and more than 200 conference presentations. In 1998, he founded theInformatics and Telematics Institute, currently part of the Centre for Researchand Technology Hellas, Thessaloniki.

Dr. Strintzis was awarded the Centennial Medal of the IEEE in 1984 and theEmpirikeion Award for Research Excellence in Engineering in 1999.

A Channel Coding Approach for Human

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