appeared in proc. of ieee international workshop on information...

A Bayesian Approach for Modeling SensorInfluence on Quality, Liveness and Match Score

Values in Fingerprint VerificationAjita Rattani #1, Norman Poh ∗2, Arun Ross #3

# Dept. of Computer Science and Engineering, Michigan State University, USA1 [email protected]

3 [email protected]∗ Dept. of Computing, University of Surrey, UK

2 [email protected]

Abstract—Recently a number of studies in fingerprint verifi-cation have combined match scores with quality and livenessmeasures in order to thwart spoof attacks. However, theseapproaches do not explicitly account for the influence of thesensor on these variables. In this work, we propose a graphicalmodel that accounts for the impact of the sensor on matchscores, quality and liveness measures. The proposed graphicalmodel is implemented using a Gaussian Mixture Model basedBayesian classifier. Effectiveness of the proposed model has beenassessed on the LivDet11 fingerprint database using Biometrikaand Italdata sensors.

I. INTRODUCTION

Recent research has highlighted the vulnerability of bio-metric systems to spoof attacks. A spoof attack occurs whenan adversary mimics the biometric trait of another individualin order to circumvent the system. For instance, it has beenshown that a person can fool a fingerprint system by usinga finger-like object made of gelatin or play-doh that has thefingerprint ridges of another individual impressed on it [1].

In the context of fingerprints, liveness detection algorithmshave been proposed as a counter-measure against spoof at-tacks. These algorithms attempt to discriminate live biometricsamples from spoof (fake) artefacts by examining the textural,anatomical and/or physiological attributes of the finger [2], [3].The output of these liveness detection algorithms is a single-valued numerical entity referred to as liveness measure.

Liveness detection algorithms are not designed to oper-ate in isolation; rather, they have to be integrated with theoverall fingerprint recognition system. Accordingly, recentstudies have combined match scores generated by a fingerprintmatcher with liveness values [4], [5] as well as image qualityvalue [6], in order to render a decision on the recognitionprocess. Typically, a learning-based scheme is used in sucha fusion framework [7]. For example, in [4] the authorscombine fingerprint match scores with liveness measures usinga Bayesian Belief Network. In [6], fingerprint match scores are

WIFS‘2013, November 18-21, 2013, Guangzhou, China.ISBN 978-1-4673-5593-3 c⃝2013 IEEE.

combined with quality and liveness measures using a density-based fusion framework. The work in [6] also establishedthe benefits of incorporating both image quality and livenessmeasures in the fusion framework. In [5], face match scoresare combined with liveness measures using logistic regression.However, in the aforementioned schemes, the influence of thesensor on the 3 variables - match scores, liveness values andquality - has not been considered. Such a consideration isessential for several reasons: (a) the quality of an image isimpacted by the sensor used; (b) most liveness measures arelearning-based and are impacted by the sensor that was used tocollect live and spoof training data; (c) understanding sensorinfluence, can help in facilitating sensor interoperability [8]for fingerprint matchers and liveness detectors.

In order to address this issue, we propose a fusion frame-work based on graphical models where the influence of thesensor on match scores, liveness measures and quality valuesis accounted for. The proposed graphical model is based onthe assumption that data from a set of fingerprint sensors areavailable during the training stage. However, the actual sensoridentity is not known during the testing stage1.

The contributions of this work are as follows: (1) develop-ment of a graphical model for fusing match scores, livenessmeasures and quality values while accounting for sensorinfluence; (2) implementation of the proposed model usinga Gaussian Mixture Model (GMM) based Bayesian classifierin designing a fingerprint verification system that is robust tozero-effort impostors as well as non-zero-effort spoof attacks;and (3) evaluation of the proposed model using fingerprintdata from two different sensors in the LivDet 2011 fingerprintdatabase.

This paper is organized as follows: Section 2 presents theproposed graphical model. Section 3 discusses the databaseand experimental protocol used in this work. Experimentalresults are reported and discussed in section 4. Conclusionsare drawn in section 5.

1In principal, data from the sensor used during testing does not have to beavailable during training.

Appeared in Proc. of IEEE International Workshop on Information Forensics and Security (WIFS), (Guangzhou, China), November 2013

II. THE PROPOSED GRAPHICAL MODEL AND ITSIMPLEMENTATION USING GMM

A graphical model is an effective tool to express therelationship between different variables [9], [10]. This isoften depicted as a directional graph with nodes representingprobabilities of a variable and arrows representing conditionalprobabilities (e.g., an edge from A to B defines P (B|A)).

We formulate the spoof-resilient fingerprint verificationproblem as follows. An input fingerprint sample has to becompared against a live 2 template fingerprint sample. Livenessmeasures and quality values are extracted from both samples.Further, a match score is computed between the two samples.Let y ∈ R be the match score, qt ∈ R (qi ∈ R) represent thequality of the template (input) fingerprint sample (q = [qt, qi])and lt ∈ R (li ∈ R) denote liveness measure of the template(input) fingerprint sample (l = [lt, li]). The output is one ofthree classes: the genuine class, G, when the input is deemedto be a live sample with the same identity as that of thetemplate; the impostor class, I , when the input is deemed tobe a live sample whose identity is not the same as that of thetemplate; the spoof class, S, when the input is not deemed tobe a live sample. Let k ∈ {G, I, S}. Further, let d signify oneof N sensors used for training dataset acquisition. While theset of sensors used for training dataset acquisition is known,the actual sensor used to acquire biometric data during systemdeployment (or testing) does not have to be known.

Table I shows three graphical models and the conditionalprobabilities between match score (y), quality (q), livenessmeasure (l) and sensor information (d), conditioned on theclass label (k) to represent a) a conventional classifier (ModelA); b) a fusion framework based on [6] that combines l, q andy (Model B); and c) the proposed classifier that incorporatesthe influence of the sensor on l, q and y (Model C).Next, we will explain these graphical models and how theycan be realized through a GMM-based Bayesian classifier [7] .

a) Conventional classifier: Model A in Table I represents theconventional generative classifier that attempts to model thescore (y) conditioned on class label (k ∈ {G, I}), i.e., p(y|k).A conventional classifier assumes the attacker is simply a zero-effort impostor (k = I) and does not consider the possibilityof concerted spoof attacks. It can be implemented using thelog-likelihood ratio based test statistic as follows:

yllra = logp(y|k = G)

p(y|k = I). (1)

b) Fusion framework against spoof attacks: Model B inTable I models the joint density of match scores, qualityand liveness measures conditioned on class k. This modelis based on the framework mentioned in [6] for fingerprintverification against zero-effort impostor and spoof attacks. Thejoint distribution represented by model B is in the following

2In this work, the template is assumed to be that of a live fingerprint sample.Its liveness value is nevertheless computed.

Graphical Model Conditional Probabilities

• k → y ; p(y|k)

• q → y ; p(y|q)• l → y ; p(y|l)• k → y ; p(y|k)= p(y|k, q, l)

• d → y; p(y|d)• k → y; p(y|k)= p(y|k, d)• d → q; p(q|d)• d → l; p(l|d)= p(q, l|d)

TABLE I: Three graphical models that describe the relation-ship between match scores (y), quality (q), liveness measures(l) and sensor information (d), conditioned on the class label(k).

form:p(y, k, q, l) = p(y|k, q, l)p(q)p(l)P (k) (2)

Model B can be realized using the log-likelihood ratio basedtest statistic as follows:

yllrb = logp(y, q, l|k = G)

p(y, q, l|k ̸= G),

= log p(y|k=G,q,l)p(y|k ̸=G,q,l) + log

p(q|k = G)

p(q|k ̸= G)︸︷︷︸+ logp(l|k = G)

p(l|k ̸= G)︸︷︷︸ .(3)

where (k ̸= G) ∈ {I, S}. The underbraced terms in (3) will bezero as quality (q) and liveness (l) measures are assumed tohave no discriminatory information for distinguishing betweenthe genuine and impostor classes. Therefore, the log-ratio forthese terms will be zero. Further, p(y|k, q, l) cannot be directlyestimated using off-the-shelf algorithms. This is because theconditioning variables q and l in (3) are continuous. Alterna-tively, model B can be effectively realized by the joint densityestimate of y, q, l for class k i.e., p(y, q, l|k). This methodwas reported to be more effective than model A (the baseline)


under zero-effort impostors as well as spoof attacks in [6], aswill also be confirmed by our experiments here.

c) Proposed model: Model C in Table I is an extension ofmodel B and models the influence of the sensor. This modelattempts to model the dependency of score (y) on class label(k ∈ {G, I, S}) as well as the sensor (d). Further, the quality(q) and liveness measures (l) are categorized according to thesensor (d) used in the training dataset.

The joint densities represented by model C are as follows:

p(y, k, q, l, d) = p(y|k, d)p(q, l|d)P (d)P (k) (4)

Model C can be effectively realized by extending (3) as:

yllrc = log

∑d p(y, q, l|k = G, d)P (d|q)∑d p(y, q, l|k ̸= G, d)P (d|q)

. (5)

P (d|q) in (5) can be estimated using the Bayes rules as:

P (d|q) = p(q|d)P (d)

p(q). (6)

There is an integration over the sensor (d) in (5) becausesensor (d) to be used during the testing (or system deployment)is not known in advance and its probability is inferred fromthe quality (q) of the operational data i.e., P (d|q) in (5).

Model C is based on a conjecture that match scores, qualityand liveness measures are sensor dependent (d → {y, q, l} inmodel C, Table I(c)). Further, their exists no significant corre-lation between quality (q) and liveness (l) measures (absenceof an arrow between q and l in model C). These conjectureswill be validated by empirical evidence (see Section IV).

The densities p(y, q, l|k) in (3), p(y, q, l|k, d) in (5) andp(q|d) in (6) to estimate P (d|q) in (5) are themselves es-timated using the Gaussian Mixture Model (GMM). GMMhas been successfully used to estimate joint densities [11].Let ϕN (x, µ,Σ) be the N -variate gaussian density with meanvector µ and covariance matrix Σ, i.e.,

ϕN (x, µ,Σ) = (2π)−N/2|Σ|−1/2exp(−1

2(x−µ)TΣ−1(x−µ))

(7)The estimates of p(x|k) (where x is an observation vectorwhich is (y, q, l) in our case) for class k is obtained as amixture of Gaussians as:

p(x|k) =Mk∑j=1

wk,jϕN (x, µk,j,Σk,j) (8)

where Mk is the number of mixture components used to modelthe densities of class k. wk,j is the weight assigned to thejth mixture component in p(x|k),

∑Mk

j=1 wk,j = 1. Selectionof the appropriate number of components is one of the mostchallenging issues in mixture density estimation. The GMMfitting algorithm proposed in [11] automatically estimatesthe appropriate number of components and the componentparameters using an EM algorithm and the minimum message

length criterion. Hence, the GMM fitting algorithm proposedin [11] was used in this study3.

III. DATABASE, PROTOCOL AND PERFORMANCE METRICS

The LivDet11 dataset was used to evaluate fingerprintliveness detection algorithms submitted to the Second In-ternational Competition on Fingerprint Liveness Detection(LivDet11) [12]. It consists of 1000 live and 1000 fake finger-print images in the training set and the same number of imagesin the test set. All images collected using the Biometrika andItaldata sensors were used in this study4. The live images wereobtained from 200 different fingers with 5 samples per fingerfor each set. The fake fingerprints were fabricated using thefollowing five materials: gelatine, silicone, woodglue, ecoflexand latex. 200 fake fingerprints were fabricated per material(200× 5 = 1000) from 20 fingers with ten samples per fingerfor each set (training and testing).

The NIST Bozorth35 software was used for obtaining amatch score between a pair of fingerprint images. The qualityof live as well as fake fingerprint impressions was measuredusing the IQF freeware developed by MITRE6. The qualityfactor ranges between 0 and 100, with 0 being the lowestand 100 being the highest quality. Finally, fingerprint livenesswas assessed using the liveness measure proposed by Nikamand Aggarwal [3], which is based on Local Binary Pattern(LBP) features. A two class Support Vector Machine (SVM)(implemented using LIBSVM package7) was trained usingLBP features extracted from live and fake images in thetraining set. The output score (probability estimate) of SVMwas then used as a liveness measure. Equal Error Rate (EER)using this liveness measure was evaluated to be 10.95% and18.95% on the test partition of the LivDet11 database forBiometrika and Italdata sensors, respectively.

Protocol and Performance metrics: Following theLivDet2011 protocol described in [12], we used 1000live and 1000 fake images to train the models and theremaining 1000 live and 1000 fake images were used toevaluate the performance of the models.

a) Learning-based fusion framework: The observation vectorconsists of a match score (y) and a pair of quality values(q) as well as liveness measures (l) extracted from a pair oftraining images - the input and the template. This observationvector is mapped to one of three output classes: G, I , orS (4000 observation vectors were used for each class). Thisinformation, i.e., (y, l, q, k) is used to train the GMM-basedBayesian classifiers in model B (3) and model C (5).

b) Performance assessment metric: In a spoof-resilient fin-gerprint verification system, as defined in this work, the G

3We used the MATLAB code available at http://www.lx.it.pt/∼mtf/mixturecode.zip

4Data from other sensors in the LivDet11 dataset could not be used due tofew correspondences in the subject identity between live and fake images.

5http://www.nist.gov/itl/iad/ig/nbis.cfm6http://www.mitre.org/tech/mtf/7http://www.csie.ntu.edu.tw/∼cjlin/libsvm/


class indicates an “Accept” while the I and S classes indicatea “Reject”. Therefore, we define overall false acceptancerate (OFAR) as the proportion of impostor and spoof inputsamples that are incorrectly classified as being genuine. Gen-uine Acceptance Rate (GAR) is defined as the proportion ofgenuine input samples that are correctly classified as such.The False Reject Rate (FRR), which is 1-GAR, denotesthe proportion of genuine input samples that are incorrectlyclassified as being an impostor or a spoof. Overall Equal ErrorRate (O-EER) is the rate at which OFAR is equal to FRR.

Further, with respect to the impostor class, there is falseaccept rate of impostor samples (IFAR). With respect tothe spoof class, there is false accept rate of spoof samples(SFAR). SFAR (IFAR) is calculated as proportion ofspoofed (impostor) samples incorrectly classified as genuine.

IV. EXPERIMENTAL RESULTS

1) Assessment of model B under same- and cross-sensoroperation: First we evaluated the performance of model Bunder same- and cross-sensor conditions. Figure 1a showsthe ROC curves for the performance of model B trainedand tested using Biometrika (legend “Model-B Bio-Bio”), andthat trained using Italdata and tested using Biometrika (legend“Model-B Ital-Bio”). Comparative assessment has been madewith the baseline (legend “Model-A Bio-Bio”) under zero-effort impostor and spoof attacks. Similarly, Figure 1b showsthe performance of model B trained and tested using Italdata(legend “Model-B Ital-Ital”), and that trained using Biometrikaand tested using Italdata (legend “Model-B Bio-Ital”). It can beseen from these Figures that model B, when trained and testedusing the same sensor (legend “Model-B Bio-Bio” in Figure 1aand “Model-B Ital-Ital” in Figure 1b) can significantly enhancethe performance of fingerprint verification under zero-effortimpostor as well as spoof attacks by 59.2% and 41.95% overthe baseline (legends “Model-A Bio-Bio” and “Model-A Ital-Ital”) for Biometrika and Italdata sensors, respectively.

However, the performance of model B significantly de-grades on cross-sensor operation. For instance, there is a65.44% increase in the O-EER of model B that is trainedusing Italdata and tested using Biometrika (legend “Model-B Ital-Bio”, Figure 1a) over that trained and tested usingBiometrika (legend “Model-B Bio-Bio”, Figure 1a). Similarly,there is a 58.98% increase in the O-EER of model B thatis trained using Biometrika and tested using Italdata (legend“Model-B Bio-Ital”, Figure 1b) over that trained and testedusing Italdata (legend “Model-B Ital-Ital”, Figure 1b). Thedegradation in the performance of model B on cross-sensoroperation is due to the fact that match scores, quality andliveness measures are impacted by the acquisition sensor usedbut has not been accounted for.

2) Validation of the conjectures for model C: Model C isbased on the conjectures that 1) match scores (y), quality (q)and liveness measures (l) are influenced by the acquisitionsensor used (see section II(c)), 2) there exists no significantcorrelation between quality (q) and liveness measures (l)

(a) Model B tested using Biometrika sensor.

(b) Model B tested using Italdata sensor.

Fig. 1: ROC curves for the matching performance of modelB under same- and cross-sensor operating conditions forBiometrika and Italdata sensors. Comparative assessment hasbeen made with model A under zero-effort impostor and spoofattacks.

of the fingerprint samples, and 3) quality measures offerdiscriminatory information to infer the probability of sensoridentity, i.e., P (d|q) in (5).

Figure 2 shows that match score, quality and liveness mea-sures are influenced by the acquisition sensor used. Further,Figure 3 shows the quality (IQF ) and liveness value (LM )of live and fake fingerprint samples of a randomly selecteduser acquired using Biometrika and Italdata sensors. Scatterplot of liveness measure and quality of the fingerprint samples(Figure 4) acquired using the Biometrika sensor show that nosignificant correlation (ρ = 0.25) exists between quality (q)and liveness measures (l). A similar observation was made forthe Italdata sensor. Note that correlation between q and l may


0 20 40 60 80 100 120 140 1600

0.02

0.04

0.06

0.08

0.1

0.12

Scores

Like

lihoo

d

Genuine−Biometrika Spoof−BiometrikaImpostor−BiometrikaGenuine−ItaldataSpoof−ItaldataImpostor−Italdata

Biometrika Italdata20

30

40

50

60

70

80

Sensors

Qu

alit

y

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Liveness measure

Lik

elih

oo

d

BiometrikaItaldata

Fig. 2: Score distribution, boxplot of quality and likelihood of liveness measures for fingerprint images from the Biometrikaand Italdata sensors. It can be seen that scores, quality and liveness measures are sensor dependent.

(a) Live samples

(b) Fake samples

Fig. 3: Quality (IQF ) and liveness measure (LM) of live aswell as fake fingerprint samples of a subject acquired usingBiometrika and Italdata sensors.

vary depending upon the dataset and the choice of livenessand quality measurement algorithms. In such cases, modelC may derive further advantage on establishing correlationbetween the two variables. These figures validate the first twoconjectures for the graphical model C. Next, we tested thefeasibility of estimating the posterior probability of sensorsgiven quality measures, P (d|q) (see (5)). In our context, thisclassifier was built from the density p(q|d) using the Bayesrule (see (6)). Equal error rate of the classifier (6) in inferringthe actual sensor identity is 8.4% and 5.4% for Biometrika andItaldata sensors, respectively. This suggests the effectivenessof quality (q) values in inferring the actual sensor identity,

20 25 30 35 40 45 50 55 60 650.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Quality

Liv

enes

s m

easu

res

Fig. 4: Scatter plot between liveness measure and quality ofthe fingerprint samples acquired using the Biometrika sensor.It can be seen that no significant correlation (ρ = 0.25) existsbetween the two variables.

TABLE II: SFAR, IFAR and O-EER of model B and modelC for the Biometrika and Italdata sensors. In all cases, thedecision threshold has been set at the O-EER point.

Model SFAR[%] IFAR[%] O-EER[%]Model-C Both-Bio 12.99 1.47 7.39Model-B Both-Bio 15.96 5.95 11.10Model-C Both-Ital 14.88 5.80 10.46Model-B Both-Ital 25.30 1.60 13.61

therefore reinforcing the influence of the sensor on imagequality.

3) Assessment of model C in a multi-sensor environment:In this section, we evaluate the performance of model C.Comparative assessment has been made with model B whentrained using information from both the sensors and testedusing each sensor individually. In comparison to model C,


Fig. 5: ROC Curves for the performance of model C underoperation with Biometrika and Italdata sensors. Comparativeassessment is made with model B when trained using imagesfrom both the sensors.

model B does not take into account sensor information whenusing training data from multiple sensors. Further, model Bdoes not infer the sensor identity during the testing stage.

Figure 5 shows the performance of model B and C (whentrained using data from both the sensors) for the Biometrikaand Italdata sensors. O-EER of model C operating withBiometrika (legend “Model-C Both-Bio”) and Italdata sensors(legend “Model-C Both-Ital”) is evaluated to be 7.39% and10.46%, respectively. Further, model B when trained usinginformation from both the sensors and tested on images fromBiometrika (legend “Model-B Both-Bio”) and Italdata sensors(legend “Model-B Both-Ital”) resulted in a performance degra-dation of 33.4% and 23.14%, respectively, with respect to thatof model C. This shows the advantage of Model C over ModelB.

Further, Figure 5 and Figure 1 indicate that the O-EER ofmodel C (legend “Model-C Both-Bio” and “Model-C Both-Ital”, Figure 5) is equivalent to the O-EER of model Btrained and tested using the same sensor (legend “Model-BBio-Bio” and “Model-B Ital-Ital”, Figure 1). For instance,the O-EER of model B trained and tested using Biometrikasensor (legend “Model-B Bio-Bio” in Figure 1) is 7.25% andthat of model C tested using Biometrika (legend “Model-CBoth-Bio” in Figure 5) is 7.39%. These observations conveythe effectiveness of model C in facilitating operation usingmulti-sensors during the deployment stage. In Table II, wetabulate SFAR, IFAR and O-EER of model B and modelC, when the decision threshold is defined by the O-EERpoint. It can be seen that “Model-C Both-Bio” and “Model-CBoth-Ital” obtain reduced SFAR, IFAR and O-EER over“Model-B Both-Bio” and “Model-B Both-Ital”, respectively.

V. CONCLUSION

Recent studies have addressed the security of fingerprintverification systems by combining match scores with qual-ity values and liveness measures in a learning-based fusionframework. We advance the state of the art by modelingsensor influence on these variables. This is realized througha graphical model that accounts for the impact of the sensoron match scores, quality and liveness measures. Experimentalinvestigations on the LivDet11 fingerprint database indicatethat a) existing learning-based fusion framework cannot op-erate effectively in a multi-sensor scenario, and b) the pro-posed graphical model can effectively operate in a multi-sensor environment with performance quite comparable to afusion framework that is trained and tested using images fromthe same sensor. The effectiveness of the proposed modelcan be further enhanced by improving the sensitivity of theunderlying liveness measure and incorporating user-specificscore characteristics for spoof attacks [13].

ACKNOWLEDGMENT

Ross was supported by US NSF CAREER Award # IIS0642554. Poh was partially supported by Biometrics Evalua-tion and Testing (BEAT), an EU FP7 project with grant no.284989.

REFERENCES

[1] T. Matsumoto, H. Matsumoto, K. Yamada, and S. Hoshino, “Impact ofartificial “gummy” fingers on fingerprint systems,” in Proc. of SPIE Opt.Sec. Counterfeit Deterrence Tech. IV, 2002, pp. 275–289.

[2] A. Abhyankar and S. Schuckers, “Fingerprint liveness detection usinglocal ridge frequencies and multiresolution texture analysis techniques,”in Proc. of IEEE Intl. Conf. on Image Processing, Georgia, USA, 2006,pp. 321–324.

[3] S. Nikam and S. Aggarwal, “Local binary pattern and wavelet-basedspoof fingerprint detection,” Intl. Journal of Biometrics, vol. 1, no. 2,pp. 141–159, 2008.

[4] E. Marasco, Y. Ding, and A. Ross, “Combining match scores withliveness values in a fingerprint verification system,” in Proc. of IEEEIntl. Conf. on Biometrics: Theory, Applications and Systems (BTAS),Washington, USA, 2012, pp. 1–8.

[5] I. Chingovska, A. Anjos, and S. Marcel, “Anti-spoofing in action: jointoperation with a verification system,” in Proc. of IEEE Intl. Workshopon Biometrics (CVPRW), USA, 2013, pp. 1–8.

[6] A. Rattani and N. Poh, “Biometric system design under zero and non-zero effort attacks,” in Proc. of Intl. Conf. on Biometrics (ICB), Madrid,Spain, 2013.

[7] A. Ross, K. Nandakumar, and A. K. Jain, Handbook of Multibiometrics.Springer Verlag, 2006.

[8] A. Ross and A. K. Jain, “Biometric sensor interoperability: A casestudy in fingerprints,” in Proc. of Intl. ECCV Workshop on BiometricAuthentication (BioAW), Prague, Czech Republic, 2004, pp. 134–145.

[9] F. Jensen, An Introduction to Bayesian Networks. Springer, 1996.[10] N. Poh, J. Kittler, and T. Bourlai, “Quality-based score normalization

with device qualitative information for multimodal biometric fusion,”IEEE Transactions on Systems, Man, and Cybernetics, Part A, vol. 40,no. 3, pp. 539–554, 2010.

[11] M. Figueiredo and A. Jain, “Unsupervised learning on finite mixturemodels,” IEEE Trans. on Pattern Analysis and Machine Intelligence,vol. 24, 2002.

[12] D. Yambay, L. Ghiani, P. Denti, G. L. Marcialis, F. Roli, and S. Schuck-ers, “Livdet2011 - fingerprint liveness detection competition,” in Proc.of 5th Intl. Conf. on Biometrics (ICB), Delhi, India, 2012, pp. 208–215.

[13] A. Rattani, N. Poh, and A. Ross, “Analysis of user-specific scorecharacteristics for spoof biometric attacks,” in Proc. of IEEE ComputerSociety Conf. on Computer Vision and Pattern Recognition Workshops(CVPRW), Providence, USA, 2012, pp. 124–129.


appeared in proc. of ieee international workshop on information...

Documents