- Email: [email protected]
A supervised method to discriminate between impostors and genuine in biometry
Expert Systems with Applications 36 (2009) 10401–10407
Contents lists available at ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
A supervised method to discriminate between impostors and genuine in biometry Loris Nanni *, Alessandra Lumini DEIS, University of Bologna, via Venezia 52, 47023 Cesena, Italy
a r t i c l e
i n f o
Keywords: Score normalisation Supervised classification Unconstrained cohort normalisation Biometric identification
a b s t r a c t In this paper, we describe a supervised technique that allows to develop a more robust biometric system with respect to those based directly on the similarities of the biometric matchers or on the similarities normalised by the unconstrained cohort normalisation. In order to discriminate between genuine and impostors a quadratic discriminant classifier is trained using four features: the similarities of the biometric matcher; the similarities of the biometric matcher after the unconstrained cohort normalisation (UCN); the average scores among the test pattern and the users that belong to the background model; the difference between the user-specific threshold and the user-independent threshold. The proposed technique is validated by extensive experiments carried out on several biometric datasets (palm, finger, 2D and 3D faces, and ear). The experimental results demonstrate that the capabilities provided by our supervised method can significantly improve the performance of a standard biometric matcher or the performance of the standard UCN. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction One of the important problems in biometrics (Jain, Ross, & Prabhakar, 2004) is the score normalisation. The concept of score normalisation was originally introduced for the speaker recognition, due to the fact that the statistical speaker matchers provide the verification score as the probability of the observed test utterance x, given the target model k (Ariyaeeinia, Sivakumaran, Pawlewski, & Loomes, 1999; Fortuna, Sivakumaran, Ariyaeeinia, & Malegaonkar, 2004). In the literature (Alsaade, Ariyaeeinia, Malegaonkar, Pawlewski, & Pillay, 2007) it is shown that score normalisation can improve the performance of other biometric matchers, and in particular the unconstrained cohort normalisation (UCN) can be very useful to separate the genuine scores from the impostors scores. The application of UCN can improve the biometrics performance since, if an adequately large set of background models is available, an impostor targeting a particular client model is likely to match some of the background models more strongly (Alsaade et al., 2007). Moreover, it has been shown (Ariyaeeinia et al., 1999) that the UCN approach works effectively regardless of whether the operating framework is probabilistic or non-probabilistic. To the best of our knowledge the UCN was applied only in speaker recognition and face recognition (Alsaade et al., 2007). In this paper we extend the application of UCN to four different biometric characteristics: palm, finger, face (both 2D and 3D) and ear,
discovering that UCN gives a considerable advantage in distinguishing genuine users from impostors only in some of the tested biometrics. In particular our results demonstrate that UCN is well suited for ear recognition, while it is not suited for palm and finger recognition. Moreover, in this paper we propose a supervised method to discriminate between impostors and genuine users based on a quadratic discriminant classifier trained using the following four features: the similarities of the biometric matcher; the similarities of the biometric matcher after the unconstrained cohort normalisation (UCN); the average score among the test pattern and the users that belong to the background model; the difference between the user-specific threshold and the user-independent threshold. Our tests, carried out on five well-known biometric benchmarks show that our supervised method improves not only the performance obtained using the scores provided by a biometric matcher but also the performance obtained using standard UCN. The validity of our approach is demonstrated considering many different indicators (EER, EUC, DET-curve and ROC curve) at the state-ofthe-art of biometric performance evaluation. The paper is organised as follows: in Section 2 the new supervised technique for biometric verification is explained, in Section 3 the experimental results are presented and commented. Finally, in Section 4 some concluding remarks are given. 2. System description
* Corresponding author. E-mail addresses: [email protected] (L. Nanni), [email protected] (A. Lumini). 0957-4174/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2009.01.037
In this section, we describe a novel supervised technique that permits to better discriminate between impostors and genuine
10402
L. Nanni, A. Lumini / Expert Systems with Applications 36 (2009) 10401–10407
users, with respect to a system directly based on the similarities of the biometric matcher or on the similarities normalised by the unconstrained cohort normalisation. First the features extracted for the simple biometric matcher are described, which are the same for all the tested datasets, then the matcher adopted for the classification task is detailed. The biometric features are extracted from the grey-level image, by applying the LaplacianFaces approach (He, Yan, Hu, Niyogi, & Zhang, 2005). LaplacianFaces is a reliable system proposed for face recognition based on the combination of principal component analysis (PCA) and Laplacian EigenMaps (LEM)1: PCA is applied to the grey-level image to project the data onto a 100-dimensional subspace before the application of LEM as a feature transformation. LEM is a geometrically motivated algorithm for representing high-dimensional data which provides a computationally efficient approach to nonlinear dimensionality transformation that has locality-preserving properties and a natural connection to clustering. The pure biometric score is obtained from the 100-dimensional feature vector by means of a Parzen window classifier (PWC) Duda, Hart, & Stork, 2000, as described below. 2.1. Classification task The classification between the two classes ‘‘genuine” and ‘‘impostor” is performed by a quadratic discriminant classifier trained by the four features described below. The quadratic discriminant classifier2 (QDC) assumes that the classes are normally distributed, with class-specific covariance matrices. The estimates of the parameters (the mean vector and the covariance matrix for each class) are calculated from the training data. For the mathematical description of QDC see (Duda et al., 2000, pp. 46–47). The first feature is the score obtained by the biometric matcher. As biometric matcher we use the Parzen window classifier (PWC) Duda et al., 2000. PWC is a one-class classifier, which is well suited for biometric verification because using a one-class classifier we can build a classifier for each user without any knowledge of the others individuals (Nanni, 2006). Given a set of n d-dimensional samples D = {x1, x2,. . ., xn} belonging to C classes (i.e., users), it is possible, given the feature vector x of an input pattern and a claimed identity c, to estimate of the conditional pdf p(x|c) of each user c using the Parzen window method as:
pðxkcÞ ¼
X
1 /ðx xi ; hÞ #Dc x Dc i
where Dc is the set of samples belonging to the user c and #Dc represents its cardinality; u(,) is the window function and h is the window width parameter (see Duda et al., 2000 for more details). In this work we have used the standard Gaussian as window function and set h = 1000. The second feature is the score obtained by the biometric matcher normalised by UCN. In UCN the probability function p(x) for the feature vector x is given by the sum of its conditional probabilities for each user of a set of background models B:
pB ðxÞ ¼
X
In Fig. 1 the scheme of the UCN is reported. We obtain good results (reported in Section 3) without considering the log domain.The third feature is the average score among the test pattern x and the users that belong to the background models:
AVGðxÞ ¼
1 X pðxjbÞ: B b¼1...B
The fourth feature is the difference between the user-specific threshold and the user-independent threshold. In a verification system, using user-independent thresholds some users will be more systematically subjected to false rejects than others (Richiardi & Drygajlo, 2007). For this reason this feature can be useful to discriminate between genuine and impostors. The user-independent threshold is calculated as the threshold at the equal error rate (EER) point of the users that belong to the background models. The user-specific threshold of user c is calculated as the threshold at the equal error rate (EER) point for the following set of matches: – the genuine matches are obtained using a leave-one-out on the images that belong to the user c, – the impostor matches are obtained matching the users that belong to the background models to the training model of the user i. Of course in order to have the genuine matches, at least two samples per users are needed both for the claimed identities and the users of the background models. The EER (Fig. 2) is a biometric indicator that measures the error rate where the frequency of fraudulent accesses (FAR) and the frequency of rejections of people who should be correctly verified (FRR) assume the same value (Maltoni, Maio, Jain, & Prabhakar, 2003).
⎛ ⎞ Normalized Score = log(p (x | c) )− log⎜ ∑ p (x | b) ⎟ ⎝ b =1... B ⎠
Target Model
BackGround Models
λc
λ1
λB
Test Pattern Fig. 1. UCN of scores: kc represent the model of the claimed users and k1. . .kB form the background models.
pðxjbÞ
b¼1...B
where p(x|b), b = 1,. . .,B, are the probabilities obtained for the pattern, using a set of B background models. The normalised score of a pattern x and a claimed identity c is given, in the log domain, by:
UCNðxjcÞ ¼ logðpðxjcÞÞ logðpB ðxÞÞ 1
Matlab code shared by Mikhail Belkin and Partha Niyogi. QDC is implemented as in PRTools 3.1.7 Matlab Toolbox, regularization parameter r = 0.1.
…
2
Fig. 2. Plot FAR/FRR.
L. Nanni, A. Lumini / Expert Systems with Applications 36 (2009) 10401–10407
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Fig. 3. Samples from the palm dataset.
Fig. 4. Samples from the finger dataset.
3. Experiments For the performance evaluation we adopt the equal error rate (EER) Maio & Nanni, 2006, the receiver operating characteristic (ROC) curve Fawcett (2004), the DET-curve and the error under the ROC curve (EUC)3 (Huang & Dai, 2005). The ROC curve is a 2D measure of classification performance that plots the probability of classifying correctly the positive examples against the rate of incorrectly classifying negative examples. The EUC is a scalar measure to evaluate performance which can be interpreted as the probability that the classifier will assign a lower score to a randomly picked genuine sample than to a randomly picked impostor sample. The DETcurve (Martin, 1997) is a 2D measure of classification performance that plots the probability of false acceptation against the probability of false rejection. 3.1. Dataset description The proposed approach has been tested in four different datasets: palm; finger; face-2D; face-3D; ear database. Palm dataset: it contains 700 right-hand images, seven samples from each user for 100 users, acquired by a digital Camera. The palm is extracted using a method similar to that proposed in Connie, Jin, Ong, and Ling (2005), then the images are resized to the same dimension of 100 100 pixels and pre-processed by the technique used in Connie et al. (2005). Fig. 3 shows some extracted palms from the dataset. For a good review of the palm verification methods please read (Ribaric & Fratric, 2005). In our experiments we have included four randomly selected samples per user in the training set and the remaining three in the test set. Finger dataset: it contains the middle-fingers extracted from the same hand images used for the palm dataset, thus it is composed by seven samples per user, for 100 users. The middle-finger is extracted using the datum points (Connie et al., 2005), then the images are resized to the same dimension of 75 125 pixels and
Fig. 5. 2D face and its corresponding 3D face (depth information) from the face dataset.
pre-processed by contrast-limited adaptive histogram equalisation4 (Zuiderveld, 1990) and the method proposed in Li, Qiu, Sun, and Wu (2004). Fig. 4 shows some fingers from the dataset. The division among training set and test set is performed as in the palm dataset. Face datasets: the tests on face-2D and face-3D have been conducted on a subset of the Notre-Dame dataset5 collection D (http://www.nd.edu/~cvrl/). From the total of 275 persons included we consider the 198 individuals that has two or more sessions of usable 2D and 3D data; the total number of samples is 953. For more details on the acquisition of the datasets please read (Chang, Bowyer, & Flynn, 2005). From the 3D dataset we consider the solely depth information (i.e., a 2D representation of the z-axes). Fig. 5 shows an example of 2D face and its corresponding 3D face (depth information). Both the 2D and 3D face images are cropped starting from the given eye position, then they are resized to the same dimension of 100 90. The training set is built randomly extracting half of the samples per user, the remaining samples build the test set. Ear dataset: it consists of 464 ears acquired at the University of Notre-Dame in Fall 2002 (Chang, Bowyer, Sarkar, & Victor, 2003). 4
3
Implemented as in DDtool 0.95 Matlab Toolbox.
5
Implemented as in adapthisteq.m of the Matlab 7.0 Image Processing Toolbox. http://www.nd.edu/~cvrl/.
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Fig. 6. Samples from the ear dataset.
Table 1 Results in terms of EER and EUC on the five datasets. Methods
BIO
UCN
NEW
Palm
EER EUC
4.4 0.0187
4.75 0.0282
4.02 0.0162
Finger
EER EUC
3.01 0.0065
3.5 0.0104
3.01 0.0065
Face-2D
EER EUC
13.3 0.054
10.6 0.043
10.3 0.041
Face-3D
EER EUC
28.5 0.21
26.5 0.185
23.6 0.17
Ear
EER EUC
11.6 0.0588
7.6 0.0464
7.6 0.0403
The images are obtained from 114 users, on different days, with different conditions of pose and lighting, and consist in a set of 3–9 samples per user. Fig. 6 shows some samples from the dataset. The interested reader can see (Hurley, Arbab-Zavar, & Nixon, 2007) for a good review of ear recognition. The images are processed and extracted as in Nanni and Lumini (2007). The training set is built
randomly extracting half of the samples per user, the remaining samples build the test set. 3.2. Testing protocol In the following we explain our procedure to build the training set, the validation set and the testing set. The 50% of the users of each dataset are used to build the validation set and to generate the background models. From the remaining users a training set and a test set for the simple biometric matcher (i.e., the PWC classifier) are extracted as detailed above. Finally, in order to train the global matcher (i.e., the QDC classifier), a leave-one-out-person cross-validation is performed on the users not belonging to the validation set. In the ith step of the cross-validation, all the matches where at least one of the two images belongs to the individual i are treated as test set for QDC, all the other matches are used to train QDC. We perform 100 experiments, each time re-sampling the validation, the training and the test sets: we report the average results obtained in these experiments.
Fig. 7. DET-curve (left) and ROC curve (right) on the palm dataset.
L. Nanni, A. Lumini / Expert Systems with Applications 36 (2009) 10401–10407
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Fig. 8. DET-curve (left) and ROC curve (right) on the finger dataset.
Fig. 9. DET-curve (left) and ROC curve (right) on the face-2D dataset.
3.3. Experimental results
BIO: the verification is performed using the scores obtained by the simple biometric matcher (i.e., PWC); UCN: the scores of PWC are normalised by UCN; NEW: our novel supervised method based on the QDC classifier.
NEW, hence all the results are directly comparable (they have been obtained considering the same number of genuine and impostor matches). In Table 1 the performance of the three methods on the five datasets are reported in terms of both EER and EUC. Figs. 7–11 report the DET and the ROC curves of BIO (the black line), UCN (the green line) and NEW (the red line).6 From all the reported results it is clear the good behaviour of the proposed method NEW. In particular the following considerations may be drawn:
All the results reported for BIO and UCN are obtained using the same leave-one-out-person cross-validation protocol used for
6 For interpretation of color in Figs. 7–11, the reader is referred to the web version of this article.
The results reported in this subsection are aimed to compare several verification methods. In particular we test the following methods:
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L. Nanni, A. Lumini / Expert Systems with Applications 36 (2009) 10401–10407
Fig. 10. DET-curve (left) and ROC curve (right) on the face-3D dataset.
Fig. 11. DET-curve (left) and ROC curve (right) on the ear dataset.
Our supervised method has performance better or equal than UCN and BIO in all the datasets. UCN outperforms BIO in several but not all the datasets. In the finger dataset the UCN normalisation is not useful; the performance obtained by UCN is worse than that obtained by BIO. In our opinion, this can be probably explained by the fact that when the biometric feature is good (i.e., very discriminant) the number of background models needs to be larger in order to be useful to discover an impostor.
4. Conclusions In this paper, we investigated a supervised technique to discriminate between impostors and genuine users in biometry.
The experimental results obtained on five different datasets are encouraging: our method (NEW) improves the performance (EER and EUC) of the approaches directly based on the similarities of the biometric matchers (BIO) or on the similarities normalised by the unconstrained cohort normalisation (UCN). In particular the choice of a supervised classifier trained by a set of four features, including the biometric and the UCN scores, have proven to be useful to improve the performance of the basic UCN normalisation procedure also in the biometric characteristics where UCN does not work well. The main drawback of UCN is that it needs a quite large number of background models to improve the performance of the simple biometric matcher. Our method works well also in presence of a small number of background models, but it also needs a further training set to train the classifier.
L. Nanni, A. Lumini / Expert Systems with Applications 36 (2009) 10401–10407
Anyway, in our opinion, the need of a large dataset is not a significant drawback, since nowadays several datasets are available that contain more than 100 of users. Acknowledgment This work has been supported by European Commission IST2002-507634 Biosecure NoE projects. References Alsaade, F., Ariyaeeinia, A. M., Malegaonkar, A. S., Pawlewski, M., & Pillay, S. G. (2007). Enhancement of multimodal biometric segregation using unconstrained cohort normalisation. Pattern Recognition. doi:10.1016/j.patcog.2007.06.028. Ariyaeeinia, A. M., Sivakumaran, P., Pawlewski, M., & Loomes, M. J. (1999). Dynamic weighting of the distortion sequence in text-dependent speaker verification. In Eurospeech’ 99, pp. 967–970. Chang, Kyong I., Bowyer, Kevin W., & Flynn, Patrick J. (2005). An evaluation of multimodal 2D + 3D face biometrics. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(4), 619–624. Chang, K. C., Bowyer, K. W., Sarkar, S., & Victor, B. (2003). Comparison and combination of ear and face images in appearance-based biometrics. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25, 1160–1165. Connie, T., Jin, A. T. B., Ong, M. G. K., & Ling, D. N. C. (2005). An automated palmprint recognition system. Image and Vision Computing, 23, 501–515. Duda, R. O., Hart, P. E., & Stork, D. G. (2000). Pattern classification (2nd ed.). New York: Wiley. Fawcett, T. (2004). ROC graphs: Notes and practical considerations for researchers. Technical report, Palo Alto, USA: HP Laboratories.
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Fortuna, J., Sivakumaran, P., Ariyaeeinia, A., & Malegaonkar, A. (2004). Relative effectiveness of score normalization methods in open-set speaker identification. In Proceedings of the speaker odyssey (pp. 369–376). He, X., Yan, S., Hu, Y., Niyogi, P., & Zhang, H.-J. (2005). Face recognition using Laplacianfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(3), 328–340. Huang, L., & Dai, Y. (2005). A support vector machine approach for prediction of T cell epitopes. In Proceedings of the third Asia-Pacific bioinformatics conference (APBC2005) (pp. 312–328), Singapore, January 17–21. Hurley, D. J., Arbab-Zavar, B., & Nixon, M. S. (2007). The ear as a biometric. In EUSIPCO 2007, Poznan, Poland. Jain, A. K., Ross, A., & Prabhakar, S. (2004). An introduction to biometric recognition. In IEEE transactions circuits and systems for video technology (Vol. 14, pp. 4–19). Li, Q., Qiu, Z., Sun, D., & Wu, J. (2004). Personal identification using knuckleprint. Sinobiometrics, 680–689. Maio, D., & Nanni, L. (2006). Combination of different fingerprint systems: A case study FVC2004. Sensor Review, 26(1), 51–57. Maltoni, D., Maio, D., Jain, A. K., & Prabhakar, S. (2003). Handbook of fingerprint recognition. Springer. Martin, A. et al. (1997). The DET curve in assessment of decision task performance. In Proceedings of the EuroSpeech (pp. 1895–1898). Nanni, L. (2006). Experimental comparison of one-class classifiers for on-line signature verification. Neurocomputing, 69(7–9), 869–873. Nanni, L., & Lumini, A. (2007). RegionBoost learning for 2D + 3D based face recognition. Pattern Recognition Letters, 15(28), 2063–2070. Ribaric, S., & Fratric, I. (2005). A biometric identification system based on eigenpalm and eigenfinger features. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(11), 1698–1709. Richiardi, J., & Drygajlo, A. (2007). Reliability-based voting schemes using modalityindependent features in multi-classifier biometric authentication. In M. Haindl, J. Kittler, & F. Roli (Eds.), MCS 2007, LNCS 4472 (pp. 377–386). Zuiderveld, K. (1990). Contrast limited adaptive histogram equalization. Graphics Gems IV, 474–485.
Contents lists available at ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
A supervised method to discriminate between impostors and genuine in biometry Loris Nanni *, Alessandra Lumini DEIS, University of Bologna, via Venezia 52, 47023 Cesena, Italy
a r t i c l e
i n f o
Keywords: Score normalisation Supervised classification Unconstrained cohort normalisation Biometric identification
a b s t r a c t In this paper, we describe a supervised technique that allows to develop a more robust biometric system with respect to those based directly on the similarities of the biometric matchers or on the similarities normalised by the unconstrained cohort normalisation. In order to discriminate between genuine and impostors a quadratic discriminant classifier is trained using four features: the similarities of the biometric matcher; the similarities of the biometric matcher after the unconstrained cohort normalisation (UCN); the average scores among the test pattern and the users that belong to the background model; the difference between the user-specific threshold and the user-independent threshold. The proposed technique is validated by extensive experiments carried out on several biometric datasets (palm, finger, 2D and 3D faces, and ear). The experimental results demonstrate that the capabilities provided by our supervised method can significantly improve the performance of a standard biometric matcher or the performance of the standard UCN. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction One of the important problems in biometrics (Jain, Ross, & Prabhakar, 2004) is the score normalisation. The concept of score normalisation was originally introduced for the speaker recognition, due to the fact that the statistical speaker matchers provide the verification score as the probability of the observed test utterance x, given the target model k (Ariyaeeinia, Sivakumaran, Pawlewski, & Loomes, 1999; Fortuna, Sivakumaran, Ariyaeeinia, & Malegaonkar, 2004). In the literature (Alsaade, Ariyaeeinia, Malegaonkar, Pawlewski, & Pillay, 2007) it is shown that score normalisation can improve the performance of other biometric matchers, and in particular the unconstrained cohort normalisation (UCN) can be very useful to separate the genuine scores from the impostors scores. The application of UCN can improve the biometrics performance since, if an adequately large set of background models is available, an impostor targeting a particular client model is likely to match some of the background models more strongly (Alsaade et al., 2007). Moreover, it has been shown (Ariyaeeinia et al., 1999) that the UCN approach works effectively regardless of whether the operating framework is probabilistic or non-probabilistic. To the best of our knowledge the UCN was applied only in speaker recognition and face recognition (Alsaade et al., 2007). In this paper we extend the application of UCN to four different biometric characteristics: palm, finger, face (both 2D and 3D) and ear,
discovering that UCN gives a considerable advantage in distinguishing genuine users from impostors only in some of the tested biometrics. In particular our results demonstrate that UCN is well suited for ear recognition, while it is not suited for palm and finger recognition. Moreover, in this paper we propose a supervised method to discriminate between impostors and genuine users based on a quadratic discriminant classifier trained using the following four features: the similarities of the biometric matcher; the similarities of the biometric matcher after the unconstrained cohort normalisation (UCN); the average score among the test pattern and the users that belong to the background model; the difference between the user-specific threshold and the user-independent threshold. Our tests, carried out on five well-known biometric benchmarks show that our supervised method improves not only the performance obtained using the scores provided by a biometric matcher but also the performance obtained using standard UCN. The validity of our approach is demonstrated considering many different indicators (EER, EUC, DET-curve and ROC curve) at the state-ofthe-art of biometric performance evaluation. The paper is organised as follows: in Section 2 the new supervised technique for biometric verification is explained, in Section 3 the experimental results are presented and commented. Finally, in Section 4 some concluding remarks are given. 2. System description
* Corresponding author. E-mail addresses: [email protected] (L. Nanni), [email protected] (A. Lumini). 0957-4174/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2009.01.037
In this section, we describe a novel supervised technique that permits to better discriminate between impostors and genuine
10402
L. Nanni, A. Lumini / Expert Systems with Applications 36 (2009) 10401–10407
users, with respect to a system directly based on the similarities of the biometric matcher or on the similarities normalised by the unconstrained cohort normalisation. First the features extracted for the simple biometric matcher are described, which are the same for all the tested datasets, then the matcher adopted for the classification task is detailed. The biometric features are extracted from the grey-level image, by applying the LaplacianFaces approach (He, Yan, Hu, Niyogi, & Zhang, 2005). LaplacianFaces is a reliable system proposed for face recognition based on the combination of principal component analysis (PCA) and Laplacian EigenMaps (LEM)1: PCA is applied to the grey-level image to project the data onto a 100-dimensional subspace before the application of LEM as a feature transformation. LEM is a geometrically motivated algorithm for representing high-dimensional data which provides a computationally efficient approach to nonlinear dimensionality transformation that has locality-preserving properties and a natural connection to clustering. The pure biometric score is obtained from the 100-dimensional feature vector by means of a Parzen window classifier (PWC) Duda, Hart, & Stork, 2000, as described below. 2.1. Classification task The classification between the two classes ‘‘genuine” and ‘‘impostor” is performed by a quadratic discriminant classifier trained by the four features described below. The quadratic discriminant classifier2 (QDC) assumes that the classes are normally distributed, with class-specific covariance matrices. The estimates of the parameters (the mean vector and the covariance matrix for each class) are calculated from the training data. For the mathematical description of QDC see (Duda et al., 2000, pp. 46–47). The first feature is the score obtained by the biometric matcher. As biometric matcher we use the Parzen window classifier (PWC) Duda et al., 2000. PWC is a one-class classifier, which is well suited for biometric verification because using a one-class classifier we can build a classifier for each user without any knowledge of the others individuals (Nanni, 2006). Given a set of n d-dimensional samples D = {x1, x2,. . ., xn} belonging to C classes (i.e., users), it is possible, given the feature vector x of an input pattern and a claimed identity c, to estimate of the conditional pdf p(x|c) of each user c using the Parzen window method as:
pðxkcÞ ¼
X
1 /ðx xi ; hÞ #Dc x Dc i
where Dc is the set of samples belonging to the user c and #Dc represents its cardinality; u(,) is the window function and h is the window width parameter (see Duda et al., 2000 for more details). In this work we have used the standard Gaussian as window function and set h = 1000. The second feature is the score obtained by the biometric matcher normalised by UCN. In UCN the probability function p(x) for the feature vector x is given by the sum of its conditional probabilities for each user of a set of background models B:
pB ðxÞ ¼
X
In Fig. 1 the scheme of the UCN is reported. We obtain good results (reported in Section 3) without considering the log domain.The third feature is the average score among the test pattern x and the users that belong to the background models:
AVGðxÞ ¼
1 X pðxjbÞ: B b¼1...B
The fourth feature is the difference between the user-specific threshold and the user-independent threshold. In a verification system, using user-independent thresholds some users will be more systematically subjected to false rejects than others (Richiardi & Drygajlo, 2007). For this reason this feature can be useful to discriminate between genuine and impostors. The user-independent threshold is calculated as the threshold at the equal error rate (EER) point of the users that belong to the background models. The user-specific threshold of user c is calculated as the threshold at the equal error rate (EER) point for the following set of matches: – the genuine matches are obtained using a leave-one-out on the images that belong to the user c, – the impostor matches are obtained matching the users that belong to the background models to the training model of the user i. Of course in order to have the genuine matches, at least two samples per users are needed both for the claimed identities and the users of the background models. The EER (Fig. 2) is a biometric indicator that measures the error rate where the frequency of fraudulent accesses (FAR) and the frequency of rejections of people who should be correctly verified (FRR) assume the same value (Maltoni, Maio, Jain, & Prabhakar, 2003).
⎛ ⎞ Normalized Score = log(p (x | c) )− log⎜ ∑ p (x | b) ⎟ ⎝ b =1... B ⎠
Target Model
BackGround Models
λc
λ1
λB
Test Pattern Fig. 1. UCN of scores: kc represent the model of the claimed users and k1. . .kB form the background models.
pðxjbÞ
b¼1...B
where p(x|b), b = 1,. . .,B, are the probabilities obtained for the pattern, using a set of B background models. The normalised score of a pattern x and a claimed identity c is given, in the log domain, by:
UCNðxjcÞ ¼ logðpðxjcÞÞ logðpB ðxÞÞ 1
Matlab code shared by Mikhail Belkin and Partha Niyogi. QDC is implemented as in PRTools 3.1.7 Matlab Toolbox, regularization parameter r = 0.1.
…
2
Fig. 2. Plot FAR/FRR.
L. Nanni, A. Lumini / Expert Systems with Applications 36 (2009) 10401–10407
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Fig. 3. Samples from the palm dataset.
Fig. 4. Samples from the finger dataset.
3. Experiments For the performance evaluation we adopt the equal error rate (EER) Maio & Nanni, 2006, the receiver operating characteristic (ROC) curve Fawcett (2004), the DET-curve and the error under the ROC curve (EUC)3 (Huang & Dai, 2005). The ROC curve is a 2D measure of classification performance that plots the probability of classifying correctly the positive examples against the rate of incorrectly classifying negative examples. The EUC is a scalar measure to evaluate performance which can be interpreted as the probability that the classifier will assign a lower score to a randomly picked genuine sample than to a randomly picked impostor sample. The DETcurve (Martin, 1997) is a 2D measure of classification performance that plots the probability of false acceptation against the probability of false rejection. 3.1. Dataset description The proposed approach has been tested in four different datasets: palm; finger; face-2D; face-3D; ear database. Palm dataset: it contains 700 right-hand images, seven samples from each user for 100 users, acquired by a digital Camera. The palm is extracted using a method similar to that proposed in Connie, Jin, Ong, and Ling (2005), then the images are resized to the same dimension of 100 100 pixels and pre-processed by the technique used in Connie et al. (2005). Fig. 3 shows some extracted palms from the dataset. For a good review of the palm verification methods please read (Ribaric & Fratric, 2005). In our experiments we have included four randomly selected samples per user in the training set and the remaining three in the test set. Finger dataset: it contains the middle-fingers extracted from the same hand images used for the palm dataset, thus it is composed by seven samples per user, for 100 users. The middle-finger is extracted using the datum points (Connie et al., 2005), then the images are resized to the same dimension of 75 125 pixels and
Fig. 5. 2D face and its corresponding 3D face (depth information) from the face dataset.
pre-processed by contrast-limited adaptive histogram equalisation4 (Zuiderveld, 1990) and the method proposed in Li, Qiu, Sun, and Wu (2004). Fig. 4 shows some fingers from the dataset. The division among training set and test set is performed as in the palm dataset. Face datasets: the tests on face-2D and face-3D have been conducted on a subset of the Notre-Dame dataset5 collection D (http://www.nd.edu/~cvrl/). From the total of 275 persons included we consider the 198 individuals that has two or more sessions of usable 2D and 3D data; the total number of samples is 953. For more details on the acquisition of the datasets please read (Chang, Bowyer, & Flynn, 2005). From the 3D dataset we consider the solely depth information (i.e., a 2D representation of the z-axes). Fig. 5 shows an example of 2D face and its corresponding 3D face (depth information). Both the 2D and 3D face images are cropped starting from the given eye position, then they are resized to the same dimension of 100 90. The training set is built randomly extracting half of the samples per user, the remaining samples build the test set. Ear dataset: it consists of 464 ears acquired at the University of Notre-Dame in Fall 2002 (Chang, Bowyer, Sarkar, & Victor, 2003). 4
3
Implemented as in DDtool 0.95 Matlab Toolbox.
5
Implemented as in adapthisteq.m of the Matlab 7.0 Image Processing Toolbox. http://www.nd.edu/~cvrl/.
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Fig. 6. Samples from the ear dataset.
Table 1 Results in terms of EER and EUC on the five datasets. Methods
BIO
UCN
NEW
Palm
EER EUC
4.4 0.0187
4.75 0.0282
4.02 0.0162
Finger
EER EUC
3.01 0.0065
3.5 0.0104
3.01 0.0065
Face-2D
EER EUC
13.3 0.054
10.6 0.043
10.3 0.041
Face-3D
EER EUC
28.5 0.21
26.5 0.185
23.6 0.17
Ear
EER EUC
11.6 0.0588
7.6 0.0464
7.6 0.0403
The images are obtained from 114 users, on different days, with different conditions of pose and lighting, and consist in a set of 3–9 samples per user. Fig. 6 shows some samples from the dataset. The interested reader can see (Hurley, Arbab-Zavar, & Nixon, 2007) for a good review of ear recognition. The images are processed and extracted as in Nanni and Lumini (2007). The training set is built
randomly extracting half of the samples per user, the remaining samples build the test set. 3.2. Testing protocol In the following we explain our procedure to build the training set, the validation set and the testing set. The 50% of the users of each dataset are used to build the validation set and to generate the background models. From the remaining users a training set and a test set for the simple biometric matcher (i.e., the PWC classifier) are extracted as detailed above. Finally, in order to train the global matcher (i.e., the QDC classifier), a leave-one-out-person cross-validation is performed on the users not belonging to the validation set. In the ith step of the cross-validation, all the matches where at least one of the two images belongs to the individual i are treated as test set for QDC, all the other matches are used to train QDC. We perform 100 experiments, each time re-sampling the validation, the training and the test sets: we report the average results obtained in these experiments.
Fig. 7. DET-curve (left) and ROC curve (right) on the palm dataset.
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Fig. 8. DET-curve (left) and ROC curve (right) on the finger dataset.
Fig. 9. DET-curve (left) and ROC curve (right) on the face-2D dataset.
3.3. Experimental results
BIO: the verification is performed using the scores obtained by the simple biometric matcher (i.e., PWC); UCN: the scores of PWC are normalised by UCN; NEW: our novel supervised method based on the QDC classifier.
NEW, hence all the results are directly comparable (they have been obtained considering the same number of genuine and impostor matches). In Table 1 the performance of the three methods on the five datasets are reported in terms of both EER and EUC. Figs. 7–11 report the DET and the ROC curves of BIO (the black line), UCN (the green line) and NEW (the red line).6 From all the reported results it is clear the good behaviour of the proposed method NEW. In particular the following considerations may be drawn:
All the results reported for BIO and UCN are obtained using the same leave-one-out-person cross-validation protocol used for
6 For interpretation of color in Figs. 7–11, the reader is referred to the web version of this article.
The results reported in this subsection are aimed to compare several verification methods. In particular we test the following methods:
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Fig. 10. DET-curve (left) and ROC curve (right) on the face-3D dataset.
Fig. 11. DET-curve (left) and ROC curve (right) on the ear dataset.
Our supervised method has performance better or equal than UCN and BIO in all the datasets. UCN outperforms BIO in several but not all the datasets. In the finger dataset the UCN normalisation is not useful; the performance obtained by UCN is worse than that obtained by BIO. In our opinion, this can be probably explained by the fact that when the biometric feature is good (i.e., very discriminant) the number of background models needs to be larger in order to be useful to discover an impostor.
4. Conclusions In this paper, we investigated a supervised technique to discriminate between impostors and genuine users in biometry.
The experimental results obtained on five different datasets are encouraging: our method (NEW) improves the performance (EER and EUC) of the approaches directly based on the similarities of the biometric matchers (BIO) or on the similarities normalised by the unconstrained cohort normalisation (UCN). In particular the choice of a supervised classifier trained by a set of four features, including the biometric and the UCN scores, have proven to be useful to improve the performance of the basic UCN normalisation procedure also in the biometric characteristics where UCN does not work well. The main drawback of UCN is that it needs a quite large number of background models to improve the performance of the simple biometric matcher. Our method works well also in presence of a small number of background models, but it also needs a further training set to train the classifier.
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