- Email: [email protected]
Fusion of multiple fingerprint matchers by single-layer perceptron with class-separation loss function
Pattern Recognition Letters 26 (2005) 1830–1839 www.elsevier.com/locate/patrec
Fusion of multiple fingerprint matchers by single-layer perceptron with class-separation loss function Gian Luca Marcialis *, Fabio Roli Department of Electrical and Electronic Engineering, University of Cagliari, Piazza d’Armi, 09123 Cagliari, Italy Available online 29 April 2005
Abstract In this paper, a perceptron-based algorithm for fusion of multiple fingerprint matchers is presented. The person to be identified submits to the personal authentication system her/his fingerprint and claimed identity. Multiple fingerprint matchers provide a set of verification scores, that are then fused by a single-layer perceptron with class-separation loss function. Weights of such perceptron are explicitly optimised to increase the separation between genuine users and impostors (i.e., unauthorized users). Reported experiments show that such modified perceptron allows improving the performances and the robustness of the best individual fingerprint matcher, and outperforming some commonly used fusion rules. 2005 Elsevier B.V. All rights reserved. Keywords: Automatic fingerprint verification; Fusion of multiple fingerprint matchers; Multiple classifiers systems; Neural networks; Pattern recognition
1. Introduction Fingerprints are widely used for automatic personal authentication (Jain et al., 1999a), in order to control the access to restricted areas or resources. The person to be ‘‘authenticated’’ submits to the system her/his fingerprint and identity. The system matches the input fingerprint with the one *
Corresponding author. Tel.: +39 070 675 5776; fax: +39 070 675 5782. E-mail address: [email protected] (G.L. Marcialis).
associated to the given identity and stored in its database. A degree of similarity, named ‘‘score’’, is computed. If the score is higher than a certain value (the so called ‘‘acceptance’’ threshold), the claimed identity is accepted and the person is classified as a genuine user. Otherwise, she/he is classified as an impostor and the access to the required resource is denied. The selection of the acceptance threshold is a crucial issue that strongly affects fingerprint verification performances. In order to compute the optimal threshold, accurate estimates of genuine and
0167-8655/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.patrec.2005.03.004
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
impostor users distributions are necessary. Unfortunately, available training data are often not completely representative of the target population, and, in particular, data on impostor users are very difficult to be collected. In real operational conditions (e.g., fingerprint verification for ATM applications), acquisition of realistic and representative impostor data is basically unfeasible. It is easy to see that increasing the separation between genuine and impostor classes can be very useful to address issues related to the acceptance threshold selection. If genuine and impostor classes are well separated, errors that usually affect estimates of class distributions have a smaller impact on threshold selection, and consequently, on system performances. Fig. 1 illustrates this concept. In this paper, a fusion rule explicitly aimed to maximize the separation between genuine and impostor classes is proposed. This rule is implemented by a perceptron with a ‘‘class-separation’’ loss function. Our perceptron takes as input the scores of multiple matchers and produces as output ‘‘fused’’ scores that maximize the separation between impostor and genuine users classes. Section 2 quickly provides the basic concepts used in this paper. Section 3 presents our fuser based on the perceptron with class-separation loss function. Section 4 briefly describes the individual
Estimated impostor distribution True impostor distribution
1831
fingerprint matchers used. Section 5 reports experimental results. Section 6 draws preliminary conclusions.
2. Background concepts The so called verification score ‘‘s’’ provides the degree of similarity between two fingerprint patterns, and takes values in [0, 1]. A fingerprint pattern belongs to the genuine class if the identity of her/his possessor corresponds to the claimed one. The opposite holds for the impostor class. The design of any fingerprint verification system depends on the estimate of the two posterior probabilities p(sjgenuine) and p(sjimpostor), and the selection of the acceptance threshold s*. If the score is higher than the acceptance threshold, the claimed identity is accepted and the person is classified as a genuine user. Otherwise, she/ he is classified as an impostor. Authentication errors obviously depends on the acceptance threshold. They are called ‘‘false acceptance’’ errors if an impostor is accepted, and ‘‘false rejection’’ errors if a genuine user is rejected. The probabilities of false acceptance and false rejection are called False Acceptance Rate (FAR) and False Rejection Rate (FRR):
Estimated Impostor distribution Estimated Genuine distribution
True Impostor distribution True Genuine distribution
Optimal Acceptance Threshold
Estimated Acceptance Threshold
(a)
Estimated Genuine distribution
True Genuine distribution
score
Optimal Acceptance threshold
Estimated Acceptance threshold
score
(b)
Fig. 1. Impact of errors affecting estimates of class distributions on (a) not well separated genuine and impostor classes. (b) Well separated genuine and impostor classes. It is easy to see that errors have a smaller impact on threshold selection, and consequently, on system performances for the case (b) of well separated distributions.
1832
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
FARðs Þ ¼
Z
1
pðsjimpostorÞds
ð1Þ
pðsjgenuineÞds
ð2Þ
s
FRRðs Þ ¼
Z
s 0
Usually, the acceptance threshold s* is computed in order to obtain FAR(s*) = FRR(s*). Such error value is called Equal Error Rate point (EER). For high-security systems, it is often requested to minimise FAR or FRR under some constraint on the dual performance parameter. For example, the so called 1% FAR performance measure assesses the False Rejection Rate when the False Acceptance Rate is constrained to 1%. On the contrary, 1% FRR measure assesses the FAR when FRR = 1%.
3. Fusion by single-layer perceptron with class-separation loss function 3.1. The fusion model In order to design our fusion module, we used the perceptron classifier. Let s1, . . . , sN be the matching scores provided by N individual matchers. The logistic function of perceptron produces the fused score s: s¼
1 1 þ exp ½ðw0 þ w1 s1 þ þ wN sN Þ
ð3Þ
Eq. (3) points out that the inputs of perceptron are the scores provided by the N individual matchers, and the output s is the final verification score. According to our goal, we substituted the standard loss functions of perceptron with a function explicitly aimed to maximize the statistical separation between genuine and impostor classes. It should be remarked that the use of logistic transform for fusing multiple fingerprint matchers has been previously proposed in (Jain et al., 1999b). However, the goal of Jain et al. was to estimate the parameters of the logistic transform in order to minimize FRR for a given FAR. Although these authors were aware about the increase of class separation achievable by logistic
transform (see Fig. 3 in Jain et al., 1999b), their work was not focused on this aspect, and no experimental evidence of the increase of class separation was reported. In this work, we followed Jain et al. suggestion on the possible use of logistic transform for increasing class separation. We designed a perceptron-based fusion rule that explicitly estimate the parameters of the logistic transform in order to maximize the statistical separation between genuine and impostor classes. In addition, we investigated by experiments the achievable increase of separation. Finally, it should be noted that, although loss functions based on class separation measures have been already investigated in the neural networks field (Haykin, 1999), no previous work used them in order to design a perceptron-based fusion rule aimed to maximize the separation between genuine and impostor classes. 3.1.1. The learning algorithm We used a parametric distance, called Fisher distance (FD), as measure of statistical separation between the genuine and impostor classes. The Fisher distance is the parametric version of more general class separation measures (Oh et al., 1999; Prabhakar and Jain, 2002). Let us indicate with lgen and r2gen the sample mean and variance of the fused scores of the genuine class, and with limp and r2imp the sample mean and variance of the fused scores of the impostor class. With the term ‘‘fused’’ score, we indicate the output of the fusion module, i.e., the output of our perceptron. The FD expression is as follows: 2 lgen limp FD ¼ 2 ð4Þ rgen þ r2imp The weights update is performed by the delta-rule wi
wi þ g
oFD owi
ð5Þ
Using the Fisher distance, the gradient computation is simple, as it depends on the four parameters in Eq. (4). The ‘‘contribute’’ of wi to the FD gradient expression can be written as follows:
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
oFD 2 lgen limp o lgen limp ¼ owi r2gen þ r2imp owi 2 2 2 o r þ r lgen limp gen imp 2 ow i r2gen þ r2imp
ð6Þ
A ‘‘batch’’ learning method is required for the computation related to Eq. (5), because the gradient computation refers to the sample mean and variances of the fused scores by the logistic function. It is worth noting that the logistic function derivative plays an active role in Eqs. (4)–(6)1. For the sake of brevity, details of the gradient computation are omitted. However, the complete expression of the gradient is not difficult to obtain. From Eq. (6) it is easy to see that our learning algorithm search for weights that separate distributions in terms of their means and reduce variances.
Besides the logistic transformation, the following fusion rules have been used: the maximum score value (Max), the minimum score value (Min), the average of the scores (Mean), and the product of the scores (Product). Such rules are called ‘‘fixed’’ fusion rules because they do not require a training phase (Roli and Kittler, 2002). We also used the standard Linear Discriminant Analysis, which also maximises the Fisher distance by deterministic way, for comparing the results obtained with our gradientdescent approach. Because, in this case, the output of the LDA classifier is a simple linear combination of the two matching scores, we applied to this output a logistic transformation, appropriately tuned, for normalising the LDA output into the interval [0, 1]. • The fused score value s is compared with the acceptance threshold. The claimed identity is classified as ‘‘genuine’’ if, s > th
4. Fusion of multiple fingerprint matchers
4.2. The selected fingerprint matchers
At this stage of our research, the input of perceptron is constituted by two verification scores produced by two selected fingerprint verification algorithms (Section 4.2). Given the input fingerprint image associated to the claimed identity i: • For each algorithm, the verification score between the given fingerprint and the ‘‘template’’ fingerprint stored in the database and associated to the identity i is computed. Let sm and st be the matching scores provided by the two individual algorithms. • The following fusion rule is applied to the above scores sm and st:
1
ð8Þ
otherwise it is classified as ‘‘impostor’’.
4.1. Methodology
s ¼ f ðsm ; st Þ
1833
ð7Þ
This makes results of our fusion approach quite different from that based on the standard LDA classifier used e.g. in (Ross et al., 2003).
So far two main types of fingerprint verification algorithms have been proposed: the so called minutiae-based and texture-based algorithms (Jain et al., 1997, 1999b, 2000; Prabhakar and Jain, 2002; Marcialis and Roli, 2003; Ross et al., 2003). Therefore, we selected one algorithm for each type. The selected minutiae-based algorithm is commonly referred as ‘‘String’’ algorithm (Jain et al., 1997). The ridge bifurcations and endings, called ‘‘minutiae’’ (Fig. 2), are extracted from the input fingerprint image. Such ‘‘minutiae’’ set is compared with that of the template fingerprint. Such comparison is performed by considering each set as a ‘‘string’’. A ‘‘string’’ distance is computed and converted into a matching score. The selected texture-based algorithm (Fig. 3) is also known as ‘‘Filter’’ algorithm (Jain et al., 2000). The input fingerprint image is ‘‘partitioned’’ around its centre (the so called ‘‘core’’ point) by a tessellation. A set of Gabor filters is applied to each sector of such tessellation. The outcome of
1834
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
‘‘core’’ point requested by the Filter algorithm could not be extracted in a reliable way. Consequently, we used an experimental protocol aimed to overcome this small sample size issue. 5.2. Experiment protocol
Fig. 2. Fingerprint representation based on the ‘‘map’’ of the minutiae-point locations and orientations. The reader is referred to Jain et al. (1997) for further details.
Fig. 3. Fingerprint texture representation by the so called ‘‘finger-code’’. The reader is referred to Jain et al. (2000) for further details.
each Gabor filter is evaluated for all pixels of each sector and the related standard deviation is computed. The feature vector made up of the standard deviations computed for each Gabor filter and for each sector is called ‘‘finger-code’’. The verification score is obtained by computing the Euclidean distance between the finger-code of the input image and the one of the template image. 5. Experimental results 5.1. Data set For our experiments, we used the FVC-DB1 data base that was recently introduced as a benchmark data set for fingerprint verification algorithms (Maio et al., 2002). This data set is made up of 800 fingerprint images acquired from a low-cost optical sensor. The image size is 300 · 300 pixels and the resolution is 500 dpi. The number of identities is 100, and the number of images per identity is eight. In our experiments, 276 fingerprints were disregarded because the
Our experimental protocol is very similar to the one proposed in the FVC competition (Maio et al., 2002), with a modification to overcome the issue due the rejection of a certain number of fingerprint images during the ‘‘enrolment’’ phase with the Filter matcher. The following evaluation protocol was used: • For each matcher, or any combination of the two selected matching algorithms, we computed two sets of scores. The first one is the ‘‘genuinematching scores’’ set G, made up of all comparisons among fingerprints of the same identity (in our experiments, all images were compared with all the other images of a given identity). The second set is the ‘‘impostor matching scores’’ set I, made up of all comparisons among fingerprints of different identities. The total number of genuine matching scores was 1440, and the total number of impostor matching scores was 135,586. • We randomly subdivided the above sets in two parts of the same size, so that: G = G1 [ G2, I = I1 [ I2. G1 and G2, as well as I1 and I2, are disjoint sets. • The training set Tr = {G1, I1} was used to estimate the EER point and to compute the weights of the logistic fusion rule and the standard LDA classifier. • The test set Tx = {G2, I2} was used to assess the performance of the individual and combined algorithms on unknown patterns. • To increase the statistical significance of our results and to overcome the issue due to the reduction of the original FVC-DB1 data base, we performed our experiments on five different training-test couples {Tr1, Tx1}, . . . , {Tr5, Tx5} and averaged the results. The individual fingerprint matchers and the different combinations of the two selected algorithms
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
were assessed and compared in terms of average EER on the training set, and average 1% FAR and 1% FRR on the test set. 5.3. Experiments performed It is well-known that the effectiveness of multiple matchers fusion depends on the degree of correlation of the individual algorithms and on the differences in verification accuracy (Kittler et al., 1998; Roli and Kittler, 2002). In order to investigate the effectiveness of our perceptron-based fusion rule for different degrees of correlation and performances of matchers, we created three experimental conditions: (a) low degree of correlation between matchers and different verification accuracy of the individual matchers; (b) high degree of correlation between matchers and different verification accuracy of the individual matchers; (c) low degree of correlation between matchers and similar verification accuracy of the individual matchers. The different degrees of correlation and performance allowed us to point out the experimental conditions under which the use of our perceptron fuser can be effective. In order to create the above three experimental conditions, we designed two different versions of the String matcher by varying two parameters that affect its precision. The first version of the String matcher was designed by reducing the maximum Euclidean distance that is allowed between the template minutiae and the input minutiae. The String algorithm so tuned was called ‘‘String 1’’.
1835
The second version of the String matcher was designed by reducing the maximum angular distance that is allowed between the template minutiae and the input minutiae. The String algorithm so tuned was called ‘‘String 2’’. It is worth remarking that the angular distance affects performances more than the Euclidean distance, because it can notably increase or decrease the tolerance of String matcher to the elastic distortions of fingerprints. Recognition accuracy of String 2 matcher is lower because no elastic distortion is tolerated. Therefore, the performance of String 2 is notably worse than that of String 1. However, they exhibit a very high degree of correlation, as they use the same approach to score computation. On the other hand, Filter matcher exhibits a low degree of correlation with the two versions of the String matcher, and also exhibits different performances with respect to String 1. Table 1 reports the average correlation coefficient and the average performance differences (in terms of EER) among the selected individual algorithms. It is easy to see that correlation decreases when using different matching algorithms. On the basis of the experimental analysis summarized in Table 1, we realised the above experimental conditions indicated with (a–c) by the following experiments: • Experiment (a): fusion of String 1 and Filter; • Experiment (b): fusion of String 1 and String 2; • Experiment (c): fusion of String 2 and Filter. 5.4. Comparison of individual and combined matchers We compared our fusion rule (indicated as FD-perceptron) with other commonly used rules and the standard LDA. Results are reported in
Table 1 Average correlation coefficient and performance differences among selected matchers
String 1 vs. Filter String 1 vs. String 2 String 2 vs. Filter
Correlation coefficient
Performance difference (at EER) (%)
0.32 0.75 0.33
5.0 5.6 0.6
These average values have been assessed in various experiments.
1836
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
Table 2 Equal error rate values computed on the training set
Experiment (a) Experiment (b) Experiment (c)
Best matcher (%)
Best fixed rule (%)
FD-perceptron (%)
Standard LDA (%)
1.5 (String) 1.5 (String 1) 6.5 (Filter)
1.4 (Product) 1.9 (Mean) 4.6 (Mean)
1.2 1.5 3.3
3.7 2.0 5.4
For each experiment, results provided by our FD-perceptron are reported. For the sake of comparison, results of the best individual matcher, the best fixed fusion rule and the fusion by standard LDA are also given.
Table 3 1% FAR values computed on the test set
Experiment (a) Experiment (b) Experiment (c)
Best matcher (%)
Best fixed rule (%)
FD-perceptron (%)
Standard LDA (%)
2.9 (String) 2.9 (String 1) 16.9 (Filter)
1.8 (Product) 3.0 (Max) 8.5 (Mean)
1.7 2.0 7.7
6.4 2.7 11.2
For each experiment, results provided by our FD-perceptron are reported. For the sake of comparison, results of the best individual matcher, the best fixed fusion rule and the fusion by standard LDA are also given.
Table 4 1% FRR values computed on the test set
Experiment (a) Experiment (b) Experiment (c)
Best matcher (%)
Best fixed rule (%)
FD-perceptron (%)
Standard LDA (%)
3.8 (String) 3.8 (String 1) 40.4 (String)
2.4 (Product) 5.0 (Max) 21.9 (Product)
3.1 2.5 15.0
27.3 4.0 36.9
For each experiment, results provided by our FD-perceptron are reported. For the sake of comparison, results of the best individual matcher, the best fixed fusion rule and the fusion by standard LDA are also given.
Tables 2–4. Table 2 reports the EER values on the training set. Tables 3 and 4 report 1% FAR and 1% FRR values on the test set. Results of Experiment (a) in Tables 2–4 confirm that fixed fusion rules works well for low correlated matchers (Roli and Kittler, 2002). In particular, the product rule appears appropriate to improve the overall performance. Improvement provided by our perceptron over fixed fusion rules is not significant for the case of Experiment (a). However, we show in Section 5.5 that our perceptron exhibits a better performance in terms of ‘‘robustness’’. Results of Experiments (b) point out the wellknown limit of fixed rules, namely, high score correlation often decreases their effectiveness (Roli and Kittler, 2002). Although the EER values of fixed rules and our perceptron are comparable (Table 2, second row), 1% FAR and 1% FRR val-
ues show the performance improvement achievable by our FD-perceptron (more than 1%). Results of Experiment (c) show that our perceptron can outperform the fixed rules in the case of low correlation and low differences in verification performances. This result does not agree with practical guidelines for which fixed rules should be appropriate in case of low correlation and low performance differences (Roli and Kittler, 2002). We believe that such result is due to the data set characteristics and the particular errors made by String 2 and Filter. Probably, many patterns wrongly classified by String 2 are correctly classified by Filter, and vice versa. So, being our FDperceptron a ‘‘trained’’ rule, it is able to handle such complex condition better than fixed rules. Although results of Experiment (c) could not be confirmed for other data sets and other matchers, it is worth noting the considerable decrease of all
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
error rates and, in particular, the 1% FRR value reported in Table 4 (third row). In all cases, the FD-perceptron fusion rule strongly outperforms the standard LDA classifier (Tables 2–4). This could be explained by considering that: (a) the standard LDA classifier is designed to find the linear transformation of the features (in our case, of the matching scores derived by the individual algorithms) which maximises the Fisher ratio, but it can assure to perform optimally only if the individual scores distributions belong to the exponential family, which is not our case (see e.g. Prabhakar and Jain (2002) about the String and Filter matching score distributions); (b) the proposed FD-based perceptron is explicitly designed to project the individual matching scores by a non-linear transformation: in fact, the logistic function has not only the role of normalization function, but it also plays an active role in the gradient computation of the Fisher distance. Therefore, it can be expected that the proposed FD-perceptron is more flexible (thanks to the gradient-descent approach to the FD maximisation) than the standard LDA classifier, and can also perform better. To sum up, reported results point out that: (i) in case of high correlation and performance difference, the FD-perceptron fusion rule performs better than fixed rules (Experiment (b)); (ii) in case of low correlation, the performance of the FD-perceptron in terms of error rate is comparable with that of fixed rules (Experiment (a)), although there
1837
could be some favourable cases (Experiment (c)) in which the FD-perceptron outperforms such fixed rules. The next section shows the clear advantages of our FD-perceptron in terms of performance ‘‘robustness’’. 5.5. Robustness of the proposed class separation-based fusion rule In this section, we show that: (1) performances of our perceptron-based fusion rule around the acceptance threshold are more ‘‘stable’’ than those of the other fusion rules investigated in this paper; (2) our perceptron-based fusion rule has a larger range of acceptance thresholds that provide the same verification accuracy, so increasing the robustness of the authentication system. It is worth noting that the above features allow reducing the issues related to the selection of the optimal acceptance threshold (Section 1). Figs. 4–6(a) and (b) show the behaviours of the functions dFAR(dscore) = FAR(th + dscore) FAR(th) and dFRR(dscore) = FRR(th + dscore) FRR(th) on the test set for the Experiments (a), (b), and (c). th is the acceptance threshold at the EER computed on the training set, and dscore 2 [0.01, 0.01]. These functions are aimed to analyse the performance stability of the investigated fusion rules around the acceptance
Fig. 4. (a) dFAR(dscore) = FAR(th + dscore) FAR(th). (b) dFRR(dscore) = FRR(th + dscore) FRR(th). th is the threshold, th at EER computed on training set. It is easy to see that the performance variation of the FD-based perceptron is negligible with respect to the one of the other fusion rules. Reported results refer to Experiment (a).
1838
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
Fig. 5. (a) dFAR(dscore) = FAR(th + dscore) FAR(th). (b) dFRR(dscore) = FRR(th + dscore) FRR(th). th is the threshold, th at EER computed on training set. It is easy to see that the performance variation of the FD-based perceptron is negligible with respect to the one of the other fusion rules. Reported results refer to Experiment (b).
Fig. 6. (a) dFAR(dscore) = FAR(th + dscore) FAR(th). (b) dFRR(dscore) = FRR(th + dscore) FRR(th). th is the threshold, th at EER computed on training set. It is easy to see that the performance variation of the FD-based perceptron is negligible with respect to the one of the other fusion rules. Reported results refer to Experiment (c).
threshold. All the figures report the best fixed rule and the best individual matcher for comparison purposes. In all cases, the slopes of the functions dFAR(dscore) and dFRR(dscore) clearly show that the performances of FD-based perceptron are more stable around the acceptance threshold than the ones of the best fusion rule and the best individual matcher. This result can be explained by the higher increase of separation between genuine and impostor classes provided by our fusion rule. This performance robustness allows having a larger range of acceptance thresholds that provide the same verification performances, so simplifying the crucial issue of threshold selection discussed in Section 1.
6. Conclusions In this paper, we proposed the use of a perceptron with a class-separation loss function for combining multiple fingerprint matchers. Reported results showed that such perceptron-based fusion rule performs better than some commonly used rules in terms of verification accuracy, and its performances are very stable around the selected acceptance threshold. In particular, our fusion rule exhibited better performance in terms of 1% FAR and 1% FRR for the cases of high correlation and performance differences among individual matchers (Experiments (b) and (c)).
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
Moreover, our fusion rule showed stable performances around the estimated acceptance threshold. This feature allows having a larger range of acceptance thresholds that provide the same verification accuracy, so simplifying the crucial issue of threshold selection discussed in Section 1. It is worth remarking that such feature is the direct consequence of the increase of genuine and impostor classes separation achieved by the proposed fusion rule. References Haykin, S., 1999. Neural Networks: a Comprehensive Foundation, second ed. Prentice-Hall, Englewood Cliffs, NJ. Jain, A.K., Hong, L., Bolle, R., 1997. On-line fingerprint verification. IEEE Transactions on Pattern Analysis and Machine Intelligence 19 (4), 302–314. Jain, A.K., Bolle, R., Pankanti, S. (Eds.), 1999a. BIOMETRIC—Personal Identification in Networked Society. Kluwer Academic Publishers, Boston/Dordrecht/London. Jain, A.K., Prabhakar, S., Chen, S., 1999b. Combining multiple matchers for a high security fingerprint verification system. Pattern Recognition Letters 20 (11–13), 1371–1379.
1839
Jain, A.K., Prabhakar, S., Hong, L., Pankanti, S., 2000. Filterbank-based fingerprint matching. IEEE Transactions on Image Processing 9 (5), 846–859. Kittler, J., Hatef, M., Duin, R.P.W., Matas, J., 1998. On combining classifiers. IEEE Transactions on Pattern Analysis and Machine Intelligence 20 (3), 226–239. Maio, D., Maltoni, D., Cappelli, R., Wayman, J.L., Jain, A.K., 2002. FVC-2000: Fingerprint verification competition. IEEE Transactions on Pattern Analysis and Machine Intelligence 24 (3), 402–412. Marcialis, G.L., Roli, F., 2003. Experimental results on fusion of multiple fingerprint matchers. In: Kittler, J., Nixon, M.S. (Eds.), Proceedings of the 4th International Conference on Audio and Video-based Person Authentication AVBPA03. Springer LNCS2688, pp. 814–820. Oh, I., Lee, J.S., Suen, C.Y., 1999. Analysis of class separation and combination of class-dependent features for handwriting recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 21 (10), 1089–1094. Prabhakar, S., Jain, A.K., 2002. Decision-level fusion in fingerprint verification. Pattern Recognition 35 (4), 861– 874. Roli, F., Kittler, F., 2002. Multiple classifier systemsLecture Notes in Computer Science, vol. 2364. Springer-Verlag. Ross, A., Jain, A.K., Reisman, J., 2003. A Hybrid Fingerprint Matcher. Pattern Recognition 36 (7), 1661–1673.
Fusion of multiple fingerprint matchers by single-layer perceptron with class-separation loss function Gian Luca Marcialis *, Fabio Roli Department of Electrical and Electronic Engineering, University of Cagliari, Piazza d’Armi, 09123 Cagliari, Italy Available online 29 April 2005
Abstract In this paper, a perceptron-based algorithm for fusion of multiple fingerprint matchers is presented. The person to be identified submits to the personal authentication system her/his fingerprint and claimed identity. Multiple fingerprint matchers provide a set of verification scores, that are then fused by a single-layer perceptron with class-separation loss function. Weights of such perceptron are explicitly optimised to increase the separation between genuine users and impostors (i.e., unauthorized users). Reported experiments show that such modified perceptron allows improving the performances and the robustness of the best individual fingerprint matcher, and outperforming some commonly used fusion rules. 2005 Elsevier B.V. All rights reserved. Keywords: Automatic fingerprint verification; Fusion of multiple fingerprint matchers; Multiple classifiers systems; Neural networks; Pattern recognition
1. Introduction Fingerprints are widely used for automatic personal authentication (Jain et al., 1999a), in order to control the access to restricted areas or resources. The person to be ‘‘authenticated’’ submits to the system her/his fingerprint and identity. The system matches the input fingerprint with the one *
Corresponding author. Tel.: +39 070 675 5776; fax: +39 070 675 5782. E-mail address: [email protected] (G.L. Marcialis).
associated to the given identity and stored in its database. A degree of similarity, named ‘‘score’’, is computed. If the score is higher than a certain value (the so called ‘‘acceptance’’ threshold), the claimed identity is accepted and the person is classified as a genuine user. Otherwise, she/he is classified as an impostor and the access to the required resource is denied. The selection of the acceptance threshold is a crucial issue that strongly affects fingerprint verification performances. In order to compute the optimal threshold, accurate estimates of genuine and
0167-8655/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.patrec.2005.03.004
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
impostor users distributions are necessary. Unfortunately, available training data are often not completely representative of the target population, and, in particular, data on impostor users are very difficult to be collected. In real operational conditions (e.g., fingerprint verification for ATM applications), acquisition of realistic and representative impostor data is basically unfeasible. It is easy to see that increasing the separation between genuine and impostor classes can be very useful to address issues related to the acceptance threshold selection. If genuine and impostor classes are well separated, errors that usually affect estimates of class distributions have a smaller impact on threshold selection, and consequently, on system performances. Fig. 1 illustrates this concept. In this paper, a fusion rule explicitly aimed to maximize the separation between genuine and impostor classes is proposed. This rule is implemented by a perceptron with a ‘‘class-separation’’ loss function. Our perceptron takes as input the scores of multiple matchers and produces as output ‘‘fused’’ scores that maximize the separation between impostor and genuine users classes. Section 2 quickly provides the basic concepts used in this paper. Section 3 presents our fuser based on the perceptron with class-separation loss function. Section 4 briefly describes the individual
Estimated impostor distribution True impostor distribution
1831
fingerprint matchers used. Section 5 reports experimental results. Section 6 draws preliminary conclusions.
2. Background concepts The so called verification score ‘‘s’’ provides the degree of similarity between two fingerprint patterns, and takes values in [0, 1]. A fingerprint pattern belongs to the genuine class if the identity of her/his possessor corresponds to the claimed one. The opposite holds for the impostor class. The design of any fingerprint verification system depends on the estimate of the two posterior probabilities p(sjgenuine) and p(sjimpostor), and the selection of the acceptance threshold s*. If the score is higher than the acceptance threshold, the claimed identity is accepted and the person is classified as a genuine user. Otherwise, she/ he is classified as an impostor. Authentication errors obviously depends on the acceptance threshold. They are called ‘‘false acceptance’’ errors if an impostor is accepted, and ‘‘false rejection’’ errors if a genuine user is rejected. The probabilities of false acceptance and false rejection are called False Acceptance Rate (FAR) and False Rejection Rate (FRR):
Estimated Impostor distribution Estimated Genuine distribution
True Impostor distribution True Genuine distribution
Optimal Acceptance Threshold
Estimated Acceptance Threshold
(a)
Estimated Genuine distribution
True Genuine distribution
score
Optimal Acceptance threshold
Estimated Acceptance threshold
score
(b)
Fig. 1. Impact of errors affecting estimates of class distributions on (a) not well separated genuine and impostor classes. (b) Well separated genuine and impostor classes. It is easy to see that errors have a smaller impact on threshold selection, and consequently, on system performances for the case (b) of well separated distributions.
1832
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
FARðs Þ ¼
Z
1
pðsjimpostorÞds
ð1Þ
pðsjgenuineÞds
ð2Þ
s
FRRðs Þ ¼
Z
s 0
Usually, the acceptance threshold s* is computed in order to obtain FAR(s*) = FRR(s*). Such error value is called Equal Error Rate point (EER). For high-security systems, it is often requested to minimise FAR or FRR under some constraint on the dual performance parameter. For example, the so called 1% FAR performance measure assesses the False Rejection Rate when the False Acceptance Rate is constrained to 1%. On the contrary, 1% FRR measure assesses the FAR when FRR = 1%.
3. Fusion by single-layer perceptron with class-separation loss function 3.1. The fusion model In order to design our fusion module, we used the perceptron classifier. Let s1, . . . , sN be the matching scores provided by N individual matchers. The logistic function of perceptron produces the fused score s: s¼
1 1 þ exp ½ðw0 þ w1 s1 þ þ wN sN Þ
ð3Þ
Eq. (3) points out that the inputs of perceptron are the scores provided by the N individual matchers, and the output s is the final verification score. According to our goal, we substituted the standard loss functions of perceptron with a function explicitly aimed to maximize the statistical separation between genuine and impostor classes. It should be remarked that the use of logistic transform for fusing multiple fingerprint matchers has been previously proposed in (Jain et al., 1999b). However, the goal of Jain et al. was to estimate the parameters of the logistic transform in order to minimize FRR for a given FAR. Although these authors were aware about the increase of class separation achievable by logistic
transform (see Fig. 3 in Jain et al., 1999b), their work was not focused on this aspect, and no experimental evidence of the increase of class separation was reported. In this work, we followed Jain et al. suggestion on the possible use of logistic transform for increasing class separation. We designed a perceptron-based fusion rule that explicitly estimate the parameters of the logistic transform in order to maximize the statistical separation between genuine and impostor classes. In addition, we investigated by experiments the achievable increase of separation. Finally, it should be noted that, although loss functions based on class separation measures have been already investigated in the neural networks field (Haykin, 1999), no previous work used them in order to design a perceptron-based fusion rule aimed to maximize the separation between genuine and impostor classes. 3.1.1. The learning algorithm We used a parametric distance, called Fisher distance (FD), as measure of statistical separation between the genuine and impostor classes. The Fisher distance is the parametric version of more general class separation measures (Oh et al., 1999; Prabhakar and Jain, 2002). Let us indicate with lgen and r2gen the sample mean and variance of the fused scores of the genuine class, and with limp and r2imp the sample mean and variance of the fused scores of the impostor class. With the term ‘‘fused’’ score, we indicate the output of the fusion module, i.e., the output of our perceptron. The FD expression is as follows: 2 lgen limp FD ¼ 2 ð4Þ rgen þ r2imp The weights update is performed by the delta-rule wi
wi þ g
oFD owi
ð5Þ
Using the Fisher distance, the gradient computation is simple, as it depends on the four parameters in Eq. (4). The ‘‘contribute’’ of wi to the FD gradient expression can be written as follows:
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
oFD 2 lgen limp o lgen limp ¼ owi r2gen þ r2imp owi 2 2 2 o r þ r lgen limp gen imp 2 ow i r2gen þ r2imp
ð6Þ
A ‘‘batch’’ learning method is required for the computation related to Eq. (5), because the gradient computation refers to the sample mean and variances of the fused scores by the logistic function. It is worth noting that the logistic function derivative plays an active role in Eqs. (4)–(6)1. For the sake of brevity, details of the gradient computation are omitted. However, the complete expression of the gradient is not difficult to obtain. From Eq. (6) it is easy to see that our learning algorithm search for weights that separate distributions in terms of their means and reduce variances.
Besides the logistic transformation, the following fusion rules have been used: the maximum score value (Max), the minimum score value (Min), the average of the scores (Mean), and the product of the scores (Product). Such rules are called ‘‘fixed’’ fusion rules because they do not require a training phase (Roli and Kittler, 2002). We also used the standard Linear Discriminant Analysis, which also maximises the Fisher distance by deterministic way, for comparing the results obtained with our gradientdescent approach. Because, in this case, the output of the LDA classifier is a simple linear combination of the two matching scores, we applied to this output a logistic transformation, appropriately tuned, for normalising the LDA output into the interval [0, 1]. • The fused score value s is compared with the acceptance threshold. The claimed identity is classified as ‘‘genuine’’ if, s > th
4. Fusion of multiple fingerprint matchers
4.2. The selected fingerprint matchers
At this stage of our research, the input of perceptron is constituted by two verification scores produced by two selected fingerprint verification algorithms (Section 4.2). Given the input fingerprint image associated to the claimed identity i: • For each algorithm, the verification score between the given fingerprint and the ‘‘template’’ fingerprint stored in the database and associated to the identity i is computed. Let sm and st be the matching scores provided by the two individual algorithms. • The following fusion rule is applied to the above scores sm and st:
1
ð8Þ
otherwise it is classified as ‘‘impostor’’.
4.1. Methodology
s ¼ f ðsm ; st Þ
1833
ð7Þ
This makes results of our fusion approach quite different from that based on the standard LDA classifier used e.g. in (Ross et al., 2003).
So far two main types of fingerprint verification algorithms have been proposed: the so called minutiae-based and texture-based algorithms (Jain et al., 1997, 1999b, 2000; Prabhakar and Jain, 2002; Marcialis and Roli, 2003; Ross et al., 2003). Therefore, we selected one algorithm for each type. The selected minutiae-based algorithm is commonly referred as ‘‘String’’ algorithm (Jain et al., 1997). The ridge bifurcations and endings, called ‘‘minutiae’’ (Fig. 2), are extracted from the input fingerprint image. Such ‘‘minutiae’’ set is compared with that of the template fingerprint. Such comparison is performed by considering each set as a ‘‘string’’. A ‘‘string’’ distance is computed and converted into a matching score. The selected texture-based algorithm (Fig. 3) is also known as ‘‘Filter’’ algorithm (Jain et al., 2000). The input fingerprint image is ‘‘partitioned’’ around its centre (the so called ‘‘core’’ point) by a tessellation. A set of Gabor filters is applied to each sector of such tessellation. The outcome of
1834
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
‘‘core’’ point requested by the Filter algorithm could not be extracted in a reliable way. Consequently, we used an experimental protocol aimed to overcome this small sample size issue. 5.2. Experiment protocol
Fig. 2. Fingerprint representation based on the ‘‘map’’ of the minutiae-point locations and orientations. The reader is referred to Jain et al. (1997) for further details.
Fig. 3. Fingerprint texture representation by the so called ‘‘finger-code’’. The reader is referred to Jain et al. (2000) for further details.
each Gabor filter is evaluated for all pixels of each sector and the related standard deviation is computed. The feature vector made up of the standard deviations computed for each Gabor filter and for each sector is called ‘‘finger-code’’. The verification score is obtained by computing the Euclidean distance between the finger-code of the input image and the one of the template image. 5. Experimental results 5.1. Data set For our experiments, we used the FVC-DB1 data base that was recently introduced as a benchmark data set for fingerprint verification algorithms (Maio et al., 2002). This data set is made up of 800 fingerprint images acquired from a low-cost optical sensor. The image size is 300 · 300 pixels and the resolution is 500 dpi. The number of identities is 100, and the number of images per identity is eight. In our experiments, 276 fingerprints were disregarded because the
Our experimental protocol is very similar to the one proposed in the FVC competition (Maio et al., 2002), with a modification to overcome the issue due the rejection of a certain number of fingerprint images during the ‘‘enrolment’’ phase with the Filter matcher. The following evaluation protocol was used: • For each matcher, or any combination of the two selected matching algorithms, we computed two sets of scores. The first one is the ‘‘genuinematching scores’’ set G, made up of all comparisons among fingerprints of the same identity (in our experiments, all images were compared with all the other images of a given identity). The second set is the ‘‘impostor matching scores’’ set I, made up of all comparisons among fingerprints of different identities. The total number of genuine matching scores was 1440, and the total number of impostor matching scores was 135,586. • We randomly subdivided the above sets in two parts of the same size, so that: G = G1 [ G2, I = I1 [ I2. G1 and G2, as well as I1 and I2, are disjoint sets. • The training set Tr = {G1, I1} was used to estimate the EER point and to compute the weights of the logistic fusion rule and the standard LDA classifier. • The test set Tx = {G2, I2} was used to assess the performance of the individual and combined algorithms on unknown patterns. • To increase the statistical significance of our results and to overcome the issue due to the reduction of the original FVC-DB1 data base, we performed our experiments on five different training-test couples {Tr1, Tx1}, . . . , {Tr5, Tx5} and averaged the results. The individual fingerprint matchers and the different combinations of the two selected algorithms
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
were assessed and compared in terms of average EER on the training set, and average 1% FAR and 1% FRR on the test set. 5.3. Experiments performed It is well-known that the effectiveness of multiple matchers fusion depends on the degree of correlation of the individual algorithms and on the differences in verification accuracy (Kittler et al., 1998; Roli and Kittler, 2002). In order to investigate the effectiveness of our perceptron-based fusion rule for different degrees of correlation and performances of matchers, we created three experimental conditions: (a) low degree of correlation between matchers and different verification accuracy of the individual matchers; (b) high degree of correlation between matchers and different verification accuracy of the individual matchers; (c) low degree of correlation between matchers and similar verification accuracy of the individual matchers. The different degrees of correlation and performance allowed us to point out the experimental conditions under which the use of our perceptron fuser can be effective. In order to create the above three experimental conditions, we designed two different versions of the String matcher by varying two parameters that affect its precision. The first version of the String matcher was designed by reducing the maximum Euclidean distance that is allowed between the template minutiae and the input minutiae. The String algorithm so tuned was called ‘‘String 1’’.
1835
The second version of the String matcher was designed by reducing the maximum angular distance that is allowed between the template minutiae and the input minutiae. The String algorithm so tuned was called ‘‘String 2’’. It is worth remarking that the angular distance affects performances more than the Euclidean distance, because it can notably increase or decrease the tolerance of String matcher to the elastic distortions of fingerprints. Recognition accuracy of String 2 matcher is lower because no elastic distortion is tolerated. Therefore, the performance of String 2 is notably worse than that of String 1. However, they exhibit a very high degree of correlation, as they use the same approach to score computation. On the other hand, Filter matcher exhibits a low degree of correlation with the two versions of the String matcher, and also exhibits different performances with respect to String 1. Table 1 reports the average correlation coefficient and the average performance differences (in terms of EER) among the selected individual algorithms. It is easy to see that correlation decreases when using different matching algorithms. On the basis of the experimental analysis summarized in Table 1, we realised the above experimental conditions indicated with (a–c) by the following experiments: • Experiment (a): fusion of String 1 and Filter; • Experiment (b): fusion of String 1 and String 2; • Experiment (c): fusion of String 2 and Filter. 5.4. Comparison of individual and combined matchers We compared our fusion rule (indicated as FD-perceptron) with other commonly used rules and the standard LDA. Results are reported in
Table 1 Average correlation coefficient and performance differences among selected matchers
String 1 vs. Filter String 1 vs. String 2 String 2 vs. Filter
Correlation coefficient
Performance difference (at EER) (%)
0.32 0.75 0.33
5.0 5.6 0.6
These average values have been assessed in various experiments.
1836
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
Table 2 Equal error rate values computed on the training set
Experiment (a) Experiment (b) Experiment (c)
Best matcher (%)
Best fixed rule (%)
FD-perceptron (%)
Standard LDA (%)
1.5 (String) 1.5 (String 1) 6.5 (Filter)
1.4 (Product) 1.9 (Mean) 4.6 (Mean)
1.2 1.5 3.3
3.7 2.0 5.4
For each experiment, results provided by our FD-perceptron are reported. For the sake of comparison, results of the best individual matcher, the best fixed fusion rule and the fusion by standard LDA are also given.
Table 3 1% FAR values computed on the test set
Experiment (a) Experiment (b) Experiment (c)
Best matcher (%)
Best fixed rule (%)
FD-perceptron (%)
Standard LDA (%)
2.9 (String) 2.9 (String 1) 16.9 (Filter)
1.8 (Product) 3.0 (Max) 8.5 (Mean)
1.7 2.0 7.7
6.4 2.7 11.2
For each experiment, results provided by our FD-perceptron are reported. For the sake of comparison, results of the best individual matcher, the best fixed fusion rule and the fusion by standard LDA are also given.
Table 4 1% FRR values computed on the test set
Experiment (a) Experiment (b) Experiment (c)
Best matcher (%)
Best fixed rule (%)
FD-perceptron (%)
Standard LDA (%)
3.8 (String) 3.8 (String 1) 40.4 (String)
2.4 (Product) 5.0 (Max) 21.9 (Product)
3.1 2.5 15.0
27.3 4.0 36.9
For each experiment, results provided by our FD-perceptron are reported. For the sake of comparison, results of the best individual matcher, the best fixed fusion rule and the fusion by standard LDA are also given.
Tables 2–4. Table 2 reports the EER values on the training set. Tables 3 and 4 report 1% FAR and 1% FRR values on the test set. Results of Experiment (a) in Tables 2–4 confirm that fixed fusion rules works well for low correlated matchers (Roli and Kittler, 2002). In particular, the product rule appears appropriate to improve the overall performance. Improvement provided by our perceptron over fixed fusion rules is not significant for the case of Experiment (a). However, we show in Section 5.5 that our perceptron exhibits a better performance in terms of ‘‘robustness’’. Results of Experiments (b) point out the wellknown limit of fixed rules, namely, high score correlation often decreases their effectiveness (Roli and Kittler, 2002). Although the EER values of fixed rules and our perceptron are comparable (Table 2, second row), 1% FAR and 1% FRR val-
ues show the performance improvement achievable by our FD-perceptron (more than 1%). Results of Experiment (c) show that our perceptron can outperform the fixed rules in the case of low correlation and low differences in verification performances. This result does not agree with practical guidelines for which fixed rules should be appropriate in case of low correlation and low performance differences (Roli and Kittler, 2002). We believe that such result is due to the data set characteristics and the particular errors made by String 2 and Filter. Probably, many patterns wrongly classified by String 2 are correctly classified by Filter, and vice versa. So, being our FDperceptron a ‘‘trained’’ rule, it is able to handle such complex condition better than fixed rules. Although results of Experiment (c) could not be confirmed for other data sets and other matchers, it is worth noting the considerable decrease of all
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
error rates and, in particular, the 1% FRR value reported in Table 4 (third row). In all cases, the FD-perceptron fusion rule strongly outperforms the standard LDA classifier (Tables 2–4). This could be explained by considering that: (a) the standard LDA classifier is designed to find the linear transformation of the features (in our case, of the matching scores derived by the individual algorithms) which maximises the Fisher ratio, but it can assure to perform optimally only if the individual scores distributions belong to the exponential family, which is not our case (see e.g. Prabhakar and Jain (2002) about the String and Filter matching score distributions); (b) the proposed FD-based perceptron is explicitly designed to project the individual matching scores by a non-linear transformation: in fact, the logistic function has not only the role of normalization function, but it also plays an active role in the gradient computation of the Fisher distance. Therefore, it can be expected that the proposed FD-perceptron is more flexible (thanks to the gradient-descent approach to the FD maximisation) than the standard LDA classifier, and can also perform better. To sum up, reported results point out that: (i) in case of high correlation and performance difference, the FD-perceptron fusion rule performs better than fixed rules (Experiment (b)); (ii) in case of low correlation, the performance of the FD-perceptron in terms of error rate is comparable with that of fixed rules (Experiment (a)), although there
1837
could be some favourable cases (Experiment (c)) in which the FD-perceptron outperforms such fixed rules. The next section shows the clear advantages of our FD-perceptron in terms of performance ‘‘robustness’’. 5.5. Robustness of the proposed class separation-based fusion rule In this section, we show that: (1) performances of our perceptron-based fusion rule around the acceptance threshold are more ‘‘stable’’ than those of the other fusion rules investigated in this paper; (2) our perceptron-based fusion rule has a larger range of acceptance thresholds that provide the same verification accuracy, so increasing the robustness of the authentication system. It is worth noting that the above features allow reducing the issues related to the selection of the optimal acceptance threshold (Section 1). Figs. 4–6(a) and (b) show the behaviours of the functions dFAR(dscore) = FAR(th + dscore) FAR(th) and dFRR(dscore) = FRR(th + dscore) FRR(th) on the test set for the Experiments (a), (b), and (c). th is the acceptance threshold at the EER computed on the training set, and dscore 2 [0.01, 0.01]. These functions are aimed to analyse the performance stability of the investigated fusion rules around the acceptance
Fig. 4. (a) dFAR(dscore) = FAR(th + dscore) FAR(th). (b) dFRR(dscore) = FRR(th + dscore) FRR(th). th is the threshold, th at EER computed on training set. It is easy to see that the performance variation of the FD-based perceptron is negligible with respect to the one of the other fusion rules. Reported results refer to Experiment (a).
1838
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
Fig. 5. (a) dFAR(dscore) = FAR(th + dscore) FAR(th). (b) dFRR(dscore) = FRR(th + dscore) FRR(th). th is the threshold, th at EER computed on training set. It is easy to see that the performance variation of the FD-based perceptron is negligible with respect to the one of the other fusion rules. Reported results refer to Experiment (b).
Fig. 6. (a) dFAR(dscore) = FAR(th + dscore) FAR(th). (b) dFRR(dscore) = FRR(th + dscore) FRR(th). th is the threshold, th at EER computed on training set. It is easy to see that the performance variation of the FD-based perceptron is negligible with respect to the one of the other fusion rules. Reported results refer to Experiment (c).
threshold. All the figures report the best fixed rule and the best individual matcher for comparison purposes. In all cases, the slopes of the functions dFAR(dscore) and dFRR(dscore) clearly show that the performances of FD-based perceptron are more stable around the acceptance threshold than the ones of the best fusion rule and the best individual matcher. This result can be explained by the higher increase of separation between genuine and impostor classes provided by our fusion rule. This performance robustness allows having a larger range of acceptance thresholds that provide the same verification performances, so simplifying the crucial issue of threshold selection discussed in Section 1.
6. Conclusions In this paper, we proposed the use of a perceptron with a class-separation loss function for combining multiple fingerprint matchers. Reported results showed that such perceptron-based fusion rule performs better than some commonly used rules in terms of verification accuracy, and its performances are very stable around the selected acceptance threshold. In particular, our fusion rule exhibited better performance in terms of 1% FAR and 1% FRR for the cases of high correlation and performance differences among individual matchers (Experiments (b) and (c)).
G.L. Marcialis, F. Roli / Pattern Recognition Letters 26 (2005) 1830–1839
Moreover, our fusion rule showed stable performances around the estimated acceptance threshold. This feature allows having a larger range of acceptance thresholds that provide the same verification accuracy, so simplifying the crucial issue of threshold selection discussed in Section 1. It is worth remarking that such feature is the direct consequence of the increase of genuine and impostor classes separation achieved by the proposed fusion rule. References Haykin, S., 1999. Neural Networks: a Comprehensive Foundation, second ed. Prentice-Hall, Englewood Cliffs, NJ. Jain, A.K., Hong, L., Bolle, R., 1997. On-line fingerprint verification. IEEE Transactions on Pattern Analysis and Machine Intelligence 19 (4), 302–314. Jain, A.K., Bolle, R., Pankanti, S. (Eds.), 1999a. BIOMETRIC—Personal Identification in Networked Society. Kluwer Academic Publishers, Boston/Dordrecht/London. Jain, A.K., Prabhakar, S., Chen, S., 1999b. Combining multiple matchers for a high security fingerprint verification system. Pattern Recognition Letters 20 (11–13), 1371–1379.
1839
Jain, A.K., Prabhakar, S., Hong, L., Pankanti, S., 2000. Filterbank-based fingerprint matching. IEEE Transactions on Image Processing 9 (5), 846–859. Kittler, J., Hatef, M., Duin, R.P.W., Matas, J., 1998. On combining classifiers. IEEE Transactions on Pattern Analysis and Machine Intelligence 20 (3), 226–239. Maio, D., Maltoni, D., Cappelli, R., Wayman, J.L., Jain, A.K., 2002. FVC-2000: Fingerprint verification competition. IEEE Transactions on Pattern Analysis and Machine Intelligence 24 (3), 402–412. Marcialis, G.L., Roli, F., 2003. Experimental results on fusion of multiple fingerprint matchers. In: Kittler, J., Nixon, M.S. (Eds.), Proceedings of the 4th International Conference on Audio and Video-based Person Authentication AVBPA03. Springer LNCS2688, pp. 814–820. Oh, I., Lee, J.S., Suen, C.Y., 1999. Analysis of class separation and combination of class-dependent features for handwriting recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 21 (10), 1089–1094. Prabhakar, S., Jain, A.K., 2002. Decision-level fusion in fingerprint verification. Pattern Recognition 35 (4), 861– 874. Roli, F., Kittler, F., 2002. Multiple classifier systemsLecture Notes in Computer Science, vol. 2364. Springer-Verlag. Ross, A., Jain, A.K., Reisman, J., 2003. A Hybrid Fingerprint Matcher. Pattern Recognition 36 (7), 1661–1673.