NISTIR 7346

Studies of Biometric Fusion

Brad Ulery1

Austin Hicklin1

Craig Watson2

William Fellner1

Peter Hallinan3

1

 Mitretek Systems 2

 National Institute of Standards and Technology 3

 Mitretek Systems Consultant

 1 
NISTIR 7346

Studies of Biometric Fusion

Brad Ulery

Austin Hicklin

Mitretek Systems

Craig Watson

Image Group, Information Access Division

Information Technology Laboratory

William Fellner

Mitretek Systems

Peter Hallinan

Mitretek Systems Consultant

September 2006

U.S. DEPARTMENT OF COMMERCE

Carlos M. Gutierrez, Secretary

TECHNOLOGY ADMINISTRATION

Michelle O’Neill, Acting Under Secretary of Commerce for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

William A. Jeffrey, Director

 2 
Studies of Biometric Fusion 

Brad Ulery,1 Austin Hicklin,1 Craig Watson2, William Fellner,1 Peter Hallinan3 

1 Mitretek Systems 

2 National Institute of Standards and Technology 

3 Consultant to Mitretek Systems

20 July 2006 

Abstract 

This is an evaluation of different score-level fusion techniques, and the results of a variety of fusion experiments 

using face and fingerprint data from 187,000 individuals, with matcher scores from three fingerprint and three face 

recognition systems. 

Eight score-level fusion techniques were implemented and evaluated. These differed in effectiveness, in the types of 

training data required, and in the complexity of modeling of genuine and imposter distributions. The most effective 

fusion techniques were product of likelihood ratios and logistic regression. Techniques that were nearly as effective 

were product of False Accept Rates ( FARs) and an optimized linear method. 

Multi-modal fusion is highly effective: fusing one fingerprint and face resulted in a 64-85% reduction in false reject 

rate at a constant false accept rate of 0.0001. Multi-instance fusion using fingerprints from multiple fingers is also 

highly effective: fusing two fingerprints resulted in a 48-90% reduction in false reject rate. Multi-sample fusion 

using the enrollment of two samples rather than one resulted in a 45-72% reduction in false reject rate. Multialgorithm fusion using different matchers on the same data resulted in an 8-33% reduction in false reject rate. 
Studies of Biometric Fusion 

Contents 

1 Introduction ....................................................................................................................................3

2 Data ..................................................................................................................................................3

2.1 Face Images ..............................................................................................................................3

2.2 Fingerprints..............................................................................................................................3

2.3 Matchers ...................................................................................................................................4

2.4 Data Integrity...........................................................................................................................5

3 Score-Level Fusion Techniques ....................................................................................................6

3.1 Implemented Techniques.......................................................................................................7

3.2 Evaluation of Techniques.......................................................................................................8

3.3 Considerations in the Choice of Techniques .....................................................................11

4 Results of Experiments ................................................................................................................11

4.1 Multi-Modal: Face and Fingerprint Results.......................................................................12

4.2 Multi-Instance: 2-Fingerprint Results.................................................................................13

4.3 Multi-Instance: N-Fingerprint Results ...............................................................................14

4.4 Multi-Instance/Modal: N-Fingerprint and Face Results ..................................................16

4.5 Multi-Matcher Results ..........................................................................................................17

4.6 Multi-Sample Results............................................................................................................19

5 Conclusions ...................................................................................................................................20

6 References......................................................................................................................................22

Acknowledgements 

This work was performed for the National Institute of Standards and Technology, under contract through the U.S. 

Department of Interior, Contract NBCH-D-02-0039, Delivery Order D0200390057. Portions of this work draw on 

Mitretek Sponsored Research on Biometric Fusion conducted in 2004-2005. 

We are grateful to a number of colleagues for their reviews and comments on earlier drafts of these documents, 

including Elham Tabassi and Patrick Grother (NIST); George Kiebuzinski, Larry Nadel, Harold Korves, and 

Shahram Orandi (Mitretek); and Harris Ulery. 

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Studies of Biometric Fusion 

1 Introduction 

Biometric fusion is the use of multiple types of biometric data, or methods of processing, to improve the 

performance of biometric systems. One type of fusion is score-level fusion, which is the combination of 

matcher scores to improve accuracy. The scores used in fusion can be obtained through the use of 

multiple types of data for each subject (such as face and fingerprint, or fingerprints from different 

fingers), multiple samples from each subject, multiple matchers on a single type of data, or combinations 

of these. 

The studies described in this report had two key objectives: to evaluate the effectiveness of different 

score-level fusion techniques, and to measure the benefits of different categories of fusion on a large 

quantity of operational face and fingerprint data. The categories of fusion evaluated included multimodal (finger and face), multi-instance (multiple finger positions), multi-matcher, and multi-sample 

(multiple enrollments). 

This report summarizes the studies we conducted: the reports contained in the Appendices include much 

more complete background information, details of techniques, and details of the experiments. 

2 Data 

The primary test dataset was NBDF06 (NIST Biometric Data Fusion 2006). NBDF06 contains operationally 

collected law enforcement data from approximately 187,000 subjects. At each encounter with a subject, 

one set of segmented slap fingerprints from all fingers and one face image (mugshot) was collected. 

NBDF06 includes data from one encounter with 122,000 subjects, two encounters with 60,852 subjects, 

and three encounters with 4,015 subjects. We refer to the 122,000 subjects without mated faces or 

fingerprints as imposters, and the 64,867 subjects with mates as genuine subjects. Rolled fingerprints 

were not used in this study. Appendix A describes in detail the derivation of genuine and imposter 

scores. 

2.1 Face Images 

The face images used are frontal, 24-bit color JPEG images compliant with ANSI/NIST-ITL 2000 image 

format specifications; the images are compliant with Best Practice Application Level 30 requirements 

[MugshotBP] except for size: image size is typically 384 x 480 pixels, smaller than the 480 x 600 minimum 

mandated by the Best Practices document. The images have controlled 3-point lighting, 18% gray 

backgrounds (with some exceptions), and uniform full frontal pose. The face occupies approximately 50% 

of the width of each image. The expressions are not controlled. A visual review of a sample of the face 

images shows that the images are fairly typical of recent mugshot photographs, and better than some 

databases such as BCC or US-VISIT (POE). 

2.2 Fingerprints 

NBDF06 contains slap livescan fingerprints from all ten fingers that were collected on FBI-certified 

livescan devices [FBI-Cert]. The devices used 2 to 2.5 inch high platens, smaller than the 3 inch platens 

required by the identification slaps standard [EFTS 7.1: Appendix F]. The thumbprints were collected as 

separate images. The four-finger slap images were segmented into individual fingerprint images using 

the NIST segmenter [NFIS]. Automated measures were used to identify probable segmentation failures, 

notably cases in which four fingerprints were not present or segmentation boxes touched or overlapped; 

20 July 2006 3/22 
Studies of Biometric Fusion 

these cases, comprising approximately 5% of the source data, were excluded from the dataset. It would 

not be quite correct to regard these exclusions as failures to enroll (FTE) for several reasons: 

• These were probable segmentation failures, which are distinct from failures to enroll: failure to 

segment indicates a problem with the association of an individual fingerprint image with its finger 

position, and does not imply anything about the quality or content of the fingerprint features. 

• Today, slap segmentation is required at the time of collection in order to be compliant with FBI 

standards [EFTS 7.1: Appendix N] for identification slaps, which mandates larger scanner platen 

sizes and segmentation at the time of capture. The cases excluded in this evaluation presumably 

would have been flagged for recapture at the time of collection if the collection process included slap 

segmentation. 

The dataset as tested should be expected to contain some incorrectly segmented fingerprints, although 

small samples of manually inspected fingerprints (ones that resulted in low matcher scores) did not 

reveal segmentation failures; see [SlapSeg] for an evaluation of segmentation accuracy and a discussion of 

issues in slap segmentation. 

Figure 1 shows the distribution of fingerprint quality for the NBDF06 fingerprint data, using the NFIQ 

metric [NFIQ; NFIS]. 1.3% of all fingerprints were NFIQ 5; 4.8% were NFIQ 4 or 5. 

NFIQs for all NBDF06 fingerprints

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

RT LT RI LI RM LM RR LR RL LL Worst

(all 10)

Best 

(all 10)

Best 

(RSlap)

Best 

(LSlap)

5 (worst)

4

3

2

1 (best)

Figure 1: NFIQ results for all genuine and imposter fingerprints, including the best and worst from 

each subject, and best for each slap from each subject. 

2.3 Matchers 

Three fingerprint and three face matchers were used: 

• The fingerprint matchers were three of the more accurate fingerprint matchers identified in the NIST 

SDK single finger and two-finger tests [SDK; SDK2]: matcher H, matcher I, and matcher Q. Single20 July 2006 4/22 
Studies of Biometric Fusion 

finger 1:1 matching accuracy for the fingerprint matchers ranged from a true accept rate (TAR) of 93 

to 99.5% (depending on the finger position and matcher) at a false accept rate (FAR) of 10-4. 

• The face matchers were three recent (c. 2004-5) commercially available face recognition systems, 

referred to here as A, B, and C. One-to-one matching accuracy for the face matchers ranged from a 

TAR of 72 to 78% (depending on the matcher) at a FAR of 10-4. 

2.4 Data Integrity 

Precise measurement of very small error rates on large datasets requires a detailed analysis of the data for 

potential data integrity issues, such as unconsolidated records (one person with records under different 

identifiers), misidentified records (records from different people using the same identifier), and swapped 

and repeated fingerprints (positionally mislabeled). Such issues are often due to collection problems or 

administrative errors; see [DataQuality] for a full discussion. 

In [FpVTE] and [SlapSeg] we found that fusion can be used effectively to detect possible data integrity 

errors, a process that we continued here. Redundant data (faces and multiple fingers) and multiple 

accurate matchers provide a basis for locating problems which can then be reviewed manually. To 

automate detection, metrics were developed based on two methods: score-level fusion and Mahalanobis 

analysis (which identifies outliers in the score data). Both methods were effective at identifying subject 

pairs that were misidentified as genuines. Mahalanobis analysis readily revealed partial errors, such as 

swapped thumbs of subjects whose fused scores were high because the face or other fingerprints 

matched. Manual review was conducted of cases flagged as potential data integrity errors. 

Among the 64,867 genuine subjects, we found 33 data integrity problems (0.051%): 24 had face and 

fingerprints misidentified (0.037%), and 9 had some but not all fingerprints swapped or repeated 

(0.014%). This means that a false reject rate (FRR) smaller than 0.037% is not generally possible (except 

when FAR approaches 1), and that FRR less than 0.051% is possible only when fusion tolerates these 

errors due to using additional fingerprints or face images that were not misidentified. Among all 186,867 

subjects, no unconsolidated records were detected in our analysis of this dataset. This is not surprising, as 

each non-mate (impostor) was compared to only one subject in the gallery — i.e., a full similarity matrix 

was not produced. Among the very low-scoring genuines manually reviewed, an additional 46 subjects 

(0.071%) had some or all fingerprints noted as egregiously poor quality. 

The detected data integrity errors were not removed from the data shown in this report. 

20 July 2006 5/22 
Studies of Biometric Fusion 

3 Score-Level Fusion Techniques 

Score-level fusion involves the combination of scores from two or more sources. Figure 2 shows an 

example of the univariate matcher score distributions (at bottom and at left), and how the joint 

distribution (scatterplot) enables greater discrimination between genuines and imposters. Each orange 

line corresponds to a decision threshold based on the unfused scores, which in this case fails to 

discriminate between the imposters and many genuines. This example shows linear fusion boundaries as 

well a polynomial boundary, each of which is superior to the univariate decisions. More elaborate — and 

accurate — decision boundaries follow the topology of the intersecting genuine and imposter 

distributions. Note that each decision boundary produces a single point on an ROC; each fusion 

technique implicitly defines a family of such boundaries from the sample data. 

Figure 2: Example of matcher score distributions, with genuines in black and imposters in red. The 

lines show examples of decision boundaries separating genuines from imposters: each such boundary 

corresponds to a point on an ROC. Note that in this chart 86% of all fingerprint genuine scores are at 

the maximum (rightmost) value. 

The presence of genuines in the upper left and lower right quadrants reveals that fusion succeeds 

primarily due to the fact that genuines are sometimes missed using one input, but can be identified using 

another input. More definitive exclusion of impostors is not the primary mechanism. This general rule 

appears to hold true for all the data studied. 

This distribution in Figure 2 should not be taken as characteristic of all of the data: distributions vary 

substantially depending on the data being fused, as shown in Figure 3. 

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Studies of Biometric Fusion 

Figure 3: Examples of joint distributions comparing all face and fingerprint matchers, with genuines 

in black and imposters in red. Scale has been reduced to accentuate overall form of the distributions. 

3.1 Implemented Techniques 

In this study, we surveyed a variety of proposed methods of fusion, and selected eight for evaluation: 

• Likelihood ratio-based methods. The Neyman-Pearson (NP) lemma [Neyman-33] defines a criterion 

for the optimization of an ROC based on likelihood ratios.1 While this approach is theoretically 

optimal, implementation assumes knowledge of joint genuine and imposter distributions. In practice, 

the accuracy of an NP implementation depends on accurate modeling of the distributions. Two 

likelihood ratio-based methods were implemented: 

o Product of Likelihood Ratios, as implemented here, is based on a multi-stage modeling process: 

probability density functions were separately modeled for each genuine and impostor 

distribution, using variable bandwidth kernels, log-linear tail tapering, and specific handling of 

spikes in the distributions; likelihood ratios were computed from these models for each matcher; 

scores were transformed to their likelihood ratios, then simply multiplied. Note that all of the 

 

1 The Neyman-Pearson lemma states that optimal decision boundaries are defined by equal likelihood 

contours. These can be visualized as analogous to elevation contour lines on a topographic map. If you 1) take 

an X,Y scatterplot of genuine and imposter scores, 2) map each point in the scatterplot to the ratio of genuines 

to imposters (likelihood ratios), and 3) plot those ratios in the Z dimension, then the Neyman-Pearson lemma 

states that the topological contours that follow a given “altitude” (a fixed likelihood ratio) correspond to 

optimal decision boundaries. 

20 July 2006 7/22 
Studies of Biometric Fusion 

complexity in this implementation is in the modeling of distributions, rather than fusion per se, 

and that use of the univariate (not joint) distributions makes the simplifying assumption that 

fused scores are independent. 

o Logistic Regression is a standard statistical technique that directly models the likelihood ratio. 

Successful implementation requires accurate curve fitting of density distributions, which requires 

statistical expertise, but is supported by typical statistical packages: the log of the 

genuine/imposter density ratio is modeled (e.g. as a low-order polynomial function), then 

estimated from the training data by principle of maximum likelihood; density ratios are modeled 

independently for each matcher, and fusion is performed by adding the normalized scores (log 

likelihoods). Logistic Regression generally uses joint sample data. In this analysis, however, the 

independence assumption was highly effective, and various trial models showed that coefficients 

for carriers involving multiple scores were almost always statistically insignificant, so our models 

relied exclusively on univariate distributions. 

• FAR-based methods. In cases when the genuine distribution is unavailable or unreliable, scores can 

be normalized by transformation to False Accept Rates (using only the univariate imposter 

distributions) before fusion. However, correctly modeling the imposter distribution usually remains a 

complex process. In our implementations, FARs were modeled using the same processes used in 

Product of Likelihood Ratios. The techniques we implemented were Product of FARs, Min of FARs, 

and Max of FARs. Min and Max methods are decision-level fusion: Min is AND rule decision-level 

fusion, and Max is OR rule decision-level fusion (where decision thresholds are set to result in equal 

FARs). 

• Linear methods. These involve addition of weighted scores. The methods we implemented do not 

require modeling of score distributions. 

o Simple Sum of Raw Scores assumes the inputs have comparable scale, distribution, and strength 

— which is only a valid assumption in some cases, such as fusion of left and right index fingers 

scored by one matcher. 

o Simple Sum of Z-Normalized Scores requires only small samples of univariate imposter 

distributions to perform normalization. Scores are normalized to a mean of 0 and standard 

deviation of 1, then added without weighting. 

o Best Linear is a weighted sum of z-normalized scores. The weights are based on an optimal slope 

(hyperplane) determined empirically on joint training data. This solution entails iteratively 

rotating the decision boundary and evaluating TAR at a fixed FAR. This is conceptually simple 

and does not require modeling, but does require joint training data. 

It is critical to note that the effectiveness of Product of Likelihoods, Logistic Regression, and the FARbased techniques depends greatly on how well the distributions are modeled. 

3.2 Evaluation of Techniques 

Figure 4 compares the performance of these techniques on several fusion tasks. 

20 July 2006 8/22 
Studies of Biometric Fusion 

0.001

0.01

0.1

1

R+L Index (H) R+L Index (I) Finger + Face

(H+C)

Finger + Face

(I+A)

Finger + Face

(Q+B)

R Index (H+I) R Index (H+Q)

False Reject Rate at FAR=10-4

Product of Likelihood Ratios

Logistic Regression

Product of FARs

Best Linear

Sum of Z-norm Scores

Max of FAR

Sum of Raw Scores

Min of FAR

Unfused data

Figure 4: Eight techniques compared at FAR=10-4 on a variety of fusion tasks. The legend shows 

techniques in order of average performance for this data. 

In general (summarizing a much broader set of results than shown on this chart), we found: 

• Product of Likelihood Ratios was consistently most accurate, but most complex to implement. 

• Logistic Regression, Product of FARs, and Best Linear usually performed nearly as well as Product of 

Likelihood Ratios. 

• Sum of Z-Normalized Scores performs well in the multi-instance tasks. 

• Max of FARs performs near the top. This is notable because this is essentially decision-level fusion, 

countering expectations that decision-level fusion would not be effective. 

• Sum of Raw Scores makes simplifying assumptions that rarely hold except in the case of single 

matcher, multi-instance tasks. 

• Min of FARs performs poorly. 

• The distinctions between techniques were most pronounced for multi-modal tests (finger and face), 

where the potential improvement was great and the distributions highly dissimilar. 

Figure 5 and Figure 6 show examples of ROCs for sample tests. 

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Studies of Biometric Fusion 

Figure 5: Comparison of ROCs for the implemented techniques, for an example test of multi-modal 

fusion. Logistic Regression was not included in this series of tests. The Face and Min of FAR graphs 

are superimposed. Due to the scale, little of the unfused face and fingerprint ROCs are visible on this 

chart: face (A) had a TAR=0.720 at FAR=10-4; right index (I) had a TAR=0.981 at FAR=10-4. 

20 July 2006 10/22 
Studies of Biometric Fusion 

Figure 6: Comparison of ROCs for the implemented techniques, for an example test of multi-modal 

fusion. Logistic Regression was not included in this series of tests. 

3.3 Considerations in the Choice of Techniques 

The choice of fusion techniques cannot just be governed by overall accuracy. The different fusion 

techniques — as implemented — have substantially different requirements in the quantity and type of 

training data, the expertise required, and the complexity of modeling. Table 1 summarizes these 

requirements. 

 

Data required 

Statistical 

expertise 

required 

Complexity 

(As implemented) 

Product of Likelihood Ratios Univariate Genuine and Imposter Yes High 

Logistic Regression Univariate Genuine and Imposter Yes Medium 

FAR-based methods Univariate Imposter Yes High 

Best Linear Joint Genuine and Imposter No Medium 

Sum of Z-Normalized Scores Univariate Imposter (small amount) No Low 

Sum of Raw Scores None No None 

Table 1: Summary of data and modeling requirements for fusion techniques 

4 Results of Experiments 

We conducted experiments to measure the benefits of different categories of fusion on the NBDF06 

dataset. The categories of fusion evaluated included multi-modal (finger and face), multi-instance 

(multiple finger positions), multi-matcher, and multi-sample (multiple enrollments). Product of 

20 July 2006 11/22 
Studies of Biometric Fusion 

Likelihood Ratios was used as the fusion technique unless otherwise noted. Except for the multi-sample 

experiments, the results described here all use 64,867 genuines and 122,000 imposters. 

4.1 Multi-Modal: Face and Fingerprint Results 

Score-level fusion of face and a single fingerprint is consistently very effective, as shown in Figure 7. Face 

and fingerprint data are nearly independent: the fused line is very close to — but still separable from — 

the independent chimera2 line. Some evaluations use chimeras for test data, when it is not possible to use 

face and fingerprint data collected from the same individuals; these results show that the independence 

assumption implicit in the use of chimeras will often be a valid approximation. 

Effect of Face and Single-Finger Fusion

0.001

0.01

0.1

1

L.Little L.Ring L.Middle L.Index L.Thumb R.Thumb R.Index R.Middle R.Ring R.Little

False Reject Rate at FAR=10-4

Face + Finger Chimeras

Face + Finger

Finger only (H)

Face only (A)

Figure 7: Effect of fusing face and single fingerprint scores for each finger position, using face matcher 

A, fingerprint matcher H and Product of Likelihood Ratios fusion. The fusion (blue) line shows the 

effect of fusing face (red) and fingerprint (green). The chimera (pink) line shows the effect of fusing 

face scores from one subject and fingerprint scores from another — this result indicates what the effect 

would have been if the face and fingerprint scores were independent. 

Table 2 summarizes the effect of fusion for all single fingerprint and face fusion experiments, given all ten 

finger positions, three fingerprint matchers, and three face matchers. The results are measured as 

reduction of false reject rate for a fixed false accept rate. Note the uniformity of results: fusing face and 

single fingerprint scores always reduced FRR by more than half, and usually by 75%. 

 

2 Chimeras are composites of data representing virtual “subjects” that combine biometrics from multiple 

individuals (selected at random). 

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Studies of Biometric Fusion 

 Single finger + face 

 H+face I+face Q+face 

Min 68% 71% 64%

Median 74% 76% 75%

Average 74% 77% 74%

Max 80% 84% 79%

Table 2: Summary of fusion of each of the ten fingers against each of the three face matchers, in terms 

of reduction in FRR where FAR = 10-4, relative to the stronger of the inputs. 3 

4.2 Multi-Instance: 2-Fingerprint Results 

Score-level fusion of two fingerprints is very effective, as shown in Figure 8. Note however, that 

fingerprint scores from different fingers are not independent: the distance between the fused and chimera 

lines shows that dependence substantially limits the benefits of fusion. 

Effect of Fusing Corresponding Fingers from Right and Left Hands

0.0001

0.001

0.01

0.1

1

Thumb Index Middle Ring Little

False Reject Rate at FAR = 10-4

Right+Left Chimeras

Right+Left

Right (H)

Left (H)

Figure 8: Effect of fusing scores for two corresponding fingerprints from right and left hands (matcher 

H, Product of Likelihood Ratios fusion). The fusion (blue) line shows the effect of fusing right (red)

 

3 For example, when fusing Left Thumb and Right Index, FRRLT=0.0055, FRRRI=0.0155 and the fused 

FRRLT*RI=0.0007, then the improvement in FRR = (min(0.0055, 0.0155) – 0.0007)/ min(0.0055, 0.0155) = (0.0055-

0.0007)/0.0055 = 87%. This metric was computed at FAR = 10-4, but was not highly sensitive to this operating 

point. 

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Studies of Biometric Fusion 

and left (green) fingerprint scores. The chimera (pink) line shows what the effect would have been if 

the face and fingerprint scores were independent. 

Table 3 summarizes the effect of fusion for all combinations of two distinct fingerprints, given all ten 

finger positions, and three fingerprint matchers. The results are measured as reduction of false reject rate 

for a fixed false accept rate. On average, fusing two fingerprint scores results in about the same 

improvement in accuracy as fusing face and fingerprint scores: 77% rather than 75%. However, these 

results have more variability than the face + fingerprint results shown above in Table 2: 48-90% rather 

than 64-84%. This variability reflects matcher accuracy and varying levels of score correlation among 

pairs of finger positions. 

 Two fingers 

 

H 

fingers 

I 

fingers 

Q 

fingers 

Min 59% 48% 51%

Median 83% 79% 72%

Average 82% 78% 71%

Max 90% 90% 84%

Table 3: Summary of fusion for all 45 pairwise combinations of fingers, in terms of reduction in FRR 

where FAR = 10-4, relative to the stronger of the inputs. 

Table 4 summarizes the results of [SDK2] using the same metrics. Those results correspond closely to 

ours. 

2-finger SDK Report 

Min 58%

Median 80%

Average 77%

Max 89%

Table 4: Summary of two-finger fusion results from [SDK2]4 , in terms of reduction in FRR where FAR 

= 10-4, relative to the stronger of the inputs. (Based on index finger results from ten matchers and four 

datasets, using simple sum of raw scores.) 

4.3 Multi-Instance: N-Fingerprint Results 

Figure 9 shows the results of fusing fingerprint scores in various combinations, using each of the three 

fingerprint matchers. Since these results exceed an FRR of 0.001, we show the data integrity limits 

discussed in Section 2.4: the upper line is the 0.037% limit due to the 24 subjects with face and fingerprints 

misidentified (0.037%), and the lower line is the 0.051% limit including the additional 9 subjects with 

some swapped or repeated fingers. The upper line is a hard limit; the lower line may be a limit 

depending on which fingers are used. 

 

4 Derived from Tables 3 and 6 in [SDK2]. 

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Multifinger Fusion

Fingerprint matchers H, I, Q

0.0001

0.0010

0.0100

0.1000

1.0000

R.Little

R.Index

R.Thumb

R.Middle, R.Ring

R.Index, R.Middle

R.Index, L.Index

R.Index, R.Middle,

R.Ring

R Slap

R.Thumb, R.Index

R.Thumb, R.Little

Both Thumbs

Both Thumbs &

Both Index

8 Fingers (No

thumbs)

All Fingers

FRR at FAR=10-4

Fingers (H)

Fingers (I)

Fingers (Q)

Data Integrity Limits

Figure 9: Fusion of various groupings of multiple fingers, showing data integrity limits (based on the 

number of known database errors) for fingerprint matchers H, I, & Q and Product of Likelihood 

Ratios fusion. 

A number of conclusions may be drawn from these results: 

• It is an oversimplification to say that fusing more fingers improves accuracy. The combinations of 

fingers used are at least as important as the number of fingers used. 

• Thumbs are substantially more effective than the other fingers: 

o Thumbs offer as much performance advantage over index fingers as index fingers offer over little 

fingers. Two thumbs are much more accurate than two index fingers. 

o A four-finger slap is approximately as effective as a thumb and any other finger. 

• For Matchers H and I, the combination of both thumbs and both index fingers reaches the data 

integrity limit. Note this combination has one fingerprint from each of the four images captured in a 

full set of slap fingerprints. In some experiments, the combination of both thumbs and one other 

finger reached the data integrity limit. 

• As more inputs are fused and accuracy approaches 100%, the maximum achievable accuracy is 

limited by data integrity problems (misidentifications, swapped prints, missing images). 

The primary reason that accuracy is sensitive to specific combinations of fingers is because of correlations 

between fingerprint scores. Figure 10 shows correlations between genuine scores for one fingerprint 

matcher. Note the correlations between neighboring fingers, among the four fingers collected in each 

slap, and between corresponding fingers on right and left hands (faint diagonal from top right to bottom 

left). Some of these correlations are specific to the way that these fingerprints were collected: if both 

20 July 2006 15/22 
Studies of Biometric Fusion 

thumbs were captured in a single image, they would be more correlated; if the fingers were collected 

separately rather than in a single slap image, they would be less correlated. 

Figure 10: Correlations between genuine scores for Matcher I by finger position — left little (ll) to 

right little (rl). Darker colors represent higher correlations. Values range from 0.17 to 0.47 (ignoring the 

identity diagonal). 

4.4 Multi-Instance/Modal: N-Fingerprint and Face Results 

Figure 11 shows the effect of adding face to the results shown above in Figure 9. Combining face with 

fingers is beneficial in all cases, although the relative benefit of adding face decreases as FRR approaches 

the data integrity limit. 

20 July 2006 16/22 
Studies of Biometric Fusion 

Multifinger and Face Fusion

Fingerprint matcher H; Face matcher C

0.0001

0.0010

0.0100

0.1000

1.0000

R.Little

R.Index

R.Thumb

R.Middle, R.Ring

R.Index, R.Middle

R.Index, L.Index

R.Index, R.Middle,

R.Ring

R Slap

R.Thumb, R.Index

R.Thumb, R.Little

Both Thumbs

Both Thumbs &

Both Index

8 Fingers (No

thumbs)

All Fingers

FRR at FAR=10-4

Fingers (H) + Face (C)

Fingers (H)

Face (C)

Data Integrity Limits

Figure 11: Fusion of various groupings of fingers, with and without face. This uses fingerprint matcher 

H and face matcher C, the most effective combination. (Product of Likelihood Ratios fusion) 

4.5 Multi-Matcher Results 

We evaluated the effect of fusing scores from multiple matchers, given the same input samples. Table 5

shows that for pairs of fingerprint matchers at fixed FAR=0.0001, FRR was generally reduced by 8-33%, 

varying by finger position; for pairs of face matchers, FRR was reduced by 10-13%. 

Face Fingerprint 

 H+I H+Q I+Q 

Min 10% 14% 8% 9%

Median 10% 25% 20% 20%

Average 11% 25% 16% 20%

Max 13% 33% 32% 32%

Table 5: Reduction in FRR where FAR = 10-4, for pairwise matcher fusion using the Product of 

Likelihood Ratios technique. Fingerprint results are for all ten finger positions. Face results 

summarize the three pairwise combinations of matchers. 

Figure 12 and Figure 13 show the effect of three-way matcher fusion. 

 

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Figure 12: Fusing all three face matchers reduced FRR by 20% relative to Matcher C (at FAR=10-4). 

Note that much of the benefit at high FAR (between 1 and 10-1) is directly due to Likelihood Ratio 

normalization of Matcher A, not fusion.5

Figure 13: Fusing all three matchers on left index fingers reduced FRR by 17% relative to Matcher H (at 

FAR=10-4). 

 

5 In some cases, normalization of scores by transformation to likelihood ratios improves ROC performance 

even without fusion. Face matcher A is a case in point, due to a spike in the genuine distribution at the 

minimum score value, which translates into a vertical drop at FAR=1. A similar effect but to a lesser extent 

occurs for fingerprint matcher I in Figure 13. 

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Matcher fusion often does produce a substantial increase in accuracy, although typically much less than 

that for multi-instance or multi-modal fusion. This should be expected due to the greater degree of data 

independence for instance and modal fusion. Since single-instance multi-matcher fusion uses the same 

data for both (or all) matchers, the independent information that is necessary for effective fusion must 

come from differences (if any) between matchers. Thus any improvements in accuracy reflect differences 

in the matchers that might be exploited either through score-level fusion or further improvement of 

existing matcher technology. 

4.6 Multi-Sample Results 

A multi-sample biometric system uses more than one sample from each biometric instance, such as 

multiple fingerprint images from each of a person’s fingers. Multi-sample fusion from the use of multiple 

enrollments is likely to be of interest since it leverages existing data rather than requiring the collection of 

additional data. Therefore the cost and complexity of implementing this form of multi-sample fusion is 

likely to be much less than that of multi-modal or multi-instance fusion. The method used in this study 

was to measure how accuracy would be affected if a gallery retained two fingerprint samples per finger 

position per subject rather than just one. 

NBDF06 includes 4,015 subjects with three fingerprint sets each. The fingerprint sets were captured in 

different collection encounters, on different dates. The mated (genuine) multi-sample data used in this 

analysis was comprised of the three segmented slap fingerprints per finger position for each of these 

4,015 subjects. The non-mated (imposter) multi-sample data consists of 396,210 subject pairs selected from 

among the off-diagonal scores of the similarity matrices. The matchers used were the H, I, and Q 

fingerprint matchers. As the fused scores have the same score distribution (same finger, same matcher), 

they were fused by Simple Sum of Raw Scores (and by Max of Raw Scores, which produced essentially 

the same results). 

Figure 14 shows the effect of multi-sample fusion: FRR was reduced by about half. 

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Figure 14: Example of effects of multi-sample fusion, for matcher I, left middle fingers. 

Table 6 shows summary results of multi-sample fusion for all finger positions, by matcher. The 

improvement in FRR ranged from 45% to 72%.

 H I Q 

Min 53% 49% 45%

Median 57% 56% 52%

Max 70% 72% 57%

Table 6: Effect of multi-sample fusion, using Raw Sum of Scores technique, in terms of reduction in 

FRR at FAR=10-4, relative to the stronger input. Results for each matcher are computed over all ten 

finger positions. 

5 Conclusions 

Eight score-level fusion techniques were implemented and evaluated. These differed in effectiveness, in 

the types of training data required, and in their requirements for modeling genuine and imposter 

distributions. 

• The most effective fusion techniques were Product of Likelihood Ratios and Logistic Regression, 

which are implementations of the theoretically optimal Neyman-Pearson Lemma. Product of 

Likelihood Ratios involved complex, detailed modeling of score distributions. Logistic Regression 

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achieved similar results using a standard statistical technique. Both techniques require statistical 

tools, training, and a substantial amount of training data. 

• Techniques that were nearly as effective were product of FARs and Best Linear. Product of FARs 

requires modeling the non-mated (imposter) distribution, but does not require mated (genuine) data. 

Best Linear is a conceptually simple technique that requires joint training data, but does not require 

modeling of distributions. 

• For cases in which the input scores are of similar strengths and distributions, such as fusing two 

index fingers using a single matcher, the choice of fusion technique had minimal effect on accuracy. 

A variety of fusion experiments using face and fingerprint data were conducted, using the most accurate 

of the techniques we implemented, Product of Likelihood Ratios. The baseline performance of biometric 

systems is largely determined by matcher accuracy and sample quality. The number of fused scores, the 

extent to which those scores are correlated, and the fusion techniques used determine the additional 

benefits of fusion. As more inputs are fused and accuracy approaches 100%, the maximum achievable 

accuracy is limited by data integrity problems (such as misidentifications or swapped or repeated 

images). Fusing scores from at least three or four separately collected samples (finger instances and/or 

face) largely eliminates the effect of poor image quality. 

• Multi-modal score-level fusion (face and fingerprint) was consistently highly effective, because the 

face and fingerprint matching scores are nearly independent. Fusing matcher scores from one 

fingerprint and face resulted in a 64-85% reduction in 1:1 false reject rate at a constant false accept rate 

of 0.0001. For example, an improvement of false reject rates from 1.0% (using fingerprints) to 0.25% 

(using face in addition) is a 75% reduction in false reject rates. Improved face image quality should be 

expected to result in further accuracy improvements. 

• Multi-instance score-level fusion (using fingerprints from multiple fingers) was consistently highly 

effective. Fusing two fingerprints resulted in a 48-90% reduction in false reject rate at a constant false 

accept rate of 0.0001. The accuracy of multi-fingerprint fusion is dependent on which fingers are 

used, the number of fingers, and the correlations of the fingerprint scores. Example findings: fusing 

of scores from a thumb and any other finger was as effective as fusing the scores from four fingers on 

one hand (slap); the maximum possible accuracy on this dataset (0.05% false reject rate, at a false 

reject rate of 10-4) could be achieved using both thumbs and one other finger. Fusion of scores from 

two fingers was about as accurate as fusion of scores from face and one fingerprint; fusion of scores 

from a four-finger slap was not as accurate as fusion of scores from face and two fingerprints. 

• Multi-sample score-level fusion, such as from the use of multiple enrollments, was consistently 

effective. The use of single-finger gallery samples from two enrollments rather than a single 

enrollment resulted in a 45-72% reduction in false reject rate at a constant false accept rate of 0.0001, 

using Sum of Raw Scores fusion. Multi-sample fusion may be of interest since it leverages existing 

data rather than requiring the collection of additional data. 

• Multi-matcher score-level fusion, using two matchers on the same data, was much less effective than 

the other methods, but may be of interest since it does not require the collection of additional data. A 

10-13% reduction in false reject rate was achieved at FAR= 0.0001 by fusing scores from two face 

matchers; an 8-33% reduction was achieved using fingerprint matchers. 

Although score-level fusion has clearly been shown to be effective, this does not necessarily mean that 

fusion can be successfully implemented in every situation. The extent to which the benefits of fusion can 

be realized in practice depends on 

• The availability of multi-biometric data and/or multiple matchers 

• The accuracy of the matchers 

• The correlation of the scores 

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• The representativeness and quantity of training data 

• A detailed understanding of score distributions 

• How fusion is implemented (e.g. the choice of fusion technique, details of its implementation, and its 

role in the system architecture) 

6 References 

[DataQuality] A. Hicklin and R. Khanna; “The Role of Data Quality in Biometric Systems”; 

February 2006; http://www.mitretek.org/Role_of_Data_Quality_Final.pdf 

[EFTS-7.1] Federal Bureau of Investigation, Criminal Justice Information Services (CJIS); 

Electronic Fingerprint Transmission Specification (EFTS); IAFIS-DOC-01078-7.1; May 

2, 2005. http://www.fbi.gov/hq/cjisd/iafis/efts71/cover.htm 

[FBICert] “Products Certified For Compliance with the FBI's Integrated Automated Fingerprint 

Identification System Image Quality Specifications”; 

http://www.fbi.gov/hq/cjisd/iafis/cert.htm 

[FpVTE] C. Wilson, A. Hicklin, H. Korves, B. Ulery, M. Zoepfl, M. Bone, P. Grother, R. 

Micheals, S. Otto and C. Watson; “Fingerprint Vendor Technology Evaluation 2003”; 

NIST Interagency Report 7123. June 2004. http://fpvte.nist.gov/ 

[MugshotBP] “Best Practice Recommendation for the Capture OF Mugshots”; Version 2.0; 

September 23, 1997. (http://www.itl.nist.gov/iad/894.03/face/bpr_mug3.html ) Note: 

this is identical to “Best Practice Application Level 30” in the forthcoming 

ANSI/NIST ITL-1 2006 standard. 

[Neyman-33] J. Neyman and E. S. Pearson; “On the problem of the most efficient tests of statistical 

hypotheses”; Philosophical Transactions of the Royal Society, Series A, Containing 

Papers of a Mathematical or Physical Character, 231, p. 289-337; 1933. 

[NFIQ] E. Tabassi, C. Wilson, and C. Watson; “Fingerprint Image Quality”; NIST Interagency 

Report 7151, August 2004. (http://fingerprint.nist.gov/NFIS/ir_7151.pdf) 

[NFIS] C. Watson, M. Garris; "NIST Fingerprint Image Software“. 

http://fingerprint.nist.gov/NFIS/ 

[SDK] C. Watson, C. Wilson, K. Marshall, M. Indovina and R. Snelick; “Studies of One-toOne Fingerprint Matching with Vendor SDK Matchers”; NIST Interagency Report 

7221; April 2005. http://fingerprint.nist.gov/SDK/ir_7221.pdf 

[SDK2] C. Watson, C. Wilson, M. Indovina and B. Cochran; “Two Finger Matching With 

Vendor SDK Matchers”; NIST Interagency Report 7249; July 2005. 

http://fingerprint.nist.gov/SDK/ir_7249.pdf 

[SlapSeg] B. Ulery, A. Hicklin, C. Watson, K. Kwong; “Slap Segmentation Evaluation 2004”; 

NIST Interagency Report 7209. March 2005. 

http://fingerprint.nist.gov/SlapSeg04/ir_7209.pdf 

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