Studies of Biometric Fusion 

Appendix B 

Effectiveness of Score-Level Fusion 

Brad Ulery,1 Austin Hicklin,1 Peter Hallinan,2 Craig Watson,3 William Fellner1

1 Mitretek Systems 

2 Independent consultant to Mitretek Systems 

3 National Institute of Standards and Technology 

20 July 2006 

Abstract 

This three-part appendix contains the results of experiments measuring the effectiveness of different categories of 

fusion: multi-modal (finger and face), multi-instance (multiple finger positions), multi-matcher, and multi-sample 

(multiple enrollments). 

Appendix B.1: Score-Level Fusion of Face and Multiple Fingerprints 

This is an analysis of the effectiveness of multi-modal (finger and face) and multi-instance (multiple finger 

positions) score-level fusion, focusing on the extent to which different biometric modalities and instances are 

independent, and the effect of that independence on the accuracy of fusion. It includes detailed analyses of the effects 

of fusing scores from varying combinations of fingers, and the effect of fusing face and fingerprint scores. This paper 

provides large-scale empirical evidence that score-level fusion using multiple finger positions is highly effective, as is 

fusion of fingers and face: fusing two fingerprints or one fingerprint and face generally resulted in a 50-90% 

reduction in false reject rate (FRR) relative to the stronger of the two inputs at a constant false accept rate (FAR). 

Appendix B.2: Score-Level Fusion of Multiple Matchers 

This is an analysis of the effectiveness of score-level matcher fusion, in which multiple matchers produced scores 

from comparisons of the same pairs of images. Both face and fingerprint matchers were evaluated. 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. A 10-30% reduction in missed identifications 

(relative reduction in false rejection rate) was achieved. Due to data correlation, algorithm fusion is less effective 

than either instance or mode fusion, but can still improve accuracy given limited data. 

Appendix B.3: Score-Level Fusion of Multiple Fingerprint Samples 

This is an analysis of the effectiveness of score-level sample fusion, which uses more than one sample from each 

biometric instance, such as multiple fingerprint images from each of a person’s fingers. Multi-sample fusion is of 

operational interest because it can improve matching accuracy without additional collection of data by retaining 

successfully matched probes in the gallery in addition to the originally enrolled sample. False reject rates were 

reduced by 45% to 73%. 
Studies of Biometric Fusion 

Contents 

Appendix B.1: Score-Level Fusion of Face and Multiple Fingerprints................................................................3

1 Introduction: Combining Face and Multiple Fingerprints .....................................................................4

2 Data Independence and Score-Level Fusion ............................................................................................4

3 Large-Scale Study of Face and Fingerprint Fusion using NBDF06 Data..............................................7

4 Exploratory Study of Face and Fingerprint Fusion using BSSR1 Data...............................................18

5 Discussion & Conclusions.........................................................................................................................21

Appendix B.2: Score-Level Fusion of Multiple Matchers....................................................................................23

6 Introduction: Combining Multiple Matchers .........................................................................................23

7 Previous Work ............................................................................................................................................24

8 Analysis Methods.......................................................................................................................................25

9 NBDF06 Results..........................................................................................................................................28

10 FpVTE MST Results ...................................................................................................................................32

11 Comparison of Multi-Algorithm, Multi-Instance, and Multi-Modal Performance...........................35

12 Conclusions .................................................................................................................................................37

Appendix B.3: Score-Level Fusion of Multiple Fingerprint Samples ................................................................38

13 Introduction: Multi-Sample Score-Level Fusion ....................................................................................38

14 Approach.....................................................................................................................................................39

15 Results..........................................................................................................................................................40

16 Conclusions .................................................................................................................................................41

17 References....................................................................................................................................................43

20 July 2006 2/44 
Appendix B.1: Score-Level Fusion of Face and Multiple Fingerprints 

Contents 

1 Introduction: Combining Face and Multiple Fingerprints .....................................................................4

2 Data Independence and Score-Level Fusion ............................................................................................4

2.1 Sources of Dependence.........................................................................................................................5

2.2 Examples ................................................................................................................................................6

3 Large-Scale Study on NBDF06 Data ..........................................................................................................7

3.1 Multimodal Dependencies: Face vs. Finger......................................................................................7

3.1.1 Experimental Design ............................................................................................................................................ 7

3.1.2 Results .................................................................................................................................................................. 8

3.2 Between-Hand Dependency: Finger vs. Finger ................................................................................8

3.2.1 Experimental Design ............................................................................................................................................ 8

3.2.2 Results .................................................................................................................................................................. 9

3.3 Between-Hand vs. Within-Hand Dependencies.............................................................................10

3.3.1 Experimental Design .......................................................................................................................................... 10

3.3.2 Results ................................................................................................................................................................ 11

3.4 N-Way Fusion......................................................................................................................................12

3.4.1 Experimental Design .......................................................................................................................................... 12

N-Finger Results ............................................................................................................................................................ 12

N-Finger + Face Results ................................................................................................................................................. 13

3.5 Optimal combinations ........................................................................................................................15

3.5.1 Experimental Design .......................................................................................................................................... 15

Two-finger fusion, and one-finger + face fusion.............................................................................................................. 15

Two-finger + face fusion.................................................................................................................................................. 17

4 Exploratory Study on BSSR1 Data ...........................................................................................................18

4.1 Multimodal Dependencies: Face vs. Finger....................................................................................18

4.1.1 Experimental Design .......................................................................................................................................... 18

4.1.2 Results ................................................................................................................................................................ 19

4.2 Between-Hand Dependency: Finger vs. Finger ..............................................................................20

4.2.1 Experimental Design .......................................................................................................................................... 20

4.2.2 Results ................................................................................................................................................................ 21

5 Discussion & Conclusions.........................................................................................................................21
Studies of Biometric Fusion 

1 Introduction: Combining Face and Multiple Fingerprints 

Optimizing the design of multi-biometric systems requires understanding the extent to which the 

multiple inputs or methods contribute additional, complementary information to the decision making 

process. Much of the effectiveness of fusion depends on the extent to which different biometric modalities 

and instances are independent. 

This paper investigates four questions: 

Q1 To what extent are face and fingerprint scores independent? 

Q2 To what extent are fingerprint scores from different fingers independent, and does a law of 

diminishing returns govern the number of fingers to use? 

Q3 What are effective combinations of fingerprint and face biometrics to fuse? 

Q4 Is it reasonable to train and/or evaluate biometric systems on chimeras? 

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

individuals. Chimeras are often used in evaluations that lack sufficient real data. For example, an 

evaluation that has fingerprint data from one set of subjects and face data from another set of subjects 

may choose to treat the data as if the faces and fingerprints came from the same individuals. The 

assumption behind the use of chimeras is that face and fingerprint data are fully independent. 

In this study, we used chimeras for a different purpose: to measure the extent of data independence. We 

first measured fusion performance in the standard way, so that each set of face and fingerprints all 

originated from a single subject. We then determined what the effect of fusion would be if the fused 

biometric scores were independent by using chimeras, created by associating the face and fingerprints of 

different people. By comparing the chimera results to the actual results, we could determine the extent of 

data independence. 

To answer the four questions, we conducted two studies: we first conducted a small-scale, exploratory 

study on the NIST BSSR1 public domain data set, then used the lessons learned to conduct a large-scale 

study on the NBDF06 dataset. We include the results of both studies because they involve different 

datasets and matchers: the BSSR1 data is publicly available; and the large NBDF06 dataset allowed much 

more precise measurements. 

Datasets and experimental design are discussed in Appendix A. Unless otherwise noted, all experiments 

used Product of Likelihood Ratios as the fusion technique, which was the most accurate of the techniques 

we implemented; see Appendix C for details. 

2 Data Independence and Score-Level Fusion 

Biometric score independence has been identified as an issue in the published literature, but with little 

large-scale empirical analysis. Given the general dearth of data available, researchers frequently make 

assumptions regarding the independence of data. These assumptions may be largely inconsequential for 

small empirical studies where measurement precision is limited, but can be significant to the design and 

evaluation of highly accurate systems. 

The correctness of an independence assumption has various implications: 

• Whether predictions of the benefits of fusion are valid 

• Whether the joint score data contains more information than any one score set alone (so that 

fusion has the potential to be beneficial) 

• Whether the fusion technique is well-suited to the problem (so that the potential can be realized) 

20 July 2006 4/44 
Appendix B.1 Combining Face and Multiple Fingerprints 

Corresponding to each of these implications is a distinct question regarding the validity of the 

independence assumption: 

• Does sufficient dependence exist to invalidate predictions? 

• Does sufficient independence exist to justify fusion (operational cost-benefit)? 

• Is the fusion technique sufficiently robust with respect to dependence in the data to achieve good 

results? 

In order to evaluate the validity of the independence assumption as it pertains to score-level fusion, we 

must consider that 

• Dependence is essentially a characteristic of the score data that is to be fused. Such characteristics 

can vary greatly according to the operational scenario, according to the choice of biometrics, data 

collection procedures, accuracy of matchers, etc. 

• The significance of any observed dependencies in the scores is determined by how those scores 

will be used. This includes the choice of fusion technique and operational objectives, such as 

accuracy and robustness. 

These topics are not to be confused with how data is sampled for an evaluation. For instance, in 

sampling, dependence often results from reusing subjects, as when N scores are produced by comparing 

one probe subject to N gallery subjects [FRVT, FpVTE, SDK]. Nor are we discussing cross-class 

dependencies: higher scores are assigned to genuines than to imposters. 

These topics of independence arise frequently in the literature on biometric fusion. Assumptions of 

independence are common in both empirical and theoretical works. Lacking access to large multi-modal 

(or multi-instance) datasets, many researchers have created chimerical datasets based on an assumption 

of independence [Jain-99b; Fierrez-Aguilar-03; Snelick-03; Indovina-03; Wang-03; Poh-05c; Poh-05e; 

Snelick-05]. In several cases, the researchers use chimeras while recognizing the uncertainty of the 

method. Many in the biometrics community have questioned the validity of using chimeras, e.g., [Poh05e]. 

Theoreticians (often explicitly) [Dass-05; Griffin-05; Kittler-98; Jain-05; Poh-05d; Scott-05] and analysts 

(sometimes implicitly) make independence assumptions when they develop or select fusion techniques. 

A clear example of this is the “product rule” as applied to the ratio of posterior probabilities (Product of 

Likelihood Ratios, discussed in Appendix C). 

2.1 Sources of Dependence 

In fusion, biometric inputs derive from samples that belong to the same individual, were often collected 

at one encounter (except, e.g., multi-sample gallery images), and have undergone some common 

processing. Based on these factors, the extent of independence should be expected to vary among the 

different categories of fusion: 

• Multi-modal data (such as faces and fingerprints) are generally believed to be fairly independent 

(Question 1 investigated by this study). If the different modalities are collected at a single 

encounter, they may have dependencies due to factors specific to that encounter such as quality 

problems due to a hurried subject, an uncooperative subject or an incompetent operator. 

• Multi-instance data (such as multiple fingerprints) should not be expected to be as independent 

as multi-modal data. Multi-instance data will have the encounter-specific factors mentioned 

above as well as additional sources of dependencies specific to the subject, the genetic 

relationships between fingers, and the use of a single collection device. For slap fingerprints, 

dependencies will be particularly high because of simultaneous collection. Some of the 

correlations between fingers are shown in Figure 1. Note the correlations between neighboring 

20 July 2006 5/44 
Studies of Biometric Fusion 

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). 

Figure 1: Correlations between genuine scores by finger position (left little (ll) to right little (rl)) for 

slap fingerprints from c. 65,000 subjects. Darker colors show higher correlations. Values range from 

0.17 to 0.47 (ignoring the identity diagonal).1 [NBDF06 data; Matcher I]

• Multi-sample data (such as face images from a video sequence) should be expected to be 

moderately correlated, because of sample-specific variability and subject-specific dependence. An 

analysis of multi-sample variance [Goats] showed that match scores “cannot generally be 

attributed to intrinsic characteristics of a person’s fingerprints, but should be attributed to 

collection problems or other characteristics of the specific fingerprints used.” Multi-sample 

analysis was not possible as part of this study at the time of writing. 

• Multi-algorithm data (such as results from different matchers on common samples) should be 

expected to be highly dependent, because the algorithms are working with the same data. The 

effectiveness of algorithm fusion depends on the independence of several factors: the biometric 

features used, the feature extraction algorithms, and the matching algorithms. (Matcher fusion is 

discussed in Appendix B.2) 

2.2 Examples 

Figure 2 shows examples of two scatterplots of joint score distributions, purposely shown at small scale to 

accentuate the overall form and the effect of dependence. The plot on the left shows two modalities 

 

1 The upper right and lower left of the table are mirrors of each other: e.g. the RL column and RL row 

report the same results. 

20 July 2006 6/44 
Appendix B.1 Combining Face and Multiple Fingerprints 

(BSSR1 data); the plot on the right shows two matchers on the same sample (NBDF06 data). In these 

plots, imposter scores are shown in red; genuine scores are shown in black. 

Figure 2: Effect of data independence on scatterplots: the left figure shows essentially independent 

data (face and finger), while the right figure shows much more dependent data (the same fingerprint 

images, two different matchers). Note how the dispersion of data points decreases as dependence 

increases. Completely dependent data would form a line or curve when plotted in this way. 

[Left: BSSR1 dataset, matchers V & G; Right: NBDF06 dataset, matchers H & I, left thumbs]

3 Large-Scale Study of Face and Fingerprint Fusion using NBDF06 Data 

For this study, pairs of face and fingerprint images from the NBDF06 dataset were compared using three 

face matchers (identified as A, B, and C) and three fingerprint matchers (identified as H, I, and Q). This 

data is described in IV: Description of Datasets and Pre-Fusion Data Characteristics. The resulting matcher 

scores were combined by the Product of Likelihood Ratios method as described in Appendix C. This 

method of fusion approximates Neyman-Pearson optimization to minimize the false reject rate (FRR) at a 

specific false accept rate (FAR); it was the most effective technique among several investigated. 

Throughout this paper, results are summarized by reporting FRR at FAR=10-4. 

3.1 Multimodal Dependencies: Face vs. Finger 

This experiment tests the hypothesis that face and fingerprint scores are independent. 

3.1.1 Experimental Design 

Test subjects have one face and one finger. There are ten finger positions and nine different combinations 

of face and fingerprint matchers, so we run 90 trial sets. Each trial set contains two trials, one actual 

subject and one chimera. 

Type of Trial How score pairs are constructed Subjects / Trial Trials / 

Type 

Actual subject Pair the face score and one finger score of an 

individual . 

64,867 genuines 

122,000 imposters 1 

Chimera Pair the face score of one person with one 

finger score of another person . 

64,867 genuines 

122,000 imposters 1 

Total number of trials (per type of input pair) 2 

Table 1: Description of trials, and number of trials per set 

20 July 2006 7/44 
Studies of Biometric Fusion 

3.1.2 Results 

Figure 3 shows that for the fusion of one fingerprint with face, there is little difference in accuracy 

between actual subjects and chimeras. There is a slight advantage of chimeras over actual subjects, but 

that is small in comparison to the main effects of fusion. These results show that faces and fingerprints 

are nearly independent, and therefore, to a great extent validate the use of chimeras where the face image 

comes from one individual and the finger(s) from another for purposes of system design and evaluation. 

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 3: Finger and face fusion comparing actual finger+face fusion with finger+face chimera fusion: 

face and finger modalities are nearly independent. [NBDF06 dataset, matchers H & A]

Several additional observations can be made from Figure 3: the index, middle and ring fingers perform 

similarly, thumbs are much better, and little fingers are much worse. Note that the right fingers are 

slightly better than the left, but that the left thumbs are slightly better than the right thumbs. The 

contribution from the face modality can be seen to be essentially constant from finger to finger, as 

expected due to independence. 

3.2 Between-Hand Dependency: Finger vs. Finger 

This experiment investigates the dependencies between corresponding fingers of each hand, including all 

five possible finger pairs. 

3.2.1 Experimental Design 

Subjects have two corresponding fingers (e.g., two thumbs), one from each hand. For the chimeras, each 

finger is from a different person. There are five different types of subjects and three different matchers, so 

we run 15 trial sets. Each trial set contains two trials, one actual subject trial and one chimera trial. 

20 July 2006 8/44 
Appendix B.1 Combining Face and Multiple Fingerprints 

Type of Trial How score pairs are constructed Subjects / Trial Trials / 

Type 

Actual subject Pair the scores of corresponding right and left 

fingers of one individual . 

64,867 genuines 

122,000 imposters 1 

Chimera Pair the scores of corresponding right and left 

fingers of two distinct individuals . 

64,867 genuines 

122,000 imposters 1 

Total number of trials (per type of input pair) 2 

Table 2: Description of trials, and number of trials per set 

3.2.2 Results 

Figure 4 shows that correlations among fingerprint scores significantly limit the benefits of fusion: 

chimera finger pairs perform much better (by roughly an order of magnitude) than finger pairs from 

actual subjects. Fusing corresponding fingers from opposite hands is clearly better than using single 

fingers. Right-hand fingers yield better results than left hand fingers, except for the thumb: all three 

matchers achieve greater accuracy on left thumbs than on right thumbs on this dataset. 

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 4: Effect of fusing two corresponding fingerprints from right and left hands, using fingerprint 

matcher H and Product of Likelihood Ratios fusion. The fusion (blue) line shows the effect of fusing 

right (red) and left (green) fingerprints. The chimera (pink) line shows what the effect would have 

been if the face and fingerprint data were independent. [NBDF06 dataset, matcher H]

Figure 5 compares the finger + face data of Figure 3 to the finger + finger data of Figure 4, and reveals 

very similar accuracies for these two combinations.2 This can be explained by the fact that although the 

face is a weaker biometric than the second finger, the information it provides is nearly fully independent. 

 

2 One notable exception: the face is much more effective than the little finger. 

20 July 2006 9/44 
Studies of Biometric Fusion 

Should face matcher technology continue to improve, the balance will tip in favor of using face as a 

second biometric for greater accuracy. 

Comparison of 2-Finger and Finger+Face Fusion

0.0001

0.001

0.01

0.1

1

Thumb Index Middle Ring Little

FRR at FAR=10-4

Right+Left

Right + Face

Left + Face

Right (H)

Left (H)

Face only (A)

 

Figure 5: Comparison of 2-finger and finger + face fusion. [NBDF06 dataset, matchers H & A] 

3.3 Between-Hand vs. Within-Hand Dependencies 

This experiment tests whether between-hand dependencies (fingers from right and left hands) are weaker 

or stronger than within-hand dependencies (fingers from the same hand). 

3.3.1 Experimental Design 

If within-hand dependencies exceed between-hand dependencies then we expect the performance of a 

biometric system on fingers from the same hand (within-hand models) to be worse than its performance 

on fingers from different hands (between-hand models). As an example, within-hand dependencies 

might be caused by failure to place the hand properly on the collection device, resulting in low mate 

scores for multiple fingers. However, the question is complicated by the possibility that the result could 

differ for any pair of finger types (e.g. middle and index, or thumb and little). 

In this experiment there are 10 different combinations of fingers and three different fingerprint matchers, 

so we run 30 trial sets. Each trial set contains two within-hand models and two between-hand models. 

20 July 2006 10/44 
Appendix B.1 Combining Face and Multiple Fingerprints 

Type of Trial How score pairs are constructed Subjects / Trial Trials / 

Type 

Left-Right Pair the scores of left finger x and right finger 

y from one individual. 

64,867 genuines 

122,000 imposters 1 

Left-Left Pair the scores of left finger x and left finger y 

from one individual. 

64,867 genuines 

122,000 imposters 1 

Right-Left Pair the scores of right finger x and left finger 

y from one individual. 

64,867 genuines 

122,000 imposters 1 

Right-Right Pair the scores of right finger x and right 

finger y from one individual. 

64,867 genuines 

122,000 imposters 1 

Total number of trials (per type of input pair) 2 

Table 3: Description of trials, and number of trials per set. “x” and “y” are different fingers types (i.e. 

thumb, index, middle, ring, or little). 

3.3.2 Results 

These results show that dependencies between adjacent fingers on the same hand do substantially limit 

the benefits of fusing adjacent fingers. Nevertheless, fusing adjacent fingers is highly beneficial when 

compared to not using fusion. 

Section 3.2 showed strong effects of dependencies between two fingers, one from each hand. These 

results show that dependencies are slightly greater when the two fingers are selected from the same 

hand. Notice that, although the finger combinations differ, Figure 4 and Figure 6 can be compared by 

examining the results for Index, Middle and Ring fingers which all perform similarly. See Table 6 for 

tabular results for all pairwise combinations. 

Between-Hand vs. Within-Hand Dependencies

(Matcher H)

0.0001

0.001

0.01

0.1

1

Thumb-Index

Thumb-Middle

Thumb-Ring

Thumb-Little

Index-Middle

Index-Ring

Index-Little

Middle-Ring

Middle-Little

Ring-Little

FRR at FAR=10-4

Right & Right

Right & Left

Left & Right

Left & Left

Data Integrity Limit

 

Figure 6: Hand to Hand Correlations: fusing data from opposite hands is beneficial. 

[NBDF06 dataset, matcher H]

20 July 2006 11/44 
Studies of Biometric Fusion 

3.4 N-Way Fusion 

3.4.1 Experimental Design 

Test subjects have N-fingers, or N-fingers plus face. We use fourteen different combinations of (one or 

more) fingers and nine different combinations of matchers (3 fingerprint * 3 face). Each trial set contains 

four trials: one fingers-only trial of actual subjects, one fingers and face trial of actual subjects, one fingers 

and face chimera trial, and one “reference” trial (face only). 

Type of Trial How score pairs are constructed Subjects / Trial Trials / 

Type 

Fingers Only Combine scores of N different fingers from one 

individual. 

64,867 genuines 

122,000 imposters 1 

Fingers+Face Combine scores of N different fingers and face 

from one individual. 

64,867 genuines 

122,000 imposters 1 

Reference Face score from one individual. 64,867 genuines 

122,000 imposters 1 

Total number of trials (per finger combination) 3 

Table 4: Description of trials, and number of trials per set 

3.4.2 N-Finger Results 

Figure 7 shows the effect of fusing various combinations of fingers. The accuracy of the fused 

combinations is limited primarily by database errors (due to misidentified subjects, or swapped or 

repeated fingers). The dashed lines indicate “data integrity limits,” or the number of known database 

errors, which limit achievable performance to a TAR of approximately 0.9995. In the NBDF06 dataset, 33 

subjects out of 64,867 (0.051%) were found to have some or all of their fingers misidentified, of whom 24 

(0.037%) also have their faces misidentified: these are the two red lines. FRR can pass the 0.051% limit 

with some finger combinations, but not the 0.037% limit. Some additional data integrity errors may 

remain undetected, especially if they involve the face but not the fingerprints. The methods used to 

identify data integrity errors are described in Appendix A. 

20 July 2006 12/44 
Appendix B.1 Combining Face and Multiple Fingerprints 

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 7: Fusion of multiple fingers, showing data integrity limits (based on the number of known

database errors) — matchers H, I, & Q 

Several comments and observations can be made based on 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 4-finger slap is approximately as effective as a thumb and one 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. 

3.4.3 N-Finger + Face Results 

Figure 8 and Figure 9 show the results of N-finger and face fusion for two pairs of matchers: the other 

combinations of matchers generally lie between these two. 

20 July 2006 13/44 
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 8: Fusion of multiple fingers and multiple fingers with face, showing data integrity limits

(based on the number of known database errors) — matchers H & C

Multifinger and Face Fusion

Fingerprint matcher Q; Face matcher B

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 (Q) + Face (B)

Fingers (Q)

Face (B)

Data Integrity Limits

 

Figure 9 Fusion of multiple fingers and multiple fingers with face, showing data integrity limits

(based on the number of known database errors) — matchers Q & B

20 July 2006 14/44 
Appendix B.1 Combining Face and Multiple Fingerprints 

Combining face with the fingers is beneficial in all cases: 

• Adding face data to one or two fingers reduces FRR by nearly an order of magnitude. 

• Index+Middle+Face (or L.Index+R.Index+Face) is more effective than a 4-finger slap. 

3.5 Optimal combinations 

3.5.1 Experimental Design 

These results are similar to those of the previous subsection, but focus on the gains achieved through 

different combinations of biometrics. These results include all pairwise combinations of fingers and face, 

and some 3-way combinations. This analysis is intended to help guide the selection of specific 

combinations of biometrics. 

Type of Trial How score pairs are constructed Samples / 

Trial 

Trials / 

Type 

One Face Face score from one individual. 186,867 1 

One Finger Finger score for each of 10 different fingers from 

one individual. 186,867 10 

Two Fingers Combine scores of 2 different fingers from one 

individual. 186,867 45 

One Finger+Face Combine scores of one finger and face from one 

individual. 186,867 10 

Two Fingers+Face Combine scores of 2 different fingers and face from 

one individual. 186,867 45 

Total number of trials (per finger combination) 111 

Table 5: Description of trials, and number of trials per set 

3.5.2 Two-finger fusion, and one-finger + face fusion 

Table 6 compares the effectiveness of all 45 pairwise combinations of two fingers (matcher H), and all 30 

combinations of the three face matchers with one finger (matcher H). The top row and left column show 

the accuracy before fusion. Note the substantial improvement in every case, especially the lowest FRR 

values, which are all combinations of a thumb with another finger. Some of these results approach the 

data integrity limits (FRR≈0.0005 at FAR=10-4), meaning that 2-finger fusion sometimes approaches the 

maximum measurable accuracy for this dataset. 

20 July 2006 15/44 
Studies of Biometric Fusion 

 RT RI RM RR RL LT LI LM LR LL 

 0.0068 0.0155 0.0167 0.0155 0.0337 0.0055 0.0202 0.0241 0.0193 0.0653

R.Thumb 0.0068 

 

0.0010 

85%

0.0009 

87%

0.0007 

89%

0.0010 

85%

0.0010 

82%

0.0009 

87%

0.0008 

88%

0.0008 

88%

0.0012

82%

R.Index 0.0155 

 

0.0029 

81%

0.0022 

86%

0.0030 

81%

0.0007 

87%

0.0023 

85%

0.0018 

89%

0.0015 

90%

0.0032

79%

R.Middle 0.0167 

 

0.0046 

70%

0.0034 

80%

0.0008 

86%

0.0024 

86%

0.0037 

78% 

0.0024 

86%

0.0039

76%

R.Ring 0.0155 

 

0.0043 

72%

0.0008 

86%

0.0020 

87%

0.0030 

81% 

0.0025 

84%

0.0037

76%

R.Little 0.0337 

 

0.0010 

82%

0.0024 

88%

0.0030 

87%

0.0032 

83%

0.0101

70%

L.Thumb 0.0055 

 

0.0010 

82% 

0.0009 

83%

0.0011 

81%

0.0013

76%

L.Index 0.0202 0.0047 

77% 

0.0031 

84%

0.0046

77%

L.Middle 0.0241 

 

0.0053 

72%

0.0063

74%

L.Ring 0.0193 

 

0.0080

59%

L.Little 0.0653 

Face A 0.2800 0.0019 

72%

0.0044 

72%

0.0050 

70%

0.0039 

75%

0.0086 

75%

0.0015 

72%

0.0056 

72% 

0.0068 

72% 

0.0053 

72%

0.0189

71%

Face B 0.2237 0.0021 

68%

0.0040 

74%

0.0046 

72%

0.0039 

75%

0.0076 

77%

0.0016 

71%

0.0060 

70% 

0.0060 

75% 

0.0052 

73%

0.0170

74%

Face C 0.2119 0.0017 

75%

0.0034 

78% 

0.0037 

78%

0.0033 

79%

0.0068 

80%

0.0016 

71%

0.0049 

76% 

0.0054 

77%

0.0040 

79%

0.0146

78%

0.0010

 85%

FRR at FAR = 10-4

Reduction in FRR

Best values

Medium values

Worst values

Table 6: Comparison of FRR at FAR=10-4 for all 2-finger combinations, and combinations of all single 

fingers with the three face matchers. Percentage reduction in FRR is relative to the stronger input 

alone.3 The lowest FRR values are in blue; the highest in red. The greatest FRR reductions are in blue; 

the least in red. 

[NBDF06 dataset; matcher H and all face matchers, product of likelihood ratios fusion]

Note: 

• Pairwise fusion always improves FRR substantially, with typical gains of 70-90%. 

• 2-finger fusion usually outperforms finger+face, unless the left little finger is involved. 

• The improvement in FRR shown for finger+face often approximates the TAR for the face 

matchers involved (A: 0.72; B: 0.78; C: 0.79). This is a result of the independence of the data. 

• FRR improves most for left-right and thumb-slap combinations, and least for neighboring fingers 

and left-right little fingers. 

These same results are summarized for all matchers in Table 7. Note that the comparative performance of 

two-finger vs. face+finger reflects the choice of matchers: matcher H yields substantially more accurate 

results on two fingers than finger+face; fingerprint matcher Q is slightly less accurate on two fingers than 

finger+face. 

 

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% 

20 July 2006 16/44 
Appendix B.1 Combining Face and Multiple Fingerprints 

 Two fingers Single finger + face 

 

H 

fingers 

I 

fingers 

Q 

fingers H+face I+face Q+face 

Min 59% 48% 51% 68% 71% 64% 

Median 83% 79% 72% 74% 76% 75% 

Average 82% 78% 71% 74% 77% 74% 

Max 90% 90% 84% 80% 84% 79% 

Table 7: Reduction in FRR where FAR = 10-4, relative to the stronger of the inputs. Two fingers 

summarizes all 45 pairwise combinations; Single finger + face summarizes fusion of each of the ten 

fingers against each of the three face matchers. 

[NBDF06 dataset; all matchers, product of likelihood ratios fusion]

3.5.3 Two-finger + face fusion 

Table 8 extends these results to 3-way fusion, showing all combinations of two fingers with face, for 

matchers H and C. Note that FRR continues to reduce substantially, but the benefits have begun to 

diminish. This effect is due at least in large part to data integrity limits. Table 8 also shows presents these 

same results as a percentage reduction in FRR when adding face to 2-finger fusion.4

 RT RI RM RR RL LT LI LM LR LL 

 0.0068 0.0155 0.0167 0.0155 0.0337 0.0055 0.0202 0.0241 0.0193 0.0653

R.Thumb 0.0068 0.0038 

44%

0.0005 

44%

0.0004

51%

0.0004

50%

0.0005

44%

0.0005

49%

0.0004 

51%

0.0004 

50%

0.0005

47%

0.0006

42%

R.Index 0.0155 0.0005 

51%

0.0072 

53% 

0.0008 

53%

0.0007 

72%

0.0009 

70%

0.0004

71%

0.0008 

40%

0.0007 

65% 

0.0006 

61%

0.0009

63%

R.Middle 0.0167 0.0004 

50%

0.0008 

72%

0.0102 

39%

0.0013 

39%

0.0009 

72%

0.0005

73%

0.0009 

40%

0.0013 

64% 

0.0007 

66%

0.0010

70%

R.Ring 0.0155 0.0004 

44%

0.0007 

70%

0.0013 

72%

0.0090 

42%

0.0011 

42%

0.0004

74%

0.0008 

43%

0.0011 

59% 

0.0009 

64%

0.0009

66%

R.Little 0.0337 0.0005 

49%

0.0009 

71%

0.0009 

73%

0.0011 

74%

0.0133 

60%

0.0005

60%

0.0009 

48%

0.0008 

62% 

0.0010 

72%

0.0024

69%

L.Thumb 0.0055 0.0005 

51%

0.0004 

40%

0.0005

40%

0.0004

43%

0.0005

48%

0.0028 

49%

0.0005 

49%

0.0006 

45% 

0.0006 

42%

0.0006

48%

L.Index 0.0202 0.0004 

50%

0.0008 

65% 

0.0009 

64%

0.0008 

59%

0.0009 

62%

0.0005

45%

0.0098 

52% 

0.0016 

52% 

0.0010 

66%

0.0013

67%

L.Middle 0.0241 0.0004 

47%

0.0007 

61% 

0.0013 

66%

0.0011 

64%

0.0008 

72%

0.0006 

42%

0.0016 

66% 

0.0138 

43%

0.0014 

43%

0.0017

74%

L.Ring 0.0193 0.0005 

42%

0.0006 

63% 

0.0007 

70%

0.0009 

66%

0.0010 

69%

0.0006 

48%

0.0010 

67% 

0.0014 

74%

0.0098 

49%

0.0018

49%

L.Little 0.0653 0.0006 

49% 

0.0009 

72%

0.0010 

76%

0.0009 

76%

0.0024 

77%

0.0006 

56%

0.0013 

71%

0.0017 

73%

0.0018 

77%

0.0288

56%

Table 8: FRR at FAR=10-4 for fusion of all combinations of two fingers with face, and reduction in FRR 

(due to the contribution of face relative to two fingers only). The diagonal shows fusion of each single 

finger with face as a baseline. FRR values that reach the data integrity limit are in blue. The greatest 

FRR reductions are in blue; the least in red. 

[NBDF06 dataset; matchers H and C, product of likelihood ratios fusion] 

 

4 For example, when adding face to Left Thumb and Right Index, the 2-finger FRRLT*RI=0.000737 (from 

Table 6, but with increased precision) and the face+2-finger FRRLT*RI*Face=0.000444 (from Table 8, increased 

precision), the improvement in FRR = (0.000737 – 0.000444)/ 0.000737 = 40%0.000740.0007 43 

20 July 2006 17/44 
Studies of Biometric Fusion 

4 Exploratory Study of Face and Fingerprint Fusion using BSSR1 Data 

Prior to analyzing NBDF06, an exploratory study was conducted using data from the NIST Biometric 

Scores Set, Release 1 [BSSR1], which is described in Appendix A. It is large enough for an exploratory 

study, and has the advantage of being in the public domain, permitting comparisons with other studies. 

Figure 10 illustrates scatterplots of the genuine and imposter joint distributions of the Face(G) and Rindex(V) scores. The striking separation is characteristic of all four sets. In these scatterplots, only a 

random subsample of the 133,386 imposter scores is shown. 

Figure 10: Joint distributions of genuine (black) and imposter (red) Face(G) and R-index(V) scores 

[BSSR1 dataset; matchers G and V]

4.1 Multimodal Dependencies: Face vs. Finger 

This experiment investigates the independence of two biometric modalities: faces and fingerprints. 

4.1.1 Experimental Design 

To test the hypothesis that faces and fingerprints are independent, we compare the performance of 

biometric fusion on chimeras constructed to have independent face and fingerprint data with 

performance on actual subjects. If the ROC curve for the chimeras is not noticeably different from the 

ROC curve for real individuals, then we have evidence that face and finger scores have little codependence. 

The experiment consists of four sets of thirteen trials. Each trial involves computing the ROC curve for a 

fusion run on a test set of 517 “subjects”, each of whom has one finger and one face. Thus the input to the 

fusion algorithm is a pair of matcher scores, one for the face and one for the finger. Since there are two 

20 July 2006 18/44 
Appendix B.1 Combining Face and Multiple Fingerprints 

kinds of fingers (right and left index fingers), one fingerprint matcher (V), and two face matchers (C, G), it 

is possible to construct four kinds of score pairs: R-index(V) ⊗ Face(C), R-index(V) ⊗ Face(G), L-index(V) ⊗

Face(C), L-index(V) ⊗ Face(G). Therefore we conduct four sets of trials, one set for each kind of score pair. 

Each trial set consists of 13 trials (see Table 9). Given two sources of individual fingerprint scores (i.e. 

BSSR1 Set 1 and BSSR1 Set 2), we construct two kinds of chimeras for a total of three types of trials. 

Because there is multimodal data for only 517 individuals, the number of subjects in each trial is limited 

to 517, and there can only be one trial for real individuals. However, the number of potential chimeras is 

quite large,5 so to better distinguish real effects from sample variance, six trials are run for each type of 

chimera, with each of the six trials employing a different set of chimeras. 

In every trial, the ROC is calculated from a 517 x 517 similarity matrix of fusion scores. Face and 

fingerprint scores are fused using a weighted linear combination. Two weights are used, one for 

combining fingers with Face(C) data (266*Face + Finger), and another for Face(G) data (5*Face + Finger). 

These weights are selected to optimize TAR at FAR = 10-4. 

Type of Trial How score pairs are constructed Samples / 

Trial 

Trials / 

Type 

Actual subject Pair the face and finger scores of a single individual 

from BSSR1 Set 1 517x517 1 

Chimera 1 Pair the face and finger scores of two distinct 

individuals from BSSR1 Set 1. 517x517 6 

Chimera 2 

Pair the face score of an individual from BSSR1 Set 1 

with the fingerprint score of an individual from BSSR1 

Set 2. 

517x517 6 

Total number of trials (per type of input pair) 13 

Table 9: Description of trials, and number of trials per set 

4.1.2 Results 

The results for this experiment are captured in four plots (one per set of trials). Each plot contains 13 

fusion ROC curves, plus two benchmark (face and finger) ROC curves. Figure 11 shows results for Rindex(V) ⊗ Face(C); the other three plots are very similar. As expected, the fused ROCs substantially 

outperform the ROCs of the individual face and fingerprint matchers. Once again, no significant 

difference in the results of the real and artificial subject sets confirms a negligible correlation between face 

and fingerprint data. 

The validity of using chimeras may depend on the datasets involved, however, as interpretation of the 

charts does appear to vary by dataset. One possible explanation is that if a dataset consists of two 

subpopulations, each with distinct score distributions for fingers and faces, then that source of 

dependence would be removed through the use of chimeras. 

Several caveats should be noted: 

• These results are based on small sample sizes. 

• These results are based on only one subject population 

• These results are based on matchers that are not highly accurate: NIST VTB is far less accurate 

than the top performing fingerprint matchers [FpVTE]; the face matchers date from c. 2002. 

 

5The total number of chimera pairs that can be built from BSSR1 Set 1 is 133,386. Our 6 sample sets used 

only 12,408 of these. 

20 July 2006 19/44 
Studies of Biometric Fusion 

Figure 11: Fusion performance for Right Index fingers(VTB) and Face(C). 

[BSSR1 dataset; matchers C and V]

4.2 Between-Hand Dependency: Finger vs. Finger 

This experiment investigates the dependencies between the index fingers of each hand. 

4.2.1 Experimental Design 

For this experiment, we define a test “subject” as having one left index finger and one right index finger. 

With just one matcher available (fingerprint matcher V), only one kind of score pair is possible, and we 

run just one trial set. 

In order to distinguish real effects from sample variance, multiple ROCs are generated by partitioning the 

available data. In every case, matrices of size 1000 x 1000 are used, and each probe image has one mated 

image in the gallery. The 6 trials of actual subjects were created by partitioning the original 6000 subjects 

into 6 equal-sized sets of 1000 subjects. The 3 trials of Chimeras were created by taking left fingers from 

one subset, right fingers from another (i.e., from 3 pairs of 1000 subjects). 

Type of Trial How score pairs are constructed Samples / Trial Trials / 

Type 

Actual subject Pair the left index finger and right index finger scores 

of a single individual from BSSR1 Set 2. 1000x1000 6 

Chimera Pair the left index finger and right index finger scores 

of distinct individuals from BSSR1 Set 2. 1000x1000 3 

Total number of trials 9 

Table 10: Number of trials per type 

20 July 2006 20/44 
Appendix B.1 Combining Face and Multiple Fingerprints 

For this experiment, the fusion algorithm is a simple sum of the raw scores. This is effective because the 

score distributions for the two fingers are quite similar. 

4.2.2 Results 

The results of this investigation (Figure 12) demonstrate that an independence assumption is overly 

optimistic: the two-finger chimeras result in substantially higher accuracy than those for actual subjects, 

indicating significant dependence between right and left index finger scores. This result is not surprising 

given several known sources of dependence, as discussed in Section 2.1. The improvement in FRR is 

approximately 50%, which is much less than was measured for the same fingers on the NBDF06 dataset. 

This difference is explained by differences in matcher accuracy. 

Figure 12: Comparison of accuracy between single Left and Right fingers, 2-finger fusion for actual 

subjects, and 2-finger fusion for Chimeras. The Chimera results show what fusion performance 

would have been if the fused fingers were fully independent. 

[BSSR1 dataset; matcher V, Best Linear fusion]

5 Discussion & Conclusions 

Fusion of fingers is highly effective, as is fusion of fingers and face. Fusing two fingerprints or one 

fingerprint and face generally resulted in a 50-90% reduction in false reject rate (FRR) relative to the 

stronger of the two inputs at a constant false accept rate (FAR). 

Much of the effectiveness of fusion depends upon the extent to which different biometric modalities and 

instances are independent. In this study, chimeras were used, not of necessity due to lack of data, but as 

20 July 2006 21/44 
Studies of Biometric Fusion 

a tool for directly evaluating the effects of correlated data, and this work shows that they are extremely 

useful for that purpose. 

When estimating the benefits to finger fusion, an independence assumption is overly optimistic: twofinger chimeras result in substantially higher accuracy than those for actual subjects. For the fusion of 

one fingerprint with face, however, there is little difference in accuracy between actual subjects and 

chimeras. 

For this reason, fusing the face with fingers offers a distinct advantage. The choice of fusing two fingers 

vs. one finger and face depends on the choice of matchers. Using two fingers and face was more effective 

than a 4-finger slap. As the accuracy of matchers continues to improve, there will be an on-going need to 

reassess the benefits of specific combinations. 

It is difficult to generalize the results of finger fusion because accuracy varies substantially by finger 

position, and correlations among scores vary greatly by finger positions. The much larger thumbprints 

are substantially more effective than the other fingers. The relative advantage of thumbs over index 

fingers is comparable to the relative advantage of index fingers over little fingers. In all cases, score 

correlations substantially limit the benefits to finger fusion. The strongest correlations occur among 

neighboring fingers within a slap, but all combinations show some correlation. The little finger was often 

surprisingly effective in fusion, possibly because quality problems such as incorrect placement affected 

the little fingers differently from the other fingers. 

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

data integrity problems (misidentifications, swapped prints, missing images). This limitation is most 

pronounced when working with the most accurate matchers, measuring FRR at a high FAR, and/or 

combining several scores. Data integrity had a substantial limiting effect on FRR (at FAR=10-4) when 

combining as few as three or four scores. 

20 July 2006 22/44 
Appendix B.2: Score-Level Fusion of Multiple Matchers 

Contents 

6 Introduction: Combining Multiple Matchers .........................................................................................23

7 Previous Work ............................................................................................................................................24

8 Analysis Methods.......................................................................................................................................25

9 NBDF06 Results..........................................................................................................................................28

9.1 Results...................................................................................................................................................28

9.2 Discussion of Data Dependence........................................................................................................30

10 FpVTE MST Results ...................................................................................................................................32

11 Comparison of Multi-Algorithm, Multi-Instance, and Multi-Modal Performance...........................35

12 Conclusions .................................................................................................................................................37

6 Introduction: Combining Multiple Matchers 

This is a report of the effectiveness of algorithm fusion using face and fingerprint data from the NBDF06 

dataset, as well as fingerprint data from the FpVTE MST dataset. These datasets are described in 

Appendix A. 

The categories of biometric fusion include the use of multiple types of biometric data or multiple methods 

of processing. Fusion based on multiple types of data improves accuracy due to an increased amount of 

relatively independent data, but at the cost and complexity of collecting more data. 

Algorithm fusion is a generic term for the combination of multiple methods of processing for each 

individual sample. Here the processes being fused are feature extraction and matching: 

• Feature extractors generate templates for each sample, which are then fused at the template level. 

This is generally only appropriate with compatible templates. 

• Matchers produce scores or decisions. In many cases (such as in this study) the feature extractor 

is an integral part of the “matchers” being evaluated. 

Using multiple methods of processing on the same samples is generally expected to be less effective than 

either instance or mode fusion, but can be effective if the results from the processing algorithms are 

relatively independent. Matcher fusion has the advantage of maximizing the benefit of the data available. 

It should be noted that some feature extractors and matchers internally use multiple algorithms, 

unknown to the user or evaluator; the users of a commercially available matcher may already be the 

beneficiaries of matcher fusion. 

The use of multiple algorithms to process common data is a classic problem in the pattern recognition 

and machine learning literature.6 The effectiveness for biometric fusion depends on the degree of 

independence brought by the different algorithms. This hinges on two factors: 

• Different types of algorithms. “Maximum benefit (theoretically) would be derived from 

algorithms that are based on distinctly different and independent principles (such algorithms 

may be called ‘orthogonal’).” [SC37-24722, p. 6] Ideally, the matchers being fused would use 

 

6 See [Jain-99c] for a summary of references. 

9/14/2006 23/44 
Selected Topics In Biometric Fusion 

fundamentally different types of features, different methods of feature extraction, and different 

matcher algorithms. 

• Complementary errors. If two feature extractors or matchers duplicate each other’s mistakes (or 

one is a subset of the other), no substantial gain can be expected from fusion. If errors differ due 

to limitations of specific implementations, the underlying algorithms, or data-specific 

characteristics, fusion can help fill in those differences. 

This study seeks to empirically quantify the effect of matcher fusion, identify potential sources of 

complementary technology, and assess whether there exists significant potential for the most accurate 

matchers to be further improved by fusion with other matchers. 

7 Previous Work 

Score-level matcher fusion of correlated data has been discussed in several papers: 

• Jain investigated matcher fusion using logistic regression [Jain-99c]. We found this technique to 

be highly effective (see Appendix C). They demonstrate a benefit to fusing algorithms, 

particularly with one pair of fingerprint matchers. As discussed in Appendix E, the difficulty lies 

in estimating the density distributions from sample data. 

• [Grother-04], Section 6.4 investigated matcher fusion (termed “Multi-System Fusion”). Scores 

were normalized using the empirical cumulative distribution function of the genuine scores7, 

then z-normed. Fusion was implemented as a simple sum of the normalized scores, or as a 

weighted sum, where the weight was selected to maximize the area under the curve (AUC)8. 

Grother observes that the results of maximizing AUC “are only moderately better;” however, 

note some matcher combinations are much better (e.g., fusing Visionsphere and Eyematic went 

from an averaging behavior to real benefits). 

• [Fierrez-06] investigated the fusion of a minutiae-based matcher with a ridge-based matcher 

using an adaptive scheme based on an image quality metric. Scores were normalized using 

parametric transformations (tanh and exp), then fused by one of two methods: simple sum9 and 

weighted sum. The weighting was based on the quality score, such that the weaker minutiabased matcher was progressively downweighted as image quality dropped10. On low quality 

images, a simple sum had an averaging effect, yielding performance midway between the two 

matchers; the adaptive method performed similarly to the ridge-based method.11 On high quality 

images, fusion was clearly effective; and both techniques produced similar results. 

 

7 For comparison, the Product of FARs technique evaluated in this study normalizes based on a smooth 

model of the imposter cdf. Three major differences between these implementations included: the 

distribution, smoothing, and z-norm. 

8 This study did not investigate AUC optimization. However, note that computational methods of 

optimizing AUC are approximate. When evaluating TAR at FAR=10-4 (the standard point of comparison 

in this study), special care may be required to ensure that this region (0.01% of the range of the ROC) was 

in fact optimized. Notice, for instance, in Figure 20 of [Grother-02] how the ROC shows markedly 

greater downward curvature than those achieved in this study. 

9 Actually an average of the two scores, which is effectively not different from sum. 

10 The adaptive quality weighting scheme is defined such that the score combination ranges from equal 

weighting of matcher results to using only the (more accurate) ridge-based matcher results. It is not 

explained why greater weight is never given to the minutia-based matcher. 

11 These used small datasets, and no confidence intervals were shown. 

20 July 2006 24/44 
Appendix B.2 Combining Multiple Matchers 

• [Fierrez-05b] evaluated the Simple Sum of raw scores, SVM, and Dempster-Shafer methods. 

They found that none of these methods consistently outperformed the others. This may reflect 

assumptions made by these techniques that are not always valid: for example, although they cite 

Kittler for Simple Sum, they do not first ensure that scores are normalized as specified in that 

paper. They observed “the combination of the top performing individual systems can be 

outperformed by other combinations.” While it is entirely possible for pairs other than the top 

two systems to exhibit greater independence, and hence offer greater potential for fusion, the 

results in [Fierrez-05b] more likely reflect a failure to achieve good fusion of the top two systems. 

The statistical significance of the relative rankings is not discussed, which is notable, given the 

small datasets, non-random sampling and the very large number of combinations tested: they 

combined up to 41 matchers on a dataset constructed from 100 subjects, 8 fingerprint samples per 

subject. 

8 Analysis Methods 

In matcher fusion, scores from pairs of matchers are highly correlated because the two matcher scores 

both derive from comparisons of the same pair of images. Thus, as shown in Figure 13, the usual method 

of estimating the joint density distributions as the product of univariate densities is clearly inaccurate (the 

genuine scores are clearly correlated); the independence assumption is not valid. However, detail of the 

low score range of the same graph (Figure 14) shows that in the critical region of the decision boundaries, 

not only are the scores sufficiently independent to warrant fusion, but also that this simplified method of 

joint density estimation might yield good results.12

 

12 In these two figures, only a random subsample of imposters (shown in red) is plotted. 

20 July 2006 25/44 
Selected Topics In Biometric Fusion 

Figure 13. Scatterplot for NBDF06 dataset, left thumb scores, matchers H and I. Genuine scores are 

shown in black; imposters in red. Highly dependent data would result in results clustered around a 

line or curve; independent data would be broadly scattered. 

Figure 14. Detail of scatterplot from Figure 13 (NBDF06 dataset, left thumb scores, matchers H and I), 

with decision boundaries. Genuine scores are shown in black; imposters in red; Product of Likelihood 

Ratios decision boundaries in green. Note that only a random subsample of imposters (shown in red) 

is plotted. 

20 July 2006 26/44 
Appendix B.2 Combining Multiple Matchers 

A limited analysis was conducted to compare the efficacy of fusion techniques on dependent data 

(techniques are described in Appendix C). Figure 15 shows, for an example pairing of matchers from 

FpVTE MST, the ROCs obtained by three different fusion techniques. Note that despite the simplified 

density estimation (independence assumption), the relative performance of these techniques is quite 

similar to that achieved on highly independent data. That is, the three techniques perform similarly to 

one another, and the Product of Likelihood Ratios is slightly superior to the other two. This was found to 

be typical in several pairwise comparisons of FpVTE matchers, but was not systematically confirmed in 

the FpVTE data. 

Figure 15: Comparison of three fusion techniques (combining Avalon and Golden Finger13, FpVTE 

MST dataset) 

The results in this multi-algorithm study used two methods of fusion. For the NBDF06 analysis (Section 

9), the Product of Likelihood Ratios method was used. Because that approach requires painstaking curve 

fitting of both genuine and imposter score distributions for every matcher, it was not a practical option 

for this analysis of the fourteen FpVTE MST matchers. For the FpVTE analysis (Section 10), matcher 

scores were fused using the (fully automated) “best linear” combination. As discussed in Appendix C, 

linear combinations generally achieve very good fusion results but are not optimal. “Best linear” also 

makes an interesting choice for matcher fusion because it does not assume independence. 

 

13 Specific hardware and software products identified in this report do not imply recommendation or 

endorsement by the National Institute of Standards and Technology. 

20 July 2006 27/44 
Selected Topics In Biometric Fusion 

9 NBDF06 Results 

Figure 14 (above) shows that there is a potential benefit to fusing multiple matcher scores even when 

using highly accurate fingerprint matchers. The following subsection presents ROCs that demonstrate 

this benefit on various combinations of matchers. Section 9.2 provides additional data on the joint score 

distributions to help explain these results. Matcher fusion was performed using the Product of 

Likelihood Ratios technique. 

9.1 Results 

Matcher fusion, using the Product of Likelihood Ratios technique, can reduce FRR substantially. Table 11

shows that for pairs of fingerprint matchers, FRR was generally reduced by about 10-30% (varies by 

finger position); for pairs of face matchers, FRR was reduced by 10-13%.14 

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 11: Reduction in FRR where FAR = 10-4, for pair-wise matcher fusion. Fingerprint results are for 

all ten finger positions. 

(All fusion was Product of Likelihood Ratios, using the NBDF06 dataset)

The following three charts (Figure 16 – Figure 18) show the effect of three-way matcher fusion. 

 

14 The percent improvement in FRR compares the number genuines missed when algorithms are fused to 

the number of genuines missed by the stronger algorithm alone. For example, for two matchers X and Y, 

if TARX=.9, TARY=.95 and TARX+Y=.96, then the improvement in FRR is 100*(.05-.04)/.05 = 20%. 

20 July 2006 28/44 
Appendix B.2 Combining Multiple Matchers 

Figure 16: 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 0.01) is directly due to Density Ratio 

normalization of Matcher A, not fusion. 

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

FAR=10-4). 

20 July 2006 29/44 
Selected Topics In Biometric Fusion 

Figure 18. Fusing all three matchers on left thumbs reduced FRR by 40% relative to Matcher I (at 

FAR=10-4). 

9.2 Discussion of Data Dependence 

Since single-instance multi-matcher fusion uses the same data for both (or all) algorithms, the 

independent information that is necessary for effective fusion must come from differences (if any) 

between algorithms. The H and I fingerprint matchers have been shown to be among the most accurate 

fingerprint matchers currently available [SDK], a review of the extent of independence of these 

algorithms is of note, because there is a concern that as accuracy increases, the orthogonality between 

algorithms may lessen. 

This section provides additional information about the dependence of Matcher H and I scores on NBDF06 

fingerprint data (as shown in Figure 13 and Figure 14 in Section 8) in order to help explain the results 

presented in Section 9.1. 

Measures of Dependence 

While Figure 13 shows that the overall joint score distribution of H and I has a high degree of 

dependence, Figure 14 shows substantial independence in the area of genuine and imposter overlap. The 

following charts show details of the degree of dependence between H and I. Figure 19 shows that the 

imposter score distribution for Matcher I is not highly dependent on Matcher H scores15. Figure 20 shows 

substantial dependence among the genuine scores, yet there is still considerable spread in Matcher I 

scores when Matcher H reports a score of zero (equivalent to a FAR of 1). 

 

15 Matcher I score distribution for those cases where matcher H score is zero cannot be discerned from the 

scatterplot; Matcher I score distribution for those cases where matcher H score is between FAR=10-4 and 

10-2 is intermediate (roughly centered) between the two shown. 

20 July 2006 30/44 
Appendix B.2 Combining Multiple Matchers 

Figure 19: Matcher I imposter score distribution of groups selected based on scores from Matcher H. 

Blue: H FAR=1 (minimum value); Red: H FAR<=10-2 (Left thumbs; NBDF06 dataset)

Figure 20: Matcher I genuine score distribution of groups selected based on scores from Matcher H. 

Blue: H FAR=1 (minimum value); Red: H FAR<=10-2 (Left thumbs; NBDF06 dataset)

Table 12 summarizes the joint densities. As seen in Figure 14, these data show that much of the score 

dependence occurs among the high scoring genuines (definitive matches); lower scores, in the region of 

difficult discrimination, are not as strongly correlated. 

20 July 2006 31/44 
Selected Topics In Biometric Fusion 

Imposter (n=122,000) I FAR 

 1 to 10-2 10-2 to 10-4

10-4 to Max 

Score 

Max 

score Total 

1 97.70% 0.08% 0.01% 0.00% 97.79%

<1 to 10-2 1.27% 0.00% 0.00% 0.00% 1.27%

10-2 to 10-4 0.93% 0.01% 0.00% 0.00% 0.93%

10-4 to Max Score 0.01% 0.00% 0.00% 0.00% 0.01%

Max score 0.00% 0.00% 0.00% 0.00% 0.00%

H 

FAR 

Total 99.90% 0.09% 0.01% 0.00% 100.00%

Genuine (n=64,867) I FAR 

 1 to 10-2 10-2 to 10-4

10-4 to Max 

Score 

Max 

score Total 

1 0.16% 0.01% 0.05% 0.00% 0.22%

<1 to 10-2 0.02% 0.00% 0.01% 0.00% 0.03%

10-2 to 10-4 0.11% 0.04% 0.15% 0.00% 0.30%

10-4 to Max Score 0.10% 0.09% 12.88% 39.09% 52.17%

Max score 0.00% 0.00% 0.02% 47.26% 47.29%

H 

FAR 

Total 0.39% 0.14% 13.12% 86.36% 100.00%

Table 12: Correspondence between groups of imposter and genuine scores for matchers H and I

 (Left thumbs; NBDF06 dataset)

Table 12 shows the ability of Matchers H and I to discriminate genuines from imposters in those cases 

where the other matcher returned a score equivalent to a FAR between 1 and 10-2. For example, of the 

0.22% of the genuines for which H returned a score equivalent to FAR=1, I returned scores equivalent to 

FAR<10-4 for 0.05% — nearly a quarter of those cases. 

10 FpVTE MST Results 

[FpVTE] included a brief discussion of the correlation of system results, the potential for fusion, and a 

single simplified example of fusion. This section provides a more rigorous examination of the effect of 

matcher fusion on the FpVTE MST matchers. 

Matcher scores for each pair of matchers were fused using the Best Linear fusion technique. As noted 

there, best linear fusion is not optimal, but is effective when detailed score distribution analysis and curve 

fitting is not practical. 

Table 13 reports the TAR at FAR=10-4 for each matcher alone (results along diagonal) and for the fused 

results of each matcher pair. Table 14 reports the corresponding improvement in FRR relative to the 

stronger matcher of each pair. Fusion is beneficial when the fused TAR is substantially higher than that of 

either contributing matcher alone. Notice that 

• Fusion was beneficial in almost all cases: 

o In many cases, the relative improvement in FRR (over the stronger matcher) is 30-40%. 

o The few cases of degradations in performance are not statistically significant: these all 

involve the three most accurate matchers and a very small number of misclassifications. 

• The fused results do not change the overall performance ranks of the more accurate systems: 

20 July 2006 32/44 
Appendix B.2 Combining Multiple Matchers 

o For the three most accurate matchers (NEC, Cogent, Sagem)16, no fusion combination results 

in a statistically significant improvement. 

o The only fused results that surpass the base NEC performance (99.5%) involve NEC. 

o The only fused results that surpass the base Cogent performance (99.2%) involve Cogent or 

NEC. 

o The only fused results that surpass the base Sagem performance (98.3%) involve Sagem, 

Cogent, or NEC. 

• Matchers that benefit from fusion with the NIST matcher might be improved by incorporating 

technology from the NIST matcher, which is freely available in source code form [NFIS]. 

 

16 Specific hardware and software products identified in this report do not imply recommendation or endorsement 

by the National Institute of Standards and Technology. 

20 July 2006 33/44 
123ID Antheus Avalon Biolink Cogent GoldenF Identix Motorola NEC Neuro NIST Phoenix 

123ID 0.333 0.170 0.289 0.142 0.008 0.186 0.094 0.064 0.007 0.058 0.129 0.219 Antheus 0.170 0.232 0.195 0.120 0.010 0.148 0.082 0.061 0.005 0.047 0.102 0.163 Avalon 0.289 0.195 0.459 0.162 0.009 0.216 0.100 0.064 0.005 0.060 0.142 0.228 Biolink 0.142 0.120 0.162 0.166 0.008 0.123 0.086 0.061 0.005 0.056 0.103 0.135 Cogent 0.008 0.010 0.009 0.008 0.009 0.009 0.009 0.008 0.003 0.008 0.009 0.009 Goldenfinger 0.186 0.148 0.216 0.123 0.009 0.291 0.080 0.066 0.005 0.052 0.115 0.182 Identix 0.094 0.082 0.100 0.086 0.009 0.080 0.101 0.053 0.005 0.043 0.076 0.087 Motorola 0.064 0.061 0.064 0.061 0.008 0.066 0.053 0.066 0.005 0.035 0.059 0.065 NEC 0.007 0.005 0.005 0.005 0.003 0.005 0.005 0.005 0.005 0.004 0.005 0.005 Neuro 0.058 0.047 0.060 0.056 0.008 0.052 0.043 0.035 0.004 0.060 0.052 0.052 NIST_VTB 0.129 0.102 0.142 0.103 0.009 0.115 0.076 0.059 0.005 0.052 0.154 0.128 Phoenix 0.219 0.163 0.228 0.135 0.009 0.182 0.087 0.065 0.005 0.052 0.128 0.281 Sagem 0.018 0.019 0.019 0.018 0.006 0.017 0.017 0.017 0.004 0.016 0.018 0.019 Techno 0.281 0.191 0.281 0.162 0.009 0.208 0.096 0.066 0.005 0.060 0.145 0.216 Ultrascan 0.125 0.088 0.118 0.097 0.008 0.110 0.074 0.058 0.005 0.051 0.091 0.106 

Table 13: FRR at FAR = 10-4 for fused FpVTE MST matchers. Pre-fusion performance is shown along the diagonal. Results in bl

fusion is beneficial and statistically significant; in no cases were degradations statistically significant. 

123ID Antheus Avalon Biolink Cogent GoldenF Identix Motorola NEC Neuro NIST Phoenix 

123ID 27% 13% 15% 8% 36% 7% 3% -39% 4% 16% 22% Antheus 27% 16% 28% -14% 36% 19% 7% 0% 22% 34% 30% Avalon 13% 16% 2% 0% 26% 2% 3% -1% 0% 8% 19% Biolink 15% 28% 2% 11% 26% 15% 8% -4% 7% 33% 19% Cogent 8% -14% 0% 11% 1% -1% 8% 34% 5% 0% 0% Goldenfinger 36% 36% 26% 26% 1% 21% 0% 0% 13% 25% 35% Identix 7% 19% 2% 15% -1% 21% 20% 0% 29% 24% 14% Motorola 3% 7% 3% 8% 8% 0% 20% 0% 42% 11% 2% NEC -39% 0% -1% -4% 34% 0% 0% 0% 12% -4% 0% Neuro 4% 22% 0% 7% 5% 13% 29% 42% 12% 15% 14% NIST_VTB 16% 34% 8% 33% 0% 25% 24% 11% -4% 15% 17% Phoenix 22% 30% 19% 19% 0% 35% 14% 2% 0% 14% 17% Sagem 5% 1% 2% 5% 29% 11% 9% 8% 16% 14% 6% 0% Techno 16% 18% 39% 2% 0% 29% 5% 1% -5% 0% 6% 23% Ultrascan 9% 36% 14% 29% 4% 20% 27% 12% -6% 16% 34% 22% 

Table 14: Percent FRR improvement over the more accurate of the two matchers; compare to the previous table. Statistically sig

in blue. In no cases were degradations statistically significant. 

20 July 2006 34/44 
Appendix B.2 Combining Multiple Matchers 

Figure 21 shows example ROCs for pairwise fusion of FpVTE MST matchers with the NIST VTB matcher. 

Figure 21: “Best Linear” fusion of FpVTE MST matchers with NIST VTB 

11 Comparison of Multi-Matcher, Multi-Instance, and Multi-Modal 

Performance 

Although matcher fusion clearly improves accuracy, that improvement is much less than what can be 

achieved with instance or mode fusion. For example, Figure 22 compares instance fusion of right and left 

index fingers (solid lines) against matcher fusion (green lines) using matchers H (red) and I (black), on the 

NBDF06 dataset. Single-instance multi-matcher fusion showed moderate improvement in accuracy 

(about 15-25% reduction in FRR where FAR=10-4), where single-algorithm multi-instance fusion showed a 

dramatic improvement (about 80-85% reduction in FRR where FAR=10-4). 

20 July 2006 35/44 
Studies of Biometric Fusion 

Figure 22: Comparison of matcher (algorithm) and instance fusion. (All fusion was Product of Ratios, 

using the NBDF06 dataset) 

Table 7 summarizes the variation of performance improvement for the three categories of fusion 

(measured at FAR=10-4).17

 Multi-Instance Multi-Modal Multi-Matcher 

N=45 N=30 N=3 N=10 

 H fingers I fingers Q fingers H+face I+face Q+face Faces H+I H+Q I+Q 

Min 59% 48% 51% 68% 71% 64% 10% 14% 8%18 9%

Median 83% 79% 72% 74% 76% 75% 10% 25% 20% 20%

Average 82% 78% 71% 74% 77% 74% 11% 25% 16% 20%

Max 90% 90% 84% 80% 84% 79% 13% 33% 32% 32%

Table 15: Reduction in FRR where FAR = 10-4, relative to the stronger of the inputs.19 (All fusion was 

Product of Ratios, using the NBDF06 dataset) 

Two key points can be derived from these results: 

 

17 This is a combination of Table 7 and Table 11. 

18 One H+Q data run that was not well-optimized resulted in an anomalous performance degradation (–

7%), but subsequent optimization yielded an FRR improvement of 8%. This highlights the fact that results 

are sensitive to optimization procedures. No other runs were revised. 

19 For example, fusion of inputs that separately have FRRs of 87% and 90% (at 10-4), resulting in a FRR of 

92%, is a 20% relative improvement in FRR. 

9/14/2006 36/44 
Appendix B.2 Combining Multiple Matchers 

• Matcher fusion generally results in a 10-30% reduction in FRR, which is much less than for 

instance or mode fusion. This should be expected due to the limited independence in matcher 

fusion. 

• Instance fusion generally results in a 50-90% reduction in FRR, whereas mode fusion generally 

results in a 65-85% reduction in FRR. In general, there was about the same level of improvement 

when fusing a fingerprint with a face as when fusing two fingerprints. As discussed in Appendix 

B.1, once multiple fingerprint scores have been fused, face scores become more effective than 

another finger instance due to their independence. 

12 Conclusions 

This study found that 

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

less than that for instance or mode fusion. 

o Matcher fusion generally results in a 10-30% reduction in FRR, while instance and mode 

fusion generally result in a 50-90% reduction in FRR. 

o This should be expected due to the greater degree of data independence for instance and 

mode fusion. 

• Some combinations of matchers are more effective than others. Substantial accuracy 

improvements were achieved even when combining some of the most accurate matchers. 

• It should be noted that accuracy is not the only consideration in system design. Fusing two 

weaker systems in parallel might have cost or resource advantages over a single more accurate 

system. 

• Although the scores being fused clearly are not independent, the Product of Likelihood Ratios 

fusion technique was consistently effective on the NBDF06 dataset. In this technique, the joint 

densities are estimated using an independence assumption. This result demonstrates that the 

large training sets required to model joint distributions are not required in order to implement 

effective optimization per the Neyman-Pearson Lemma. 

• The findings of this analysis are based on the fusion of single-finger matcher scores, and frontal 

image face scores. The extent to which these results generalize to other biometric modalities is 

not known. 

 

20 July 2006 37/44 
Appendix B.3: Score-Level Fusion of Multiple Fingerprint Samples 

Contents 

13 Introduction: Multi-Sample Score-Level Fusion ....................................................................................38

13.1 Background ..........................................................................................................................................38

14 Approach.....................................................................................................................................................39

14.1 Data and Matchers ..............................................................................................................................39

14.2 Scores ....................................................................................................................................................39

14.3 Fusion Techniques...............................................................................................................................40

15 Results..........................................................................................................................................................40

16 Conclusions .................................................................................................................................................41

13 Introduction: Multi-Sample Score-Level Fusion 

Multi-sample data refers to samples acquired from the same source, such as multiple images of a single 

fingerprint, images of the same face, or recordings of a speaker. This report describes experiments 

assessing the effectiveness of one use of multi-sample data: retaining multiple samples in the gallery, 

such as when an additional enrollment is added for every encounter with a subject. 

Many systems encounter multi-sample data but do not take full advantage of it. Such systems explicitly 

or implicitly involve design decisions whether to use multiple samples for selection or fusion: 

• On the gallery side after a successful match, a matching system may

o Always retain the original enrolled sample in the gallery, 

o Retain the “best” sample yet encountered for this subject, or 

o Retain the samples from each encounter in the gallery.

• On the probe side, a collection process may

o Always collect a single sample, 

o Use image quality metrics to determine whether image recapture is appropriate, 

o Use image quality metrics to select the “best” image from a series of images, or

o Collect multiple samples to use as probes.

It is tempting to assume symmetric benefits on the probe and gallery sides, that similar results might be 

expected from having a second gallery sample as a second probe sample. However, multiple probe 

samples can be expected to have highly correlated sample quality problems, as both are likely to come 

from one encounter with the subject. Multiple gallery samples collected at different times can be expected 

to have a greater degree of independence and therefore should be effective in fusion. 

13.1 Background 

[Grother-04] included an evaluation of multi-sample fusion using the face recognition data from 

[FRVT2003], showing a clear benefit: 

Performance improves substantially with K [K=number of samples] Only Visionsphere shows an anomalous 

decline in performance. For the leading systems much of the improvement is realized for K = 2. Thereafter 

20 July 2006 38/44 
Appendix B.2 Combining Multiple Matchers 

returns typically diminish. For example, looking at the Identix system for summed raw scores, for the five image 

population, the false non-match rate (i.e. 1 − PTA) decreases from 8% (K = 1) to 6% (K = 2) with only a further 

reduction of 0.7% for two more scores. [Grother-04, p. 27] 

The [Goats] study was an evaluation of multi-sample data: ten encounters each for 6,000 subjects. That 

study showed a great deal of variation between samples from each subject, in terms of scores and image 

quality metrics. That report concluded 

A hard to match fingerprint, therefore, is indicative of problems with that specific fingerprint image, and does 

not mean another fingerprint from the same finger would be hard to match. [Goats, p. 23] 

Since matcher scores vary substantially between collection encounters, then the risk of a failure to match 

(low matcher score) should decrease if the gallery contains samples from more than one collection 

encounter. 

[Hopper-05] discussed a study that was conducted to determine the efficacy of searching latent 

fingerprints against a gallery containing both rolled and flat (segmented slap) images, with these results: 

• 59.8% of successful searches matched against both rolls and flats 

• 27.8% matched only against rolls 

• 12.4% matched only against flats 

The improvement that resulted in using flats in addition to rolls could be attributed either to the use of 

two different types of fingerprint capture (roll vs. slap) or to the use of multiple samples in the gallery. 

14 Approach 

The method used in this study was to measure how accuracy would be affected if a gallery retained two 

samples per subject rather than just one. 

14.1 Data and Matchers 

As discussed in Appendix A, the NBDF06 dataset used throughout these studies had 64,867 mated 

subjects, with two face/fingerprint sets each. Of these, 4,015 subjects had 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 4,015 * 4,014 off-diagonal scores of the 

similarity matrices.20 The matchers used were the H, I, and Q fingerprint matchers. 

14.2 Scores 

The scores were generated as if two of the samples (Sample1 and Sample2) were enrolled in the gallery, 

and the third sample was used as the probe. Therefore, for each pair of subjects compared, ScoreA = 

 

20 The background set was not fully randomized, but was approximately randomized using a block 

design where each probe was compared to a gallery of approximately 100 subjects. The gallery subjects 

used varied between probes. 

20 July 2006 39/44 
Studies of Biometric Fusion 

match(Sample1, Sample3) and ScoreB = match(Sample2, Sample3). For each genuine or imposter 

comparison, 60 scores were produced (10 fingers x 3 matchers x 2 scores).

14.3 Fusion Techniques

As the scores to be fused have the same score distribution (same finger, same matcher), they are fused by 

Simple Sum of Raw Scores, which is shown in Appendix C to be highly effective when the scores come 

from a single matcher and corresponding fingers. Scores were also fused by Maximum of Raw Scores, 

Max(ScoreA, ScoreB), which implements OR decision level fusion. 

For the 30 combinations of finger positions and matchers, 

• Two baseline (unfused) ROCs were produced for ScoreA = match(Sample1, Sample3) and ScoreB = 

match(Sample2, Sample3) 

• Two fused ROCs were produced for the two techniques 

15 Results

The 30 sets of ROCs show very consistent behavior. Figure 23 and Figure 24 show characteristic results. In 

every case, the fused results result in a substantial improvement in accuracy. Note that there is no 

substantial difference in performance between the two fusion techniques.

Figure 23: Effects of multi-sample fusion 

(fingerprint matcher I, left middle finger, NBDF06 multi-sample data) 

9/14/2006 40/44 
Appendix B.2 Combining Multiple Matchers 

Figure 24: Effects of multi-sample fusion 

(fingerprint matcher H, right thumb, NBDF06 multi-sample data)

Table 16 shows summary results for all finger positions, broken down by matcher and 

fusion technique. The improvement ranged from 45% to 73%.

Matcher Technique Min Median Max Std. Dev.

H Max of raw scores 52% 58% 73% 6%

H Sum of raw scores 53% 57% 70% 5%

I Max of raw scores 49% 55% 66% 6%

I Sum of raw scores 49% 56% 72% 8%

Q Max of raw scores 45% 51% 57% 3%

Q Sum of raw scores 45% 52% 57% 4%

Table 16: Reduction in FRR at FAR=10-4, relative to the stronger input. Results are computed over all 

ten finger positions. 

16 Conclusions

This study showed that there is a clear benefit from multi-sample, score-level fusion: false reject rates 

were reduced from 45% to 73%. These benefits are due to sample-specific variability, which can be largely 

be attributed to quality problems present in one but not all samples, and the overlap of areas contained in 

each sample. Because data quality is a problem in every biometric capture process, multi-sample fusion 

can be expected to be effective for other biometric modalities. 

Based on the assumption that the multiple samples share common score distributions, the simplest of 

fusion techniques, Simple Sum and Max of Raw Scores were used. These techniques require no training 

data and are expected to scale reliably. 

Multi-sample fusion from the use of multiple enrollments is likely to be of interest since it is based von 

the retention of existing data rather than the collection of additional data. Therefore the cost and 

20 July 2006 41/44 
Studies of Biometric Fusion 

complexity of implementing this form of multi-sample fusion is likely to be much less than that of multimodal or multi-instance fusion. 

9/14/2006 42/44 
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