Studies of Biometric Fusion 

Appendix C 

Evaluation of Selected Biometric Fusion Techniques 

Brad Ulery,1 William Fellner, 1 Peter Hallinan,2 Austin Hicklin,1 Craig Watson3

1 Mitretek Systems 

2 Independent consultant to Mitretek Systems 

3 National Institute of Standards and Technology 

20 July 2006 

Abstract 

This report summarizes and evaluates several common score-level biometric fusion techniques. The literature 

contains numerous proposals for score-level biometric fusion algorithms. Selecting the most effective fusion 

techniques depends on operational issues such as accuracy requirements, availability of training data, and the 

validity of simplifying assumptions. Of the techniques evaluated, product of likelihood ratios and logistic 

regression were found to be highly effective. 
Studies of Biometric Fusion 

 Contents 

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

2 Previous Work ................................................................................................................................3

3 Fusion Techniques Evaluated.......................................................................................................5

4 Comparative Performance Results...............................................................................................7

5 Guidance on Selecting Techniques ............................................................................................11

6 Conclusions ...................................................................................................................................12

7 References......................................................................................................................................13

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Appendix C Evaluation of Selected Biometric Fusion Techniques 

1 Introduction 

In the course of this study, several score-level fusion techniques were implemented and applied to a 

variety of multi-biometric problems. This paper discusses what techniques were investigated, why those 

techniques were selected, and evaluates how the techniques compare in terms of accuracy. The paper also 

offers guidance for selecting among those techniques, as they are not all equally suited to different 

problems. Techniques for modeling score distributions are discussed in Appendix E. The set of 

techniques discussed are not fully representative of the breadth of alternatives, but are varied and 

instructive. 

The purpose of this paper is to convey how common biometric fusion strategies compare with respect to 

performance, real-world applicability, and ease of implementation to persons selecting, designing or 

calibrating fusion algorithms. 

2 Previous Work 

One finds in the literature a plethora of techniques for fusing biometric scores. One also finds other 

communities of researchers solving similar problems in dissimilar ways: much of the growing body of 

research that supports data fusion is not specifically targeted to the narrow application area of biometric 

score fusion and its special needs. The biometric community has done a great deal of work in adapting 

techniques from a variety of specialized fields (e.g., statistics, pattern recognition, artificial intelligence, 

medicine) for biometric-specific purposes, but this is still a fertile area for further work. 

A strong theoretical basis exists for biometric fusion (e.g., [Kittler-98; Verlinde-00; Poh-05d]). Many 

researchers have demonstrated that fusion is effective in the sense that the fused scores provide much 

better discrimination than the individual scores (e.g., [Ben-Yacoub-99; Dass-05; Fierrez-03; Griffin-05; 

Grother-02; Indovina-03; Jain-99b; Korves-05; Ross-01; Snelick-05; Wang-03]). Such results have been 

achieved using a variety of fusion techniques. 

Several recent papers have compared various techniques on empirical data. Selections of recent results 

that help define “conventional wisdom” include: 

• Kittler et al [Kittler-98] evaluated several classifier combination rules on frontal face, face profile, 

and voice biometrics (using a database of 37 subjects). They found that the “sum of a posteriori 

probabilities” rule outperformed the product, min, max, median, and majority of a posteriori

probability rules (at EER) due to its resilience to errors in the estimation of the densities. 

• Ben-Yacoub et al [Ben-Yacoub-99] evaluated five binary classifiers on combinations of three face 

and voice modalities (database of 295 subjects). They found that (a) a support vector machine and 

Bayesian classifier achieved almost the same performances; and (b) both outperformed Fisher’s 

linear discriminant, a C4.5 decision tree, and a multilayer perceptron. 

• Fierrez-Aguilar et al [Fierrez-03] found that a support vector machine outperformed (at EER) the 

sum of normalized scores when fusing face, fingerprint and signature biometrics (database of 100 

subjects and 50 chimeras1). 

• Jain et al [Jain-05] applied the sum of scores, max-score, and min-score fusion methods to 

normalized scores of face, fingerprint and hand geometry biometrics (database of 100 users, 

based on a fixed TAR). The normalized scores were obtained by using one of the following 

 

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

individuals. 

20 July 2006 3/14 
Studies of Biometric Fusion 

techniques: simple distance-to-similarity transformation with no change in scale (STrans), min–

max, z-score, median-MAD, double sigmoid, tanh, and Parzen. They found that (a) the min–max, 

z-score, and tanh normalization schemes followed by a simple sum of scores outperformed other 

methods; (b) tanh is better than min-max and z-score when densities are unknown; and (c) 

optimizing the weighting of each biometric on a user-by-user basis outperforms generic 

weightings of biometrics. 

• Snelick et al [Snelick-05] compared combinations of z-score, min-max, tanh and adaptive (twoquadrics, logistic and quadric-line-quadric) normalization methods and simple sum, min score, 

max score, matcher weighting, and user weighting fusion methods (database of about 1000 users, 

at a fixed FAR). They found that (a) fusing COTS fingerprint and face biometrics does outperform 

unimodal COTS systems, but the high performance of unimodal COTS systems limits the 

magnitude of the performance gain; (b) for open-population applications (e.g., airports) with 

unknown posterior densities, min-max normalization and simple-sum fusion are effective; (c) for 

closed-population applications (e.g. an office), where repeated user samples and their statistics 

can be accumulated, QLQ adaptive normalization and user weighting fusion methods are 

effective. 

• Korves et al compared various parametric techniques on the BSSR1 dataset [Korves-05]. That 

study showed that the Best Linear technique performed consistently well, in sharp contrast to 

many alternative parametric techniques, including simple sum of z-scores, Fisher’s linear 

discriminant analysis, and an implementation of sum of probabilities based on a normal 

(Gaussian) assumption. 

These studies are illuminating, but many suffer from limited available data: the datasets are too small to 

evaluate performance at low FAR, and often are not representative of operational data. Some of these 

studies also suffer from other problems:

• Conclusions are based on simplifying assumptions, such as independence or normal score 

distributions, often with no investigation into the validity of those assumptions. 

• Techniques are often not fully defined, so that it is not clear if results are due to the underlying 

concept behind an algorithm or the decisions made in the implementation. In general, 

comparisons of techniques are in fact comparisons of implementations of those techniques, so 

that negative results could be the result either of the underlying technique or an imperfect 

implementation — this is compounded if the details are not fully defined. 

• The performance of many techniques depends upon information that must be supplied but may 

not be available, such as prior probabilities or score distributions. The results of the evaluation 

may hinge on the validity of assumptions (or equivalently, the quality of available information 

and the accuracy with which it is modeled). 

• Confidence intervals on results are not discussed (and often large). Several papers discuss the 

computation of confidence intervals on ROCS [Wayman; Bolle-00b; Macskassy-04; Scott-06; 

Micheals-03] 

• Some studies are based on approaches to classification that seek to minimize the probability of 

error or expected Bayes’ cost (see [Scott-06]). Such approaches may have limited applicability in 

biometrics. 

Thus, despite the progress that has been made in this field, there remains a clear need for large-scale 

empirical comparisons of fusion techniques. There is also a need for guidance on the implementation and 

selection of techniques. 

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Appendix C Evaluation of Selected Biometric Fusion Techniques 

3 Fusion Techniques Evaluated 

We selected eight techniques based on performance in previous work. We implemented and 

systematically compared these techniques on a wide range of fusion problems, involving different 

matchers, modalities and instances. Table 1 briefly describes each technique. 

Technique Description Rationale for Choice 

Simple Sum of Raw 

Scores 

Matcher scores are simply added, with no 

prior normalization. Scores are neither 

rescaled, nor weighted to account for 

differences in matcher accuracy. 

Included largely to demonstrate its 

limited applicability, which includes 

situations where scores have 

comparable distributions, such as 

two fingers scored by one matcher, 

as in the NIST 2-finger SDK 

evaluations [SDK2]. 

Simple Sum of Znormalized Scores 1. The mean and standard deviation of the 

imposter score distribution is estimated 

from sample data. 

2. Scores are normalized by subtracting 

the mean of the imposter distribution, then 

dividing by the standard deviation of the 

imposter distribution. 

3. The normalized scores are simply 

added without weighting. 

Simple linear fusion technique. 

Best Linear Linear fusion (weighted sum), with an 

optimal slope (hyperplane) determined 

empirically on joint sample distributions. 

Solution entails iteratively rotating decision 

boundary and evaluating TAR at a fixed 

FAR. 

Many linear techniques are 

discussed in the literature, but each 

determines slope from prior 

distributional assumptions. 

Previously identified as a top 

performer [Korves-05], Best Linear 

is often far superior to alternative 

linear techniques. 

Product of Likelihood 

Ratios 

1. Probability density functions are 

separately modeled for each genuine and 

impostor distribution, using variable 

bandwidth kernels, log-linear tail tapering, 

and spike handling. 

2. Likelihood ratios are computed from 

these models for each matcher. 

3. Scores are normalized by 

transformation to their likelihood ratios 

4. Normalized scores are simply multiplied 

This multi-stage modeling process 

attempts to estimate, very directly, 

the information required for 

application of the (theoretically 

optimal) Neyman-Pearson Lemma, 

with minimal simplifying modeling 

assumptions. 

Logistic Regression 1. The log of the density ratio is modeled 

(e.g. as a low-order polynomial function), 

then estimated from the training data by 

principal of maximum likelihood 

2. Density ratios were modeled 

independently for each matcher; fusion 

was performed by adding the normalized 

scores (log densities). 

Alternatively, the joint density ratio may be 

modeled directly, in which case 

normalization and fusion are not distinct 

steps. 

A standard statistical technique that 

closely approximates the 

theoretically optimal NeymanPearson Lemma. 

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Studies of Biometric Fusion 

Technique Description Rationale for Choice 

Product of FARs 1. Scores are transformed to the estimated 

right-tail integral of the imposter density 

distribution. 

2. Distribution modeling is identical to that 

used for product of likelihood ratios (but 

only for the imposter distribution). 

Fusion technique proposed in 

[Griffin-04b] for use with the BioAPI 

standard. The estimation technique 

as implemented was developed 

here. FAR normalization is a 

practical alternative to ratio 

normalization when little is known 

about the genuine distribution. 

Min of FARs 

Max of FARs 

1. Scores are transformed to FAR, as with 

product of FARs. 

2. As implied by the names, simply the 

minimum (or maximum) of the unfused 

FARs. 

Min and max are decision-level fusion 

techniques, but calibration requires 

knowledge of score distributions. 

Fusion techniques proposed in 

[Griffin-04b] for use with the BioAPI 

standard. 

Table 1: Selected Techniques, as implemented in this study 

The ROC-based evaluation used here emphasizes tradeoffs between FAR and FRR. The error trade-off 

approach to evaluation was championed by J. Neyman and E. S. Pearson; the Neyman-Pearson Lemma 

[Neyman-33] defines a criterion under which the ROC can be optimized.2 Recently, several authors have 

noted the merits of Neyman-Pearson optimization for this type of evaluation (e.g., [Scott-05], [Griffin-05], 

[Pepe-05]). As noted by Griffin,

“One good way of defining optimization of biometric fusion for the purposes of verification is to find the 

combination of signals from each biometric such that for a given False-class acceptance rate (FAR) the Trueclass rejection rate (TRR) is minimized. The solution to this problem was given [...] by Neyman and Pearson. 

The Neyman-Pearson theorem simply states that this optimization is satisfied by using decision boundaries in 

the total sample or probability density space such that the ratio of genuine over impostor probability densities 

are held constant at the boundary. Therefore, the problem at hand is to implement in a simple way this meaning 

of optimal fusion.” [Griffin-05] 

The product of likelihood ratios technique described in this paper represents a direct approach at 

estimating distribution densities from sample data for the purpose of Neyman-Pearson optimization. 

Logistic regression is a standard statistical technique for modeling these ratios directly. Much of the 

fundamental theory and implementation issues relating these techniques are summarized in other papers 

in this series (see Parts V, VI, and VII). This paper focuses on empirical observations and practical 

guidance derived from our experience. 

The techniques tested are a small subset of those proposed in the literature. We include techniques 

expected to be appropriate in only a few circumstances (simple sum of raw scores and z-normalized 

scores), techniques expected to do well in general (product of likelihood ratios and logistic regression), 

 

2 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) replace each point in the scatterplot with the 

ratio of genuines to imposters at that point, and 3) plot those ratios in the Z dimension, then the NeymanPearson Lemma states that the topological contours that follow a given “altitude” (a fixed likelihood 

ratio) correspond to optimal decision boundaries. 

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Appendix C Evaluation of Selected Biometric Fusion Techniques 

and some “reasonable” techniques known to practitioners (Best Linear, FAR-based methods). Many of 

the techniques in the literature are variations on similar concepts; many of the more effective techniques 

are based on likelihood ratios [Sedgwick][Dass-05]. Several techniques were not evaluated due to limited 

resources that might be considered for future work, such as the use of support vector machines. 

Our use of FAR-based techniques was influenced by the BioAPI specification [BioAPI], and the ANSI 

Fusion Information Format [FIF] which use estimates of FAR as a means of making scores interoperable. 

Evaluation of the techniques included comparisons of the full ROCs, some of which are reproduced here. 

Summary results are measured at FAR=10-4: this specific operating point was selected for its 

comparability with FpVTE results, computational feasibility, as an appropriate baseline for use in 

identification systems. 

Note that for most of these techniques, almost all of the work (and complexity) lies in modeling the 

univariate (pre-fusion) score distributions. In other words, if we distinguish between normalization 

(univariate) and fusion (multivariate), these techniques are successful because of painstaking 

normalization, and fusion is merely the sum or product of the normalized scores. 

4 Comparative Performance Results 

Figure 1 provides a summary comparison of the eight techniques on 2-way fusion problems constructed 

from the following score sets: Face matchers A, B, and C; Fingerprint matchers H, I, and Q for right index 

(RI) and left index (LI) fingers. The charts on the following pages show greater detail. 

Comparison of Techniques

Measured at FAR=10-4

0.001

0.01

0.1

1

H.RI + H.LI

H.RI + C

H.RI + BH.RI + A

I.RI + I.LI

I.RI + C

I.RI + BI.RI + A

Q.RI + Q.LI

Q.RI + C

Q.RI + BQ.RI + A

H.RI + I.RI

I.RI + Q.RI

H.RI + Q.RI

False Reject Rate 

Product of Likelihood Ratios

Logistic Regression

Product of FARs

Max of FAR

Best Linear

Sum of Z-norm Scores

Sum of Raw Scores

Min of FAR

Unfused Data

Figure 1: Eight selected techniques compared at FAR=10-4 on a variety of fusion tasks. Product of 

Likelihood Ratios performs consistently well. 

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Studies of Biometric Fusion 

This chart supports several key results: 

• Product of likelihood ratios, logistic regression, product of FARs, Best Linear and max of FAR 

perform well consistently. 

• Simple sum of raw scores performs well when the scores are of the same type (the same matcher 

on corresponding fingers). In other cases, z-normalization of the scores often helps, but results 

remain variable. 

• Min of FAR is not effective. 

Additionally, it should be noted that 

• The probabilistic techniques are often sensitive to accurate modeling of the score distributions 

and implementation details (as discussed in TBD Vb and Vc). This may be a significant 

consideration when selecting a technique for a specific application (See Section 5). 

• Max and min implement decision-level fusion, not score-level fusion (Max combines decisions 

with AND; Min with OR).3 The findings of this study disprove the oft-repeated canard that 

decision-level fusion is ineffective: decision-level fusion was found to be highly effective, but not 

as effective as score-level fusion. Theoretically, Max of Likelihood Ratios (not implemented) 

should perform better than Max of FARs but not as well as the product of likelihood ratios. This 

was not verified empirically. 

Figure 2 to Figure 5 provide sets of complete ROCs to show how the various techniques compare across 

the range of operating thresholds. 

 

3 Note that although fusion is performed at the decision level, the matchers must first be set to operate at 

a common decision threshold in order to maximize TAR. Calibration may utilize score-level information. 

The example ROCs represent the range of operating points achievable by varying this common decision 

threshold. 

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Appendix C Evaluation of Selected Biometric Fusion Techniques 

Figure 2: The result of fusing two different fingers using the same matcher. This is the least 

challenging type of fusion, so many techniques do well. 

Figure 3: The result of fusing a face score and a finger score. Score distributions differ significantly, so 

benefits of better fusion techniques are more significant. The Face and Min of FAR lines are 

superimposed. 

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Studies of Biometric Fusion 

Figure 4: The result of fusing two different fingers (using the same matcher) with a face score. 

Figure 5: The result of fusing different matchers on the same source data (left little fingers). Although 

the scores are highly dependent, fusion still yields a benefit.

20 July 2006 10/14 
Appendix C Evaluation of Selected Biometric Fusion Techniques 

5 Guidance on Selecting Techniques 

As seen in the preceding section, several fusion techniques perform well, but even among the most 

accurate techniques there are performance differences. One of the key considerations when selecting a 

technique should be what resources are available for training the algorithm. This includes many factors 

such as availability of training data, modeling tools and expertise, target operational settings, integrity of 

(possibly multiple) databases, and reliability of ground-truth information for training data. Of central 

concern is the training data itself and any other knowledge of the score distributions: 

• Quantity of training data (separate counts of genuines and imposters) 

• Quality of training data (e.g. representativeness of operational data, accuracy of ground-truth 

information) 

• Design information (e.g. range of possible scores, whether scores represent similarity measures or 

probabilities, the meaning of special score values such as for FTEs, how multiple processing 

stages influence score distributions) 

• Joint distributions (i.e., the training data includes multiple scores for each subject comparison) 

Table 2 summarizes for each technique several factors that might influence the selection decision. These 

include simplifying theoretical assumptions (failure to satisfy these may substantially degrade 

performance); information required to implement the technique; observations on the difficulty of 

implementation and on the sensitivity of the technique to certain data characteristics; and how well the 

technique performed in this study. Note that this table is merely a summary: the companion papers in 

this series discuss the conceptual and implementation issues for these techniques. 

Simple Sum of Scores 

Requires no training data. Assumes inputs have comparable scale and Assumptions strength. 

Implementation Trivial: simple addition of scores. 

Inconsistent and often quite bad, but good for fusion of corresponding fingers Accuracy using the same matcher. 

Simple Sum of Z-Scores 

Requires small, univariate sample distribution (imposters only). Assumes 

Gaussian distributions, comparable strength of inputs. Highly sensitive to Assumptions assumption of comparable strength: the weaker input can pull results down. 

Not as sensitive to Gaussian assumption. 

Implementation Simple: Only requires normalization by standard deviation. 

Accuracy Inconsistent. 

Best Linear 

Requires joint sample distributions. Assumes size of dataset is large enough to 

measure target FAR accurately, but solution generally was not highly sensitive Assumptions to FAR. Does not assume fused scores are independent. Requires selection 

of appropriate target FAR. Insensitive to magnitude of outliers. 

Conceptually simple, but automated solution requires a special-purpose Implementation algorithm to determine the optimal weights for a given FAR. 

Accuracy Consistently near top 

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Studies of Biometric Fusion 

Product of Likelihood Ratios 

Assumes knowledge of univariate density distributions, for both genuine and 

Assumptions imposter scores. Assumes fused scores are independent, but apparently not 

very sensitive to this assumption. 

Successful implementation requires accurate curve fitting of genuine and 

imposter density distributions, potentially a painstaking process requiring 

Implementation advanced statistics capabilities. Variable bandwidth kernel estimates yielded a 

good initial fit, but special care was required to achieve reasonable fits to tails 

and bounded distributions. 

Accuracy Consistently top. 

Logistic Regression 

Generally requires joint sample distributions (does not assume independence). 

Assumptions In this analysis, however, independence assumption was highly effective, so 

models relied exclusively on univariate distributions. 

Successful implementation requires accurate curve fitting of density 

distributions, which is requires statistical expertise, but is supported by 

Implementation standard statistical packages. Care must be taken to select appropriate 

modeling terms: low-order polynomial terms were found to suffice. Sensitive 

to outliers, but special values (e.g., spikes, FTEs) can be handled explicitly. 

Accuracy Consistently near top 

Product of FARs 

Assumes knowledge of univariate probability distribution (impostors only). 

Assumptions Appears to be a reasonable heuristic and does not require genuine data, but 

lacks a solid theoretical underpinning. Assumes fused scores are independent. 

Successful implementation requires accurate curve fitting of imposter density 

Implementation distributions, which is a painstaking process akin to Product of Likelihood 

Ratios. 

Accuracy Consistently near top 

Min of FARs 

See Product of FARs. Note that score-level information is needed only to Assumptions calibrate the decision thresholds, not during operations. 

Implementation See Product of FARs. 

Accuracy Consistently poor performer 

Max of FARs 

See Product of FARs. Note that score-level information is needed only to Assumptions calibrate the decision thresholds, not during operations. 

Implementation See Product of FARs. 

Accuracy Usually near top (inconsistent) 

Table 2: Guidance on Selected Techniques 

6 Conclusions 

Several score-level fusion techniques were evaluated and compared in this study. There are several 

highly and consistently effective score-level fusion techniques to choose from. An important 

consideration when making a selection is what tools and information are available for modeling the score 

distributions. 

• As implemented, the product of likelihood ratios was the most sophisticated and most accurate 

method. This technique requires careful modeling of the score distributions. 

20 July 2006 12/14 
Appendix C Evaluation of Selected Biometric Fusion Techniques 

• Logistic regression is highly effective, and relies on standard statistical tools. 

• Best linear is a conceptually simple technique. This technique requires joint sample distributions 

(training data). Implementation is relatively easy for 2-way fusion. It might be an appropriate 

choice for some evaluations, benchmarks, prototypes, etc., where highly optimal accuracy is not 

required. 

• Product of FARs is most appropriate when no information on the genuine distribution is 

available; careful modeling of the imposter distribution is required. 

Many proposed techniques are based on simplifying assumptions. While any of these techniques might 

be valid in a specific situation, they are not reliable for general-purpose use and often perform poorly. 

• Simple sum of raw or z-normalized scores is not generally appropriate, but may be effective for 

combining multiple samples or instances from one matcher. 

• Examples of other such techniques include density estimation based on a normal (Gaussian) 

distribution assumption (or any parametric distribution). 

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