Score Normalization in
Multimodal Biometric Systems
Karthik Nandakumar and Anil K. Jain
Michigan State University, East Lansing, MI
Arun A. Ross
West Virginia University, Morgantown, WV
http://biometrics.cse.mse.edu
Multimodal Biometric Systems
• Multiple sources of biometric information are integrated to
enhance matching performance
• Increases population coverage by reducing failure to enroll rate
• Anti-spoofing; difficult to spoof multiple traits simultaneously
Fingerprint
Face
Hand geometry
Iris
Fusion in Multimodal Biometrics
Biometric Fusion
Prior to matching
Sensor
Level
Feature
Level
Raw Data
Feature
Sets
After matching
Dynamic
Classifier
Selection
Classifier
Fusion
Confidence
Level
Rank
Level
Abstract
Level
Matching
Scores
Class
Ranks
Class
Labels
Fusion at the Matching Score Level
• Fusion at the matching score level offers the best tradeoff
in terms of information content and ease in fusion
Classification Approach
Combination Approach
• Experiments indicate that the combination approach
performs better than the classification approach*
*A. Ross, A.K. Jain, “Information Fusion in Biometrics”, Pattern Recognition Letters, Sep. 2003
Fusion Rules*
• Problem: Classify input pattern Z into one of m possible
classes (c1, …,cm) based on evidence provided by R classifiers
• Let xi be the feature vector for the ith classifier derived from Z;
xi´s are independent
• Assign Z → cj, if g(cj) ≥ g(ck), 1 ≤ k ≤ m, k ≠ j
• Product rule: g(cr) =
R
∏ P (c
r
| xi )
i =1
R
• Sum rule: g(cr) =
∑ P (c
i =1
r
| xi )
P (cr | xi )
• Max rule: g(cr) = max
i
P(cr | xi )
• Min rule: g(cr) = min
i
*Kittler et al., “On Combining Classifiers”, IEEE PAMI, March 1998
Computing the Posteriori Probability
• To make use of the fusion rules, we need to compute P(cj|xi)
• At the matching score level, we have only the score sij (not xi)
• Verlinde et al. proposed that
sij = f(P(cj|xi)) + η(xi)
– f is a monotonic function
– η is the error introduced by the biometric system due to
problems in acquisition and feature extraction processes
• To estimate η, the biometric system should output a matching
score along with a confidence measure on that score
indicating the quality of the input feature vector xi
• If η is known, we can estimate P(cj|xi) from sij using nonparametric density estimation methods (e.g., Parzen window)
Score Normalization
• If η is unknown, the errors in the estimation of P(cj|xi) will be
very large; hence, it is better to combine the scores directly
• Combination of scores has the following problems:
• Non-homogeneous scores: distance or similarity
ƒ Ranges may be different; e.g., [0,100] or [0,1000]
ƒ Distributions may be different
• Modify the location and scale parameters of score
distributions of individual matchers to transform the scores
into a common domain
• Robustness: Should not be affected by the outliers
• Efficiency: Estimated parameters of the score distribution
should be close to the true values
Score Normalization Techniques
• Min-max normalization: Given matching scores {sk}, k=1,2,..,n
the normalized scores are given by:
s − min{s k }
s'=
max{s k } − min{s k }
• Decimal scaling: Used when scores of different matchers differ by
a logarithmic factor; e.g., one matcher has scores in the range
[0,1] and the other matcher has scores in the range [0, 1000]
s
,
n
10
n = log 10 max{s k }
s' =
Score Normalization Techniques
• Z-score:
s' =
s−µ
σ
• Median and Median Absolute Deviation (MAD):
( s − median )
s' =
MAD
MAD = median ( { s k } − median )
• Double Sigmoid function:
s' =
1
  s −t 
1 + exp  −2 

r



r = r1, if s < t
r = r2, otherwise
Score Normalization Techniques
• Tanh estimators:


( s − µ GH )  
s ' = 0.5  tanh  0.01
 + 1 ,
σ GH  


where µGH and σGH are the mean
and standard deviation estimates
of the genuine score distribution
as given by Hampel estimators*
• Min-max, Z-score, and Tanh normalization schemes are efficient
• Median, Double Sigmoid, and Tanh methods are robust
*Hampel et al., Robust Statistics: The Approach Based on Influence Functions, 1986
Experimental Setup
Face
Hand-geometry
Fingerprint
Database of 100 users with three modalities (5 samples/user)
Experimental Setup
Feature
Extraction
and Matching
df
Normalization
Sf´
Eigenfaces
Feature
Extraction
and Matching
Fusion
Rule
sp
Normalization
Decision
sp´
Minutiae
Feature
Extraction
and Matching
dh
14-D hand feature vector
Normalization
sh´
Fusion Rules
Sum rule: mean(sf´, sp´, sh´)
Min rule: min(sf´, sp´, sh´)
Max rule: max(sf´, sp´, sh´)
Distribution of Matching Scores
Face
Fingerprint
Hand-geometry
Performance of Individual Modalities
Normalization followed by Sum Rule
Sensitivity of Min-max to Outliers
Sensitivity of Z-score to Outliers
Sensitivity of Tanh to Outliers
Summary
• The effects of different score normalization techniques in a
multimodal biometric system have been studied
• Min-max, Z-score, and Tanh normalization techniques followed
by sum rule resulted in the best recognition performance
• Min-max and Z-score methods are efficient but sensitive to
outliers in the training data; Tanh is both efficient and robust
• If the parameters of the matching score distribution are known,
simple methods like Min-max and Z-score would suffice
• If the parameters are to be estimated from noisy training data,
one should choose robust methods like Tanh normalization
• If the system can provide both score and some confidence
measure on that score, non-parametric density estimation
methods can be used to estimate the posteriori probability
Efficiency of a Normalization Scheme
Before Normalization
After Sigmoid Normalization
After Min-max Normalization
After Tanh Normalization