Score Normalization in Multimodal Biometric Systems

Transcription

1 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

2 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

3 Fusion in Multimodal Biometrics Biometric Fusion Prior to matching After matching Sensor Level Raw Data Feature Level Feature Sets Dynamic Classifier Selection Classifier Fusion Confidence Level Matching Scores Rank Level Class Ranks Abstract Level Class Labels

4 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

5 Fusion Rules* Problem: Classify input pattern Z into one of m possible classes (c 1,,c m ) based on evidence provided by R classifiers Let x i be the feature vector for the i th classifier derived from Z; x i s are independent Assign Z c j, if g(c j ) g(c k ), 1 k m, k j Product rule: g(c r ) = Sum rule: g(c r ) = R i= 1 R i= 1 P( c r x i ) P( c r x i ) Max rule: g(c r ) = max P( c i r x i ) Min rule: g(c r ) = min P( c i r x i ) *Kittler et al., On Combining Classifiers, IEEE PAMI, March 1998

6 Computing the Posteriori Probability To make use of the fusion rules, we need to compute P(c j x i ) At the matching score level, we have only the score s ij (not x i ) Verlinde et al. proposed that f is a monotonic function s ij = f(p(c j x i )) + η(x i ) 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 x i If η is known, we can estimate P(c j x i ) from s ij using nonparametric density estimation methods (e.g., Parzen window)

7 Score Normalization If η is unknown, the errors in the estimation of P(c j x i ) 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 Ranges may be different; e.g., [0,100] or [0,1000] 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

8 Score Normalization Techniques Min-max normalization: Given matching scores {s k }, k=1,2,..,n the normalized scores are given by: s ' = s min{ s } max{ s } min{ s } k k 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 s ' = n 10, n = log max{ s } 10 k

9 Z-score: Score Normalization Techniques s s ' = µ σ Median and Median Absolute Deviation (MAD): ( s median) s ' = MAD MAD = median({ s } median ) Double Sigmoid function: s ' = 1 s t 1+ exp 2 r r = r 1, if s < t r = r 2, otherwise k

10 Score Normalization Techniques Tanh estimators: s ( s µ ) GH ' = 0.5 tanh , σ GH where µ GH and σ GH 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

11 Experimental Setup Face Hand-geometry Fingerprint Database of 100 users with three modalities (5 samples/user)

12 Experimental Setup Feature Extraction and Matching d f Normalization S f Eigenfaces Fusion Rule Decision Feature Extraction and Matching s p Normalization s p Minutiae Feature Extraction and Matching d h Normalization s h 14-D hand feature vector Fusion Rules Sum rule: mean(s f, s p, s h ) Min rule: min(s f, s p, s h ) Max rule: max(s f, s p, s h )

13 Distribution of Matching Scores Face Fingerprint Hand-geometry

14 Performance of Individual Modalities

15 Normalization followed by Sum Rule

16 Sensitivity of Min-max to Outliers

17 Sensitivity of Z-score to Outliers

18 Sensitivity of Tanh to Outliers

19 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

20 Efficiency of a Normalization Scheme Before Normalization After Sigmoid Normalization After Min-max Normalization After Tanh Normalization