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Fusion of HMM’s Likelihood and Viterbi Path for On-line Signature Verification

Fusion of HMM’s Likelihood and Viterbi Path for On-line Signature Verification. Bao Ly Van - Sonia Garcia Salicetti - Bernadette Dorizzi Institut National des Télécommunications. Presented by Bao LY VAN. Prague – May 2004. Overview. HMM for Online Signature

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Fusion of HMM’s Likelihood and Viterbi Path for On-line Signature Verification

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  1. Fusion of HMM’s Likelihood and Viterbi Path for On-line Signature Verification Bao Ly Van - Sonia Garcia Salicetti - Bernadette Dorizzi Institut National des Télécommunications Presented by Bao LY VAN Prague – May 2004

  2. Overview • HMM for Online Signature • Likelihood Approach: Normalized Log-Likelihood information given by the HMM • Comparison with Dolfing’s system on Philips database [Ref] J.G.A. Dolfing, "Handwriting recognition and verification, a Hidden Markov approach", Ph.D. thesis, Philips Electronics N.V., 1998. • Viterbi Path Approach: exploit the Viterbi Path information given by the HMM • Motivation of the Viterbi Path approach • Fusion Likelihood and Viterbi Path • Experiments & Results New

  3. Azimuth (0°-359°) Altitude (0°-90°) 0° 270° 180° 90° Introduction of Online Signature • Captured by a Digitizing Tablet • A signature: a sequence of sampled points • Raw data: • Coordinates: x(t), y(t) • Pressure: p(t) • Pen Inclination Angles

  4. HMM Architecture • Continuous, left-right HMM • Mixture of 4 Gaussians • Personalized number of states • 30 points to estimate a gaussian When using 5 training signatures, the personalized number of states for this signer is 10

  5. Feature Extraction • Features extracted from coordinates • Velocity • Acceleration • Curvature radius • Normalized coordinates by the gravity center • Length to Width ratio • ... • 25 features at each point of the signature:signature = sequence of feature vectors

  6. Feature A Feature A Normalize Feature Z Feature Z Personalized Feature Normalization • Goals: • Same variance for all features = same importance • A good choice of leads to a faster convergence • Avoid the overflow problem in training phase • Implementation: • Normalization factors (one per feature) of each signer are stored with his/her signature model (HMM) • A test signature will be normalized according to these factors

  7. HMM Likelihood Approach • Log-Likelihood of a signature • Normalized by the signature length • Score • Based on the Distance between the LLN of the test signature and the Average LLN of training signatures: |LLN-LLNmean| • Convert to similitude between [0, 1] • (Likelihood Score)

  8. New What is The Viterbi Path Approach? • VP is the sequence of states that maximizes the likelihood of the test signature Normalized Log-Likelihood HMM (Viterbi Algorithm) input output Signature Viterbi Path (VP)

  9. Representation of Viterbi Path • VP generated by a N states HMM is represented by a N components Segmentation Vector (SV) • Each component of SV contains the number of points modeled by the corresponding state

  10. LL = -1166.10 LLN = -14.95 SV = (21, 30, 27) LL = -296.46 LLN = -16.47 SV = (18, 0, 0) Complementarity between VP and LL • Genuine and forged signatures can have very close Normalized Log-Likelihoods although their VPs (SVs) are quite different • It is easier to forge the system when the score based on Normalized Likelihood

  11. Hamming Distance HMM Hamming Distance SV 1 Test Signature Training Signature 1 ... SV 2 Training Signature 2 … Hamming Distance … SV … SV K Training Signature K References How to use the VP (SV) information? • SVsof HMM’s training signatures are saved as References • Convert Average Distance to similitude between [0, 1] (Viterbi Score) average AverageDistance

  12. Viterbi Score vs Likelihood Score • Important overlap when using only one score • Viterbi and Likelihood scores are complementary • Simple arithmetic mean is used for fusion (no extra-training)

  13. Experiments Overview • Protocol P1: • Exploits only the likelihood score on Philips database (with the same protocol as Dolfing) [Ref] J.G.A. Dolfing, "Handwriting recognition and verification, a Hidden Markov approach", Ph.D. thesis, Philips Electronics N.V., 1998. • Protocol P2: • Performs fusion of 2 scores on Philips database • Protocol P3: • Performs fusion of 2 scores on BIOMET database

  14. NN 0.7 1 1.3 1.6 2 2.5 3.2 6 10 TE min(%) 1.32 1.59 0.97 0.92 0.88 0.97 1.10 1.23 1.98 1.98 EER (%) 1.35 2.04 1.02 0.96 0.95 1.03 1.13 1.24 1.99 2.02 P1: Likelihood Score on Philips Database • 15 signatures to train HMM • Repeat 10 times: robust results • Our result is of 0.95% EER compared to 2.2% EER of Dolfing (1998)

  15. Likelihood Viterbi Path Fusion TE min (%) 3.73 7.66 3.26 EER (%) 4.18 8.12 3.54 P2: Fusion on Philips database • Only 5 signatures to train HMM • Repeat 50 times: robust results • Fusion lowers the Error Rate by 15% (compared to likelihood)

  16. genuine test data Likelihood Viterbi Path Fusion No time variability TE min (%) 5.27 3.71 2.47 EER (%) 6.45 4.07 2.84 Time variability (5 months before) TE min (%) 14.30 7.44 6.95 EER (%) 16.70 9.21 8.57 P3: Fusion on BIOMET database • 5 signatures to train HMM • Genuine test on two session • Repeat 50 times: robust results • Fusion lowers the Error Rate by a factor 2 (compared to likelihood)

  17. P3: Confidence Level on 50 trials

  18. Conclusions • We have built a HMM-based system and introduced 2 measures of information: • Likelihood score • Viterbi score • We have compared both scores on two databases: Philips and BIOMET • The new approach using VP information can give better results than LL approach (BIOMET) • Fusion of both scores improves results which shows their complementarity

  19. Thank you for your attention! ?

  20. NN 0.7 1 1.3 1.6 2 2.5 3.2 6 10 TE min(%) 1.32 1.59 0.97 0.92 0.88 0.97 1.10 1.23 1.98 1.98 EER (%) 1.35 2.04 1.02 0.96 0.95 1.03 1.13 1.24 1.99 2.02 • Mean result of 10 trials Protocol 1: Only Likelihood • Philips database • 51 signers, 30 genuine and about 70 forgeries per signer • Forgery of high quality • Dolfing’s protocol • 15 genuine signatures to train HMM • 15 other genuine signatures and forgeries to test HMM (~4000 signatures) • Fixed partition of training and testing genuine signatures • Our result is of 0.95% EER compared to 2.2% EER of Dolfing (1998)

  21. Likelihood Viterbi Path Fusion TE min (%) 3.73 7.66 3.26 EER (%) 4.18 8.12 3.54 Protocol 2: Fusion on Philips database • Protocol • Only 5 signatures to train HMM, randomly selected from 30 • Test on the remaining 25 genuine signatures and forgeries • Repeat 50 times: robust results • Fusion lowers the Error Rate by 15% (compared to likelihood)

  22. genuine test data Likelihood Viterbi Path Fusion 2nd session TE min (%) 5.27 3.71 2.47 EER (%) 6.45 4.07 2.84 1st session (5 months before) TE min (%) 14.30 7.44 6.95 EER (%) 16.70 9.21 8.57 Protocol 3: Fusion on BIOMET • BIOMET Database • 87 signers • Two sessions spaced of 5 months: 5 + 10 genuine, 12 forgeries per signer • Protocol: • 5 signatures (2nd session) to train HMM, randomly selected from 10 • test on the remaining 5 genuine signatures of the 2nd session, on the 5 genuine of the 1st session and the forgeries • Repeat 50 times: robust results • Fusion lowers the Error Rate by a factor 2 (compared to likelihood)

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