Fusion of HMM’s Likelihood and Viterbi Path for On-line Signature Verification
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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
Prague – May 2004
Presented by Bao LY VAN
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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
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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
Altitude (0°-90°)
90°
270°
0°
Azimuth (0°-359°)
180°
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HMM Architecture• Continuous, left-right HMM• Mixture of 4 Gaussians• Personalized number of states
– 30 points to estimate a gaussian
30*4totalT
N
When using 5 training signatures, the personalized number of states for this signer is 10
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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
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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
Feature ZFea
ture
A
Feature ZFea
ture
A
x
opt xσx
*'
Normalize
optσ
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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|
)_
exp(featuresN
LLNmeanLLNSl
• Convert to similitude between [0, 1]
(Likelihood Score)
)(log OPLL
)(OlengthLLLLN
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What is The Viterbi Path Approach?
HMM
(Viterbi Algorithm)input output
Normalized Log-Likelihood
Viterbi Path (VP)
• VP is the sequence of states that maximizes the likelihood of the test signature
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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
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LL = -1166.10LLN = -14.95SV = (21, 30, 27)
LL = -296.46LLN = -16.47SV = (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
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How to use the VP (SV) information?
• Convert Average Distance to similitude between [0, 1] (Viterbi Score)
…
SV 1SV 2
SV K
References
……
HMM
• SVs of HMM’s training signatures are saved as References
SVaverage
Average Distance
)*30
exp(N
dS hv
Hamming Distance
Hamming Distance
Hamming Distance
...
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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)
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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
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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)
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
opt
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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)
Likelihood Viterbi Path Fusion
TE min (%) 3.73 7.66 3.26EER (%) 4.18 8.12 3.54
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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)
genuine test data Likelihood Viterbi Path Fusion
No time variabilityTE min (%) 5.27 3.71 2.47
EER (%) 6.45 4.07 2.84Time variability
(5 months before)TE min (%) 14.30 7.44 6.95
EER (%) 16.70 9.21 8.57
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P3: Confidence Level on 50 trials
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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
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Thank you for your attention!
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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)
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
opt
• Mean result of 10 trials
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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)
Likelihood Viterbi Path Fusion
TE min (%) 3.73 7.66 3.26EER (%) 4.18 8.12 3.54
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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)
genuine test data Likelihood Viterbi Path Fusion
2nd session TE min (%) 5.27 3.71 2.47
EER (%) 6.45 4.07 2.841st session
(5 months before)TE min (%) 14.30 7.44 6.95
EER (%) 16.70 9.21 8.57