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

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

Presented by Bao LY VAN

Prague – May 2004

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.

- Comparison with Dolfing’s system on Philips database
- 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

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

- Raw data:

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

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

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

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)

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)

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

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

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

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)

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.

- Exploits only the likelihood score on Philips database (with the same protocol as Dolfing)
- Protocol P2:
- Performs fusion of 2 scores on Philips database

- Protocol P3:
- Performs fusion of 2 scores on BIOMET database

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)

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)

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)

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

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

- 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)

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)

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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