Fusion of hmm s likelihood and viterbi path for on line signature verification
Download
1 / 22

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


  • 112 Views
  • Uploaded on

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

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Fusion of HMM’s Likelihood and Viterbi Path for On-line Signature Verification' - jace


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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
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


Introduction of online signature

Azimuth (0°-359°)

Altitude (0°-90°)

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


Hmm architecture
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
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


Personalized feature normalization

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


Hmm likelihood approach
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

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)


Representation of viterbi path
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


Complementarity between vp and ll

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


How to use the vp sv information

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


Viterbi score vs likelihood score
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
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


P1 likelihood score on philips database

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)


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)


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)



Conclusions
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



Protocol 1 only likelihood

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)


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)


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)


ad