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1891 C A L I F O R N I A I N S T I T U T E O F T E C H N O L O G Y

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CameraInitialization &Preprocessing

Filter/Predictor

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most voted quad.

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Location ofmaximum

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z �

confidence measure

U D

Hidden Markov Model

of being in state pen up (U)or pen down (D)

that estimates the likelihood

Ink presence

Segmentation

Stroke

Classification

Trajectory

Trajectory

Most likelystate sequence

Image Local InkMeasurement

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100.7 100.75 100.8 100.85 100.9−149.75

−149.7

−149.65

−149.6

−149.55

−149.5

−149.45

−149.4Sequence used for static resolution computation

100 150 200 250

−140

−120

−100

−80

−60

−40

−20

Sequence used for dynamic resolution computation

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time param. − EER = 5.00% Eucl. arc−len. − EER = 3.21%aff. arc−len. − EER = 5.29%

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time param. − EER = 1.61% Eucl. arc−len. − EER = 0.59%aff. arc−len. − EER = 0.48%

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time param. − EER = 2.60% Eucl. arc−len. − EER = 3.53%aff. arc−len. − EER = 4.16%

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time param. − EER = 4.21% Eucl. arc−len. − EER = 3.15%aff. arc−len. − EER = 3.76%

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time param. − EER = 2.00% Eucl. arc−len. − EER = 0.77%aff. arc−len. − EER = 0.43%

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time param. − EER = 2.71% Eucl. arc−len. − EER = 2.29%aff. arc−len. − EER = 3.02%

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time param. − EER = 0.87% Eucl. arc−len. − EER = 0.73%aff. arc−len. − EER = 0.58%

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time param. − EER = 5.16% Eucl. arc−len. − EER = 4.54%aff. arc−len. − EER = 4.52%

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time param. − EER = 2.54% Eucl. arc−len. − EER = 1.22%aff. arc−len. − EER = 0.94%

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FAR vs. FRR for set2 (skilled forgeries)

time param. − EER = 3.36% Eucl. arc−len. − EER = 3.28%aff. arc−len. − EER = 3.81%

0 1 2 3 4 50

1

2

3

4

5

FRR (%)

FA

R (

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FAR vs. FRR for set2 (random forgeries)

time param. − EER = 1.27% Eucl. arc−len. − EER = 1.06%aff. arc−len. − EER = 1.00%

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FAR vs. FRR for set1 (skilled forgeries)

time param. − EER = 2.90% Eucl. arc−len. − EER = 2.40%aff. arc−len. − EER = 1.89%

0 10

1

FRR (%)

FA

R (

%)

FAR vs. FRR for set1 (random forgeries)

time param. − EER = 0.88% Eucl. arc−len. − EER = 0.28%aff. arc−len. − EER = 0.12%

0 1 2 3 4 50

1

2

3

4

5

FRR (%)

FA

R (

%)

FAR vs. FRR for set2 (skilled forgeries)

time param. − EER = 1.27% Eucl. arc−len. − EER = 1.73%aff. arc−len. − EER = 1.11%

0 10

1

FRR (%)

FA

R (

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FAR vs. FRR for set2 (random forgeries)

time param. − EER = 0.28% Eucl. arc−len. − EER = 0.35%aff. arc−len. − EER = 0.22%

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time param. Eucl. arc−len.aff. arc−len.

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Subject #

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time param. Eucl. arc−len.aff. arc−len.

1 10 20 30 40 480

5

10

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Subject #

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time param. Eucl. arc−len.aff. arc−len.

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time param. Eucl. arc−len.aff. arc−len.

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1

2

3

4

5

6

7

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FA

R (

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FAR vs. FRR for set1 (skilled forgeries)

harmonic mean − EER = 1.89% DPM distance − EER = 4.52% weighted correl. − EER = 2.96%Procrustes dist. − EER = 3.60%

0 1 20

1

2

FRR (%)

FA

R (

%)

FAR vs. FRR for set1 (random forgeries)

harmonic mean − EER = 0.12% DPM distance − EER = 0.94% weighted correl. − EER = 0.20%Procrustes dist. − EER = 0.51%

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8

FRR (%)

FA

R (

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FAR vs. FRR for set2 (skilled forgeries)

harmonic mean − EER = 1.11% DPM distance − EER = 3.81% weighted correl. − EER = 1.50%Procrustes dist. − EER = 1.96%

0 1 20

1

2

FRR (%)

FA

R (

%)

FAR vs. FRR for set2 (random forgeries)

harmonic mean − EER = 0.22% DPM distance − EER = 1.00% weighted correl. − EER = 0.43%Procrustes dist. − EER = 0.31%

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90 100 110 120 130

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Signature from set s025

0 20 40 60 80

0

10

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90 100 110 120 130 140

0

10

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70

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100 120 140 160 180

0

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60 80 100 120 140 160−5

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20 40 60 80 100 120−5

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40 60 80 100 120

0

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100 120 140 160

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100 120 140 160

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0 20 40 60 80−5

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80 100 120 140 160

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80 100 120 140 160

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80 100 120 140 160 180 200

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20 40 60 80 100 120 140

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100 120 140 160 180

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80 100 120 140 160 180 200

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100 120 140 160

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100 110 120 130 140 150 160

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100 120 140 160

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y = 1.720 e0.003x

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Computation time vs. sig. length − Wj=20

y = 3.271 e0.003x

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Computation time vs. sig. length − Wj=30

y = 3.866 e0.004x

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Computation time vs. sig. length − Wj=40

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y = 0.062 x0.82

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Comp. time vs. Max. Storage for CDPM − Wj=20

y = 0.030 x1.03

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Comp. time vs. Max. Storage for CDPM − Wj=30

y = 0.016 x1.18

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y = 0.013 x1.23

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FAR vs. FRR for set2 (classif. with matching dist.)

DPM − EER = 3.81% CDPM − EER = 3.41%

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FAR vs. FRR for set1 (classif. with mult. dist.)

DPM − EER = 1.89% CDPM − EER = 2.12%

0 1 2 3 40

1

2

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FAR vs. FRR for set2 (classif. with mult. dist.)

DPM − EER = 1.11% CDPM − EER = 1.50%

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FAR vs. FRR for set1 (classif. with matching dist.)

DPM − EER = 5.40% CDPM − EER = 4.86%

0 1 2 3 4 5 6 7 8 9 100

1

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3

4

5

6

7

8

9

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FRR (%)

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FAR vs. FRR for set2 (classif. with matching dist.)

DPM − EER = 4.39% CDPM − EER = 3.86%

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FAR vs. FRR for set1 (classif. with mult. dist.)

DPM − EER = 2.14% CDPM − EER = 2.39%

0 1 2 3 4 50

1

2

3

4

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FAR vs. FRR for set2 (classif. with mult. dist.)

DPM − EER = 1.34% CDPM − EER = 1.55%

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8

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FRR (%)F

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FAR vs. FRR for set1 (classif. with matching dist.)

DPM − EER = 7.63% CDPM − EER = 6.86%

0 2 4 6 8 10 12 140

2

4

6

8

10

12

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FRR (%)

FA

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FAR vs. FRR for set2 (classif. with matching dist.)

DPM − EER = 6.38% CDPM − EER = 5.22%

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0 1 2 3 4 5 6 70

1

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4

5

6

7

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FAR vs. FRR for set1 (classif. with mult. dist.)

DPM − EER = 3.09% CDPM − EER = 3.68%

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

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FA

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FAR vs. FRR for set2 (classif. with mult. dist.)

DPM − EER = 2.71% CDPM − EER = 2.86%

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FRR (%)F

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FAR vs. FRR for set1 (classif. with matching dist.)

DPM − EER = 4.82% CDPM − EER = 4.83%

0 1 2 3 4 5 6 7 8 90

1

2

3

4

5

6

7

8

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FRR (%)

FA

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FAR vs. FRR for set2 (classif. with matching dist.)

DPM − EER = 3.49% CDPM − EER = 3.44%

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FAR vs. FRR for set1 (classif. with mult. dist.)

DPM − EER = 2.16% CDPM − EER = 2.43%

0 1 2 3 4 50

1

2

3

4

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FAR vs. FRR for set2 (classif. with mult. dist.)

DPM − EER = 1.11% CDPM − EER = 1.35%

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set1 − DPM set2 − DPM set1 − CDPMset2 − CDPM

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