Research Journal of Applied Sciences, Engineering and Technology 3(11): 1318-1322, 2011
ISSN: 2040-7467
© Maxwell Scientific Organization, 2011
Submitted: August 26, 2011
Accepted: September 17, 2011
Published: November 25, 2011
Probabilistic Model for Dynamic Signature Verification System
1
Chai Tong Yuen, 1Wai Loon Lim, 2ChingSeong Tan, 1Bok-Min Goi,
1
Xin Wang and 3Jee-Hou Ho
1
University Tunku Abdul Rahman (UTAR), 53300 Malaysia
2
Multimedia University, 63100 Malaysia
3
The University of Nottingham, Malaysia
Abstract: This study has proposed the algorithm for signature verification system using dynamic parameters
of the signature: pen pressure, velocity and position. The system is proposed to read, analyze and verify the
signatures from the SUSig online database. Firstly, the testing and reference samples will have to be
normalized, re-sampled and smoothed through pre-processing stage. In verification stage, the difference
between reference and testing signatures will be calculated based on the proposed thresholded standard
deviation method. A probabilistic acceptance model has been designed to enhance the performance of the
verification system. The proposed algorithm has reported False Rejection Rate (FRR) of 14.8% and False
Acceptance Rate (FAR) of 2.64%. Meanwhile, the classification rate of the system is around 97%.
Key words: Dynamic, signature verification, standard deviation, threshold and probabilistic model, velocity
INTRODUCTION
Signatures are composed of special character and
flourishes and therefore most of the time they can be
unreadable. Also, intrapersonal variations and
interpersonal differences make it necessary to analyze
them as complete images but not as letters and words put
together. Signatures have been the primary mechanism
both for authentication and authorization in legal
documentation in recent years.
Based on different applications, signature verification
system can be operated in two different modes
(Plamondon and Srihari, 2000, Seiler et al., 1996); online
and offline mode. In the online mode, the signature
verification is dealing with the instant inputs from the
system such as credit card verifier. For offline mode, the
verification is done on the recorded signatures such as
bank’s document verification (Dimauro et al., 1997,
Generally, signature verification system can be
categorised into two types: dynamic and static. The
dynamic signature verification system is dealing with
signal processing while the static signature verification
system is more on image processing. Some techniques
applied in static signature verification systems are neural
networks (Bajaj and Chaudhury, 1997; Huang and Yan,
1997; Karouni et al., 2011), model based approaches
(Huang and Yan, 2002; Wen et al., 2009) and wavelets
transform (Deng et al., 1997). Meanwhile, Dynamic
Time Warping (DTW) (Fenton et al., 2006) and Gaussian
Mixture Modelling (GMM) methods (Miguel-Hurtado
et al., 2007, 2008) have been introduced for dynamic
automated signature verification system. Basically, DTW
is used in pre-processing to remove the intrinsic
variability from user signature by aligning the acquired
signal. GMM is used to model the probabilistic
distribution of the set of pseudo-distances and to calculate
the likelihood ratio between the sample and reference
signature.
There are other approaches which based on the
concept of filters (Tanaka and Bargiela, 2005). Firstly,
global features of the signature, such as average velocity
are considered through Euclidian distance. In the second
filter, local features are considered. Strokes are segmented
using the minima of the velocity and encoded before
comparing them using DTW (Miguel-Hurtado et al.,
2007, 2008) and signer-specific thresholds. On the other
hand, Linear Prediction Coding (LPC) cestrum and Neural
Networks (Wu et al., 1997) are proposed in the dynamic
signature verification system. LPC is used in the preprocessing stage and its coefficients are used as the input
to the neural networks. The neural networks (Mailah and
Han, 2008) mostly used in the verification process.
Besides that, performance could be improved by fusing
static and dynamic signature verification techniques
(Alonso-Fernandez et al., 2009).
In this research, the signatures will be pre-processed
through normalization and re-sampling. A simple and
efficient method, standard deviation has been proposed
for the verification stage with estimated threshold as the
condition. Finally, a probabilistic based signature
acceptance criterion has been designed to refine the
verification results.
Corresponding Author: Chai Tong Yuen, University Tunku Abdul Rahman (UTAR), 53300 Malaysia
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Res. J. Appl. Sci. Eng. Technol., 3(11): 1318-1322, 2011
MATERIALS AND METHODS
The overview of the system is shown in Fig. 1. The
SUSig Online Databasem (Sabanci University, 2004)
consists of two parts, namely visual and blind sub-corpus.
Visual sub-corpus was collected using Interlink Elec.
ePad Ink signature tablet with built-in LCD screen while
blind sub-corpus was collected using Wacom Graphire2
pressure sensitive tablet. For each subject there are 20
genuine and 10 forgery signatures. Genuine signatures
were collected in two different sessions. The proposed
system database contains 25 genuine signers and 25
forgery signers from the SUSig database. Each signer will
produce 10 samples of signature. Thus, there are 500
signatures in total for this experiment.
For each signature, the information from three
dynamic features such as x- coordinate, y-coordinate, and
pressure, p have been used in this study. Meanwhile, the
velocity, v is derived by using differentiation. The training
samples are shown in Fig. 2.
Samples for reference signature
Sample 1 (S1): x1, y1, p1, v1
Sample 2 (S2): x2, y2, p2, v2
Sample 3 (S3): x3, y3, p3, v3
Sample 4 (S4): x4, y4, p4, v4
Sample 5 (S5): x5, y5, p5, v5
Fig.1: System overview
Sample for testing signature
Sample T (S6): xT, yT, pT, vT
1.4
1.2
Pre-processing: During the pre-processing stage, the
input signature will undergo normalisation and resampling. The main purpose of normalization is to scale
all the values into the range of zero to one as shown in
Fig. 3. Linear scaling is used for the normalization of the
vector (S) which represents signature parameters such as
x-coordinate (x), y-coordinate (y), pressure (p) and
velocity (v).
S − min( S )
S=
max( S ) − min( S )
1
0.8
0.6
0.4
0.2
0.1
0
(1)
20
40
60
80 100 120 140 160 180 200
Fig. 2: Training samples
4
1
The Maximum (max) and minimum (min) values in
the vector S are the global maximum and minimum points
for the normalized signal.
The main reason for re-sampling is to sample the
wavelength of the signature into the desired wavelength
further processing. The wavelength of the signature is
directly affected by the number of recorded data during
the signing process. The more data is recorded, the longer
the wavelength is. Thus, each signature might have
different wavelengths. In order to compare them equally,
both data needs to be re-sampled and smoothen as shown
in Fig. 4.
X10
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
20
40
60
80 100 120 140 160 180 200
Fig. 3: Normalized signatures
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Res. J. Appl. Sci. Eng. Technol., 3(11): 1318-1322, 2011
1.4
(a) 100
90
80
70
60
50
40
30
20
10
0
0.0
1.2
Percentage (%)
1
X- coordinate
FRR
FRA
0.8
0.6
0.4
0.2
0.1
0
20
60
40
0.1 0.2
80 100 120 140 160 180 200
0.3 0.4 0.5 0.6 0.7
Threshold
Fig. 4: Resampled samples
0.8
0.9 1.0
(a)
0.7
(b) 100
90
80
70
60
50
40
30
20
10
0
0.0
y- coordinate
Percentage (%)
0.6
FRR
FRA
0.5
0.4
0.3
0.2
0.1
0.1 0.2
0
0
20
40
60
80 100 120 140 160 180 200
(d) 100
Percentage (%)
A total of five signatures have been re-sampled to the
same wavelength. Let Iref be the average wavelength of
the reference signature,
I1 + I 2 + I 3 + I 4 + I5
5
(2)
90
80
70
60
50
40
30
20
10
0
0.0
FRR
FRA
0.1 0.2
IT(initial) be the wavelength of the testing signature and
lT(final) is the wavelength of the re-sampled testing
signature,
I T (initial )
(
S1 + S2 + S3 + S4 + S5
5
d = ST − Sref
)
Velocity
0.3 0.4 0.5 0.6 0.7
Threshold
0.8
0.9 1.0
0.8
0.9 1.0
(c)
(c) 100
90
80
70
60
50
40
30
20
10
0
0.0
(3)
After the re-sampling process, the reference signal,
Sref can now be constructed as,
Sref =
0.9 1.0
FRR
FRA
Pressure
Percentage (%)
I T ( final ) =
I T (initial ) × I ref
0.8
(b)
Fig. 5: Difference in magnitude between reference and sampled
signals
I ref =
0.3 0.4 0.5 0.6 0.7
Threshold
(4)
0.1 0.2
0.3 0.4 0.5 0.6 0.7
Threshold
(d)
(5)
Fig. 6: FRR & FAR for (a) X-coordinate, (b) Y-coordinate, (c)
Velocity, and (d) Pressure
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Res. J. Appl. Sci. Eng. Technol., 3(11): 1318-1322, 2011
Table 1: False rejection rate
TH
X
0.0
0.00
0.1
0.80
0.2
2.00
0.3
3.20
0.4
6.80
0.5
12.80
0.6
23.60
0.7
44.40
0.8
66.40
0.9
88.40
1.0
100.00
Y
0.00
0.40
0.40
0.80
2.80
8.00
17.60
32.80
56.40
84.80
100.00
Table 2: False acceptance rate
TH
X
Y
0.0
51.94
88.99
0.1
39.68
76.03
0.2
28.21
55.21
0.3
18.98
32.30
0.4
11.43
12.43
0.5
5.69
3.05
0.6
1.980
0.842
0.7
0.50
0.27
0.8
0.17
0.07
0.9
0.02
0.01
1.0
0.00
0.00
P
0.00
0.80
0.80
1.60
2.40
8.40
18.80
37.20
65.20
94.80
100.0
V
0.00
2.00
3.20
4.00
6.80
10.80
16.40
23.60
28.40
58.40
0100.00
P
95.98
93.33
89.08
81.44
68.06
48.34
5.96
8.02
1.09
0.04
0.01
V
78.61
72.30
66.29
61.36
56.98
53.65
48.78
41.78
23.95
2.00
0.00
SD =
2
d2
I ref
Table 4: FAR & FRR for different combination of the parameters
Selected Parameter
FRR (%)
FAR (%)
ERROR (%)
X,P,V
48.80
1.45
2.40
X,P
26.00
3.87
4.31
X,V
35.20
4.97
5.58
Y,P,V
45.60
0.93
1.82
Y,V
32.00
3.20
3.78
Y,P
22.80
2.57
2.98
X,Y
11.20
3.13
3.29
X,Y,V,P
14.80
2.64
2.89
FRR = (No. of false rejection sample /
No. of geninune signature) × 100%
FAR = (No. of false acceptance sample /
No. of forgery signature) × 100%
(9)
By using the information found in Table 1 and 2,
FRR and FAR graphs are plotted in Fig. 6. From Fig. 6,
Equal Error Rate (EER) for each parameter can be
obtained as shown in Table 3.
(6)
Probabilistic acceptance criterion: Based on the EER
obtained from the previous section, we found that the
information of x-coordinate and y-coordinate are the most
dependable followed by the pressure and velocity. A
probabilistic acceptance criterion has been proposed in
this section to accept a signature with condition:
(7)
where, d is the difference between reference and testing
signatures as shown in Fig. 5.
Threshold estimation: The purpose of doing this is to
achieve lower FAR and FRR. A good signature
verification system should have a good balance on its
sensitivity to the variation of the signature. First of all the
standard deviation between the genuine reference signal
and the genuine testing signals need to be collected for
each parameter (x, y, p and v). Minimum and maximum
standard deviation values are selected for threshold
estimation, TH_ a where TH is the controlling threshold
and a can be either x, y, p or v.
TH_a = max - (max - min) TH
EER (%)
9.166
6.235
22.43
27.42
threshold. If the value does not exceed the threshold, the
signature will be accepted and via versa. Same steps are
repeated for forgery samples to calculate FAR. As a
result, the rate of false rejection and false acceptance can
be obtained as in Table 1 and 2:
Verification: In verification process, the difference
between reference signature, Sref and testing signature, ST
can be calculated by using standard deviation and
compared it to the estimated threshold. If the difference
between standard deviation, SD and estimated threshold
is low, the signature will be accepted as the genuine
signature.
d 2 = ( ST − Sref )
Table 3: Estimated threshold for X, Y, P &V
Parameter
Threshold, TH
X
0.4394
Y
0.4660
P
0.6197
V
0.7795
(8)
Next, the difference between reference and testing
samples (FRR) is being compared to the estimated
X1Y1(PcV) = ACCEPT
(10)
To accept a signature, X and Y and either P or V
must give a TRUE output. This means the system will
accept a signature when X is accepted, Y is accepted, and
either P or V or both is accepted.
RESULTS AND DISCUSSION
In order to verify the efficiency of the proposed
probabilistic criterion in Dynamic Signature Verification
System, an experiment using different combinations of the
dynamic parameters had been conducted. The result
obtained is shown in Table 4.
From Table 4, the combination of x-coordinate, ycoordinate, pressure and velocity is the best combination
as expected. Although the error rate is not the lowest, this
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Res. J. Appl. Sci. Eng. Technol., 3(11): 1318-1322, 2011
combination provided a balance of performance between
FRR and FAR.
CONCLUSION
In conclusion, this study has presented a simple and
efficient approach for dynamic signature verification
system. A reliable signature verification system has been
designed with the success classification rate of 97%. The
algorithm has proven that, x-coordinate and y-coordinate
and pressure and velocity are sufficient and effective for
dynamic signature verification. In future, the aim will be
to reduce the FRR with more testing samples being added
with the equality of genuine and forgery signatures.
ACKNOWLEDGMENT
The authors gratefully acknowledge the support from
Universiti Tunku Abdul Rahman.
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