Enhanced Signature Verification Technique Using Data Glove Shohel Sayeed FIST, Multimedia University Jalan Ayer Keroh Lama, Bukit Beruang, 7450 Melaka, Malaysia [email protected]

Rosli Besar FET, Multimedia University Jalan Ayer Keroh Lama, Bukit Beruang, 7450 Melaka, Malaysia [email protected]

Abstract— In order to ameliorate the degree of trustiness and, high security, we have presented a new approach to hand signature verification applying data glove. Data glove is a new-fangled dimension in the field of virtualreality environments, originally designed to satisfy the stringent requirements of modern motion capture and animation professionals. In our research, we attempt to change over the carrying out of data glove from motion animation towards signature substantiation problem, making use of the offered multiple degrees of freedom for each finger as well as for the hand. Our proposed approach is tested in context of highly skilled forgeries with a large number of glove-based signature data sets and obtained a significant level of accuracy in signature verification. Keywords- Data glove; signature verification; singular value decomposition

I. INTRODUCTION The promising evolution in signature verification is utilizing the benefits of signal processing over the typical image processing techniques. The benefits of involving signal processing for this purpose include reduction of equipment complexity, increased robustness against counterfeit, sovereignty of media and signature concealment [1]. In the typical image processing technique a strong impression of the signature with prescribed ink on a stipulated media is essential and is the key for further processing. The signature image is then scanned into digital representation and that digital image is used for key construction. The process continues to search the database for a nearest match and the result determines the authentication decision [2]. Since the signature plays as a key component here, and it is perceptible and available for any misuse like forging etc. In addition, the image processing involves volumes of data and any reduction in volume needs a compromise with the efficiency of the system. The continuous enhancement to this scenario leads improving two major criteria. One is to protect the signature from forgery and the second is to reduce the volume of data

978-1-4244-6716-7/10/$26.00 ©2010 IEEE

Nidal S. Kamel Dept. of EEE, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia [email protected]

involved and hence the speed of the process can be improved. Using a data glove is a paradigm shift from image to signal processing and the first problem is immediately solved since there is no significance given to ink or paper. However the data glove used for this purpose that the subject wears on while signing for access consists of many electrodes in various positions. These electrodes produce continuous signals during the signing process and are resembles image processing in volume and needs to be reduced to overcome the drawback. Singular Value Decomposition (SVD) is a popular technique used for source separation has been introduced in this case and found to be competent in solving the problem [3-4]. In this research, we enhanced our work [4] using different matching techniques as well as different data sets using reduced number of sensors from 14 to 5 and demonstrate the level of accuracy in terms of False Acceptance Rate (FAR) and False Rejection Rate (FRR). II.

PROPOSED MODEL FOR THE GLOVE-BASED SIGNATURE VERIFICATION TECHNIQUE

Figure 1. Proposed model for the glove-based signature verification technique

Fig. 1 shows the overall system design of our signature verification system. During enrollment of a new user, input to

the system is a set of signatures produced by that user (genuine samples). The genuine reference sample data is preprocessed and the features are extracted. The signature data is then saved in a database together with a unique identifier that is used to retrieve the signatures during the matching. For verification, a test signature along with the genuine writer identity is input to the system. The same preprocessing and feature extraction methods are used. The signature is then compared to each of the reference signatures, which are retrieved from the database based on the author identifier. The resulting difference are calculated and included as false acceptance rate (FAR) and false rejection rate (FRR) in percent, and based on the threshold value for writer, the signature is accepted as genuine or rejected as a forgery. A. Data Glove Data glove is an innovative component in the field of signature verification and skilled forgery sensing. Glove signature is a virtual reality based environment to back up the signing process and it presents numerous degrees of freedom for hand and each finger as well [5].

Figure 3. Signals From 14 Electrode Channels

The total time ‘T’ taken to complete one signature is also recorded. The data (Fig. 3) per every signature is then stored as a data matrix x. x = x (i,j)

,

(2)

Where ‘i’ represents the number of channels and ‘j’ represents the number of data point captured per signature. The ‘j’ varies per signature to signature along with ‘T’. T and ‘j’ may vary to inter and intra personnel signatures. C. SVD for Signature Verification Consider a data glove of m sensors each generates n samples per signature, producing an output data matrix, A(m×n). Usually n >> m, where m denotes the number of measured channels while n denotes the number of measurements. In this section, we try to ponder the implementation of SVD and the principal components of data matrix A towards signature verification system. Theorem 1. For any real m×n matrix A, there exists a real factorization:

Figure 2. Sensor mappings for 5DT data glove 14

A 5DT Data Glove 14 Ultra model hand glove is used in this research which is shown in Fig. 2. It is consist of 14 fully enclosed fiber optic bend sensors spread two per finger as well as abduction between fingers. The data glove interfaces with the computing device via a cable to the platform independent. USB Port. This glove is made up of flexible material like lycra to fit to many hand sizes. The data captured using this glove is of 8-bit flexure resolution, and at the sampling rate of minimum 75 Hz. B. Signal Capturing We adopted a scheme of repeating all the data collection for the 14-, 10-, 9-, 8-, 7-, and 5- electrode combinations. The recording is done along with the timing information in two ways. The coordinate values ‘x’ of each sensor channel ‘n’ at time ‘t’ is recorded when the subject starts signing. x (n)t

,

where t = 0..T, n = 1.. M and M ⊂ {14, 10, 9, 8, 7, 5}.

(1)

A = U ⋅ S ⋅V T

m×m m×n n×n

,

(3)

in which the matrices U and V are real orthonormal, and matrix S is real pseudo-diagonal with nonnegative diagonal elements. The diagonal entries σi of S are called the singular values of the matrix A. It is assumed that they are sorted in non-increasing order of magnitude. The set of singular values {σi} is called the singular spectrum of matrix A. The columns ui and vi of U and V are called respectively the left and right singular vectors of matrix A. The space

S Ur = span [u1, u2, … ,

ur] is called the r-th left principal subspace. In a similar way, the r-th right singular subspace is defined.

D. Conceptual relations between SVD and oriented energy: We are now in the position to establish the link between the singular value decomposition and the concept of oriented energy distribution. Define the unit ball UB in Rm as UB = q ∈ R m q = 1

{

2

}

Theorem 2 Consider a sequence of m-vectors {ak}, k = 1, 2, …, n and the associated m×n matrix A with SVD as defined in Eq. (3) with n ≥ m. Then:

Eui [ A] = σ

2 i

,

(4)

F. Prominent Sensors Selection from the 14-Sensor Based Data Glove To find out the r most prominent sensors from the 14-sensors’ data glove is determined by the following steps [6]: Consider the reference pattern of the j sensor of the signer p, p s r(j ) ( n T ) , given by p s r(j ) ( n T

)=

1 N

N

p s i(j ) ( n T )

∑

i=1

,

(8)

p where sij( ) ( nT ) is the ith signal of sensor j of the signer p and

N is the number of signatures. T is sampling period and n is the time index.

m

∀q ∈ UB: if q = ∑ γ i ⋅ u i , then i =1

m

Eq [ A ] = ∑ γ i2 ⋅ σ i2 ,

(5)

i =1

Fj =

Proof: Trivial from Theorem 1. With the aid of Theorem 2, one can easily obtain, using the SVD, the directions and spaces of extremal energy, as follows: Corollary 1 Under the assumptions of theorem 2: 1. maxQr ⊂Rm EQr [A] = ESUr [A] = 2. minQr ⊂Rm EQr [A] = E

(S )

m−r ⊥ U

r

∑σ

2 i

,

(6)

[A] =

m

The intra writer variance Vintra,j and the inter writer variance Vinter,j for the signals of sensor j, are calculated as follows,

∑

V in tr a ,j =

σ i2 ,

(7)

i = m− r +1

)

V i n tr a , j

is used to indicate the amount of individuality provided by each sensor. The higher the F value is, the higher the amount of individuality provided by the sensor, and vice versa.

i =1

where ‘max’ and ‘min’ denote operators, maximizing or minimizing over all r-dimensional subspaces Qr of the ambient r range space Rm. SU is the r-dimensional principal subspace of ⊥ SUm − r denotes the r-dimensional matrix A while m− r orthogonal complement of SU . Proof: Property (6), (7) follow immediately from the SVD Theorem 1 and from Theorem 2. By establishing the link between the oriented energy and SVD, we proved that the first r-left singular vectors sensing the maximal energy of glove data matrix A, and thus account for most of the variation in the original data. The above properties of SVD are very desirable in signature recognition, when signature data are taken using data glove.

(

With 14 sensors data glove, a 14 reference patterns are collected for each signature. Next, the Fj value, given as V in te r , j , (9)

V in ter ,j =

N

∑∑ i =1

n

P

∑∑ p =1 n

(

p s i(j ) ( n T

⎛ (p) ⎜ s rj ( n T ⎝

)−

p s r(j ) ( n T

2

)) ,

__________

) − s rj ( n T

)

⎞ ⎟ ⎠

2

(10) ,

(11)

__________

where srj ( nT ) is the average reference pattern of P signers of sensor j, given as ___________

s rj ( n T )

=

1 P

P

∑

p =1

s r( jp ) ( n T )

,

In order to find the r prominent sensors in 14 sensors data glove, signatures form 50 signers of different ethnic and linguistic groups; English, Chinese, Arabs, Indians, are collected. Each writer is asked to sign 50 times and the reference patterns are calculated for each sensor. Next, the intra variance and the inter variance are calculated for each sensor. The Fj values of the 14 sensors are calculated and depicted in Fig. 4.

E. Angle Between Principal Subspaces (Similarilty Measures) Now, having modeled the signature through its r-principal r

subspace SU , the authenticity of the tried signature can be obtained by calculating the angle between its principal subspace and the authentic one. This angle is refereed to as similarity factor (SF) and given in percent. The SVD based algorithm for cosine is considered as the standard one at present to finding the angles between principal subspaces and is implemented in software packages, e.g., in MATLAB, version 7.01.

(12)

Figure 4. Relationship between F value and the sensors

From the Fig. 4, the Fj values of the sensors located at the far end and joint position of the fingers are higher than those located at Thumb near, Thumb far, Thumb-Index joint, Index near, Middle near, Ring near, and Little near. The significance of the 14 sensors to the signer individuality is summarized in Table I. TABLE I. SIGNIFICANCE OF THE 14 SENSORS TO THE

High individuality Index/ Middle Middle/ Ring Ring/Little

SIGNER INDIVIDUALITY Average individuality Thumb Far Thumb/Index Index Far Ring Far Middle Near Middle Far Little Far

Week individuality Thumb Near Index Near Ring Near Little Near

The sensors are grouped into three groups: 1) sensors of high individuality, Fj > 60%, 2) sensors of average individuality, 60% > Fj > 40%, and 3) sensors of week individuality, Fj < 40%. Based on the results obtained from Fj values, we have designed the best possible distribution of different sensor-based data sets. G. To Find the Best Value of r as a Trade-off Between Truncated Energy of Signature and Reduced Dimensionality of the Data Glove Output Matrix In order to find the best value of r as a trade-off between truncated energy of signature and reduced dimensionality of the data glove output matrix A, 100 data sets each contains 20 genuine signatures are collected from 14-sensors. The 14 singular values of the 20×100 signatures are calculated and the average amount of the truncated energy is obtained as a function of r and tabulated in Table II. TABLE II. THE AVERAGE AMOUNT OF TRUNCATED ENERGY AS A FUNCTION OF r Dimension of the principal subspace (r)

Truncated energy

10

0.13%

9

0.19%

8

0.26%

7

0.33%

6

0.45%

5

0.57%

4

0.81%

3

1.01%

2

1.70%

Table II shows that the dimensionality of the data glove output matrix A can be significantly reduced without affecting the amount of energy oriented towards the principal subspace. Different values for r can be used in constructing the principal subspace, but as a trade off between reduced dimensionality and truncated energy, we suggest the r value = 5 for all

authors. Using this value of r, we have 99.43 percent of the signature energy compressed into the five left singular vector of the data matrix A. This will significantly reduce the required storage space for enrollment as well as the computational time for matching. To verify the effectiveness to 5 as the r value, an experiment was conducted where the value of r changes from 3, 4, 5 and 6, respectively. For this experiment, 100 data sets, each containing 110 genuine signatures from one signature contributor, are obtained. The first 10 genuine signatures are used to find the reference signature of the users and the remaining 100 genuine signatures are matched with it using the SVD-based signature verification technique for verification. On the other hand, 100 data sets, each contains 100 skilled forgeries to an authentic signature are obtained. The forgery signatures in each data set are compared with the reference signature of the writer and 100 similarity factors are obtained. The percentage distribution of the 100×100 similarity factors as a function of the class limits is depicted in Table III. TABLE III. SIMILARITY FACTOR OF GENUINE AND FORGERY SIGNATURES BASED ON THE r VALUES Signature Type of Signature Type r = 3 r =4 r=5 r=6 Similarity Factor (%) G F G F G F G F (91-100)%

99

1

82

1.4

69

0

8

0

(86-90)%

1

2.5

13

1.9

21

0

38

0

(81-85)%

0

3.3

3

2.7

7.5

0

18

0

(76-80)%

0

6.9

2

3.35

2.5

0

18

0

Here, G and F in Table III are defined as Genuine and Forgery, respectively. From experimental point of view, it is apparent from the results depicted in the Table III that the higher values of r produced lower percentage of the False Acceptance Rate (FAR) and higher percentage of the False Rejection Rate (FRR). More specifically, if the threshold of authenticity is set at 75% the proposed technique produced 13.55%, 9.3%, 0% and 0% FAR where the values of r were used as 3, 4, 5 and 6, respectively. Conversely, it produced 0%, 0%, 0% and 18% of FRR where the same sets of r values were used, respectively. Hence, from this experimental results it is noticeable that when r = 5, it revealed reasonably better result compare to the other values of r. H. Experimental Settings We have collected three categories of signature data namely; reference, genuine and forgery using 14-, 10-, 9-, 8-, 7- and 5sensor based glove data sets. To demonstrate frog and hand’s performance of the proposed technique, numerous experiments were conducted and tested with large number of authentic and forgery signatures data sets.

III. RESULTS AND DISCUSSION The summary with the best results obtained from the similarity factors of the genuine signatures and the imposter trials based on the entire data sets is depicted in Table IV. It is noteworthy to briefly highlight the empirical observations obtained from the various experimental results which is reported in Table IV revealed that 14- and most prominent 5-sensor based signature data sets performed remarkably superior performance than rest of the signature data sets. TABLE IV: BEST RESULTS OBTAINED FROM GENUINE AND IMPOSTER TRIALS USING DIFFERENT SIGNATURE DATA SETS Signature Type Genuine Imposter Similarity Factor (%) (75% and above) for 14-sensor based data sets 10- sensor based data sets 9- sensor based data sets 8- sensor based data sets 7- sensor based data sets 5- sensor based data sets

100 93 88 91 94.5 98

0 2.2 2.7 2.9 3.4 2.3

In order to provide a more reliable assessment of our proposed technique, further experiments were conducted to produce ROC curves which provide an empirical assessment of the system performance. For these experiments, entire data sets from 14-, 10-, 9-, 8-, 7- and 5- sensors were used, respectively. The ROC curves resulting from these experiments are shown in Figures 4 to 9, respectively. Based on the performance of our proposed technique for signature verification in terms of FAR and FRR achieved values which is depicted in Table IV, the most promising result obtained from 14-sensor based data sets where it produced zero percentage of FAR and FRR. When we reduced the number of sensors from 14 to 5, the proposed approach produced 2% of FRR and 2.3% of FAR which is also a remarkable level of accuracy and it is promising for further application of online signature verification technique.

Figure 4. ROC Curve Using 14-Sensor Based Data Sets

Figure 6. ROC Curve Using 9-Sensor Based Data Sets

Figure 5. ROC Curve Using 10-Sensor Based Data Sets

Figure 7. ROC Curve Using 8-Sensor Based Data Sets

Figure 8. ROC Curve Using 7-Sensor Based Data Sets

IV.

Figure 9. ROC Curve Using 5-Sensor Based Data Sets

CONCLUSION

An innovative approach to signature verification problem with data glove as input device has been presented. This research is an initial attempt in demonstrating the data glove as an effective high bandwidth data entry device for signature verification. The technique is based on the singular value decomposition in finding a set of singular vectors sensing the maximal energy of the glove based signature. The angles between the different principal subspaces are used for signature classification. The performance of our proposed technique for signature verification in terms of FAR and FRR achieved values where the most promising result obtained from 14-sensor based data sets and it produced zero percentage of FAR and FRR. After reducing the number of sensors from 14 to 5, it produced 2% of FRR and 2.3% of FAR which is truly a significant level of accuracy and it is potential for further application of online signature verification technique. In future, data glove structure can be further simplified by interfacing with the computer wireless technology. REFERENCES [1]

S. Sayeed, S. Andrews, R. Besar, and L.C. Kiong, “Forgery Detection in Dynamic Signature Verification by Entailing Principal Component Analysis,” Discrete Dynamics in Nature and Society, vol. 2007, pp. 18, 2007.

[2]

B. Fang, Y. Y. Tang, “Reduction of Feature Statistics Estimation Error For Small Training Sample Size in Off-line Signature Verification,” Proc. in First International Conference on Biometric Authentication. Lecture Notes in Computer Science, vol. 3072, pp. 526-532, 2004.

[3]

S. Sayeed, R. Besar, and N. S. Kamel, “Dynamic Signature Verification Using Sensor Based Data Glove,” In proc. 8th International Conference on Signal Processing, pp. 2387-2390, 2006.

[4]

N. S. Kamel, S. Sayeed, and A. E. Grant, “Glove-Based Approach to Online Signature Verification,” IEEE Transactions on Pattern. Analysis and Machine Intelligence, vol. 30, no. 6, pp. 1109-1113, 2008.

[5]

http://www.5dt.com/products/pdata glove14 .html

[6]

S. Hangai, and T. Higuchi, “Writer Identification Using Finger-Bend in Writing Signature”. Lecture Notes in Computer Science. 3087, 229237, 2004.

Rosli Besar FET, Multimedia University Jalan Ayer Keroh Lama, Bukit Beruang, 7450 Melaka, Malaysia [email protected]

Abstract— In order to ameliorate the degree of trustiness and, high security, we have presented a new approach to hand signature verification applying data glove. Data glove is a new-fangled dimension in the field of virtualreality environments, originally designed to satisfy the stringent requirements of modern motion capture and animation professionals. In our research, we attempt to change over the carrying out of data glove from motion animation towards signature substantiation problem, making use of the offered multiple degrees of freedom for each finger as well as for the hand. Our proposed approach is tested in context of highly skilled forgeries with a large number of glove-based signature data sets and obtained a significant level of accuracy in signature verification. Keywords- Data glove; signature verification; singular value decomposition

I. INTRODUCTION The promising evolution in signature verification is utilizing the benefits of signal processing over the typical image processing techniques. The benefits of involving signal processing for this purpose include reduction of equipment complexity, increased robustness against counterfeit, sovereignty of media and signature concealment [1]. In the typical image processing technique a strong impression of the signature with prescribed ink on a stipulated media is essential and is the key for further processing. The signature image is then scanned into digital representation and that digital image is used for key construction. The process continues to search the database for a nearest match and the result determines the authentication decision [2]. Since the signature plays as a key component here, and it is perceptible and available for any misuse like forging etc. In addition, the image processing involves volumes of data and any reduction in volume needs a compromise with the efficiency of the system. The continuous enhancement to this scenario leads improving two major criteria. One is to protect the signature from forgery and the second is to reduce the volume of data

978-1-4244-6716-7/10/$26.00 ©2010 IEEE

Nidal S. Kamel Dept. of EEE, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia [email protected]

involved and hence the speed of the process can be improved. Using a data glove is a paradigm shift from image to signal processing and the first problem is immediately solved since there is no significance given to ink or paper. However the data glove used for this purpose that the subject wears on while signing for access consists of many electrodes in various positions. These electrodes produce continuous signals during the signing process and are resembles image processing in volume and needs to be reduced to overcome the drawback. Singular Value Decomposition (SVD) is a popular technique used for source separation has been introduced in this case and found to be competent in solving the problem [3-4]. In this research, we enhanced our work [4] using different matching techniques as well as different data sets using reduced number of sensors from 14 to 5 and demonstrate the level of accuracy in terms of False Acceptance Rate (FAR) and False Rejection Rate (FRR). II.

PROPOSED MODEL FOR THE GLOVE-BASED SIGNATURE VERIFICATION TECHNIQUE

Figure 1. Proposed model for the glove-based signature verification technique

Fig. 1 shows the overall system design of our signature verification system. During enrollment of a new user, input to

the system is a set of signatures produced by that user (genuine samples). The genuine reference sample data is preprocessed and the features are extracted. The signature data is then saved in a database together with a unique identifier that is used to retrieve the signatures during the matching. For verification, a test signature along with the genuine writer identity is input to the system. The same preprocessing and feature extraction methods are used. The signature is then compared to each of the reference signatures, which are retrieved from the database based on the author identifier. The resulting difference are calculated and included as false acceptance rate (FAR) and false rejection rate (FRR) in percent, and based on the threshold value for writer, the signature is accepted as genuine or rejected as a forgery. A. Data Glove Data glove is an innovative component in the field of signature verification and skilled forgery sensing. Glove signature is a virtual reality based environment to back up the signing process and it presents numerous degrees of freedom for hand and each finger as well [5].

Figure 3. Signals From 14 Electrode Channels

The total time ‘T’ taken to complete one signature is also recorded. The data (Fig. 3) per every signature is then stored as a data matrix x. x = x (i,j)

,

(2)

Where ‘i’ represents the number of channels and ‘j’ represents the number of data point captured per signature. The ‘j’ varies per signature to signature along with ‘T’. T and ‘j’ may vary to inter and intra personnel signatures. C. SVD for Signature Verification Consider a data glove of m sensors each generates n samples per signature, producing an output data matrix, A(m×n). Usually n >> m, where m denotes the number of measured channels while n denotes the number of measurements. In this section, we try to ponder the implementation of SVD and the principal components of data matrix A towards signature verification system. Theorem 1. For any real m×n matrix A, there exists a real factorization:

Figure 2. Sensor mappings for 5DT data glove 14

A 5DT Data Glove 14 Ultra model hand glove is used in this research which is shown in Fig. 2. It is consist of 14 fully enclosed fiber optic bend sensors spread two per finger as well as abduction between fingers. The data glove interfaces with the computing device via a cable to the platform independent. USB Port. This glove is made up of flexible material like lycra to fit to many hand sizes. The data captured using this glove is of 8-bit flexure resolution, and at the sampling rate of minimum 75 Hz. B. Signal Capturing We adopted a scheme of repeating all the data collection for the 14-, 10-, 9-, 8-, 7-, and 5- electrode combinations. The recording is done along with the timing information in two ways. The coordinate values ‘x’ of each sensor channel ‘n’ at time ‘t’ is recorded when the subject starts signing. x (n)t

,

where t = 0..T, n = 1.. M and M ⊂ {14, 10, 9, 8, 7, 5}.

(1)

A = U ⋅ S ⋅V T

m×m m×n n×n

,

(3)

in which the matrices U and V are real orthonormal, and matrix S is real pseudo-diagonal with nonnegative diagonal elements. The diagonal entries σi of S are called the singular values of the matrix A. It is assumed that they are sorted in non-increasing order of magnitude. The set of singular values {σi} is called the singular spectrum of matrix A. The columns ui and vi of U and V are called respectively the left and right singular vectors of matrix A. The space

S Ur = span [u1, u2, … ,

ur] is called the r-th left principal subspace. In a similar way, the r-th right singular subspace is defined.

D. Conceptual relations between SVD and oriented energy: We are now in the position to establish the link between the singular value decomposition and the concept of oriented energy distribution. Define the unit ball UB in Rm as UB = q ∈ R m q = 1

{

2

}

Theorem 2 Consider a sequence of m-vectors {ak}, k = 1, 2, …, n and the associated m×n matrix A with SVD as defined in Eq. (3) with n ≥ m. Then:

Eui [ A] = σ

2 i

,

(4)

F. Prominent Sensors Selection from the 14-Sensor Based Data Glove To find out the r most prominent sensors from the 14-sensors’ data glove is determined by the following steps [6]: Consider the reference pattern of the j sensor of the signer p, p s r(j ) ( n T ) , given by p s r(j ) ( n T

)=

1 N

N

p s i(j ) ( n T )

∑

i=1

,

(8)

p where sij( ) ( nT ) is the ith signal of sensor j of the signer p and

N is the number of signatures. T is sampling period and n is the time index.

m

∀q ∈ UB: if q = ∑ γ i ⋅ u i , then i =1

m

Eq [ A ] = ∑ γ i2 ⋅ σ i2 ,

(5)

i =1

Fj =

Proof: Trivial from Theorem 1. With the aid of Theorem 2, one can easily obtain, using the SVD, the directions and spaces of extremal energy, as follows: Corollary 1 Under the assumptions of theorem 2: 1. maxQr ⊂Rm EQr [A] = ESUr [A] = 2. minQr ⊂Rm EQr [A] = E

(S )

m−r ⊥ U

r

∑σ

2 i

,

(6)

[A] =

m

The intra writer variance Vintra,j and the inter writer variance Vinter,j for the signals of sensor j, are calculated as follows,

∑

V in tr a ,j =

σ i2 ,

(7)

i = m− r +1

)

V i n tr a , j

is used to indicate the amount of individuality provided by each sensor. The higher the F value is, the higher the amount of individuality provided by the sensor, and vice versa.

i =1

where ‘max’ and ‘min’ denote operators, maximizing or minimizing over all r-dimensional subspaces Qr of the ambient r range space Rm. SU is the r-dimensional principal subspace of ⊥ SUm − r denotes the r-dimensional matrix A while m− r orthogonal complement of SU . Proof: Property (6), (7) follow immediately from the SVD Theorem 1 and from Theorem 2. By establishing the link between the oriented energy and SVD, we proved that the first r-left singular vectors sensing the maximal energy of glove data matrix A, and thus account for most of the variation in the original data. The above properties of SVD are very desirable in signature recognition, when signature data are taken using data glove.

(

With 14 sensors data glove, a 14 reference patterns are collected for each signature. Next, the Fj value, given as V in te r , j , (9)

V in ter ,j =

N

∑∑ i =1

n

P

∑∑ p =1 n

(

p s i(j ) ( n T

⎛ (p) ⎜ s rj ( n T ⎝

)−

p s r(j ) ( n T

2

)) ,

__________

) − s rj ( n T

)

⎞ ⎟ ⎠

2

(10) ,

(11)

__________

where srj ( nT ) is the average reference pattern of P signers of sensor j, given as ___________

s rj ( n T )

=

1 P

P

∑

p =1

s r( jp ) ( n T )

,

In order to find the r prominent sensors in 14 sensors data glove, signatures form 50 signers of different ethnic and linguistic groups; English, Chinese, Arabs, Indians, are collected. Each writer is asked to sign 50 times and the reference patterns are calculated for each sensor. Next, the intra variance and the inter variance are calculated for each sensor. The Fj values of the 14 sensors are calculated and depicted in Fig. 4.

E. Angle Between Principal Subspaces (Similarilty Measures) Now, having modeled the signature through its r-principal r

subspace SU , the authenticity of the tried signature can be obtained by calculating the angle between its principal subspace and the authentic one. This angle is refereed to as similarity factor (SF) and given in percent. The SVD based algorithm for cosine is considered as the standard one at present to finding the angles between principal subspaces and is implemented in software packages, e.g., in MATLAB, version 7.01.

(12)

Figure 4. Relationship between F value and the sensors

From the Fig. 4, the Fj values of the sensors located at the far end and joint position of the fingers are higher than those located at Thumb near, Thumb far, Thumb-Index joint, Index near, Middle near, Ring near, and Little near. The significance of the 14 sensors to the signer individuality is summarized in Table I. TABLE I. SIGNIFICANCE OF THE 14 SENSORS TO THE

High individuality Index/ Middle Middle/ Ring Ring/Little

SIGNER INDIVIDUALITY Average individuality Thumb Far Thumb/Index Index Far Ring Far Middle Near Middle Far Little Far

Week individuality Thumb Near Index Near Ring Near Little Near

The sensors are grouped into three groups: 1) sensors of high individuality, Fj > 60%, 2) sensors of average individuality, 60% > Fj > 40%, and 3) sensors of week individuality, Fj < 40%. Based on the results obtained from Fj values, we have designed the best possible distribution of different sensor-based data sets. G. To Find the Best Value of r as a Trade-off Between Truncated Energy of Signature and Reduced Dimensionality of the Data Glove Output Matrix In order to find the best value of r as a trade-off between truncated energy of signature and reduced dimensionality of the data glove output matrix A, 100 data sets each contains 20 genuine signatures are collected from 14-sensors. The 14 singular values of the 20×100 signatures are calculated and the average amount of the truncated energy is obtained as a function of r and tabulated in Table II. TABLE II. THE AVERAGE AMOUNT OF TRUNCATED ENERGY AS A FUNCTION OF r Dimension of the principal subspace (r)

Truncated energy

10

0.13%

9

0.19%

8

0.26%

7

0.33%

6

0.45%

5

0.57%

4

0.81%

3

1.01%

2

1.70%

Table II shows that the dimensionality of the data glove output matrix A can be significantly reduced without affecting the amount of energy oriented towards the principal subspace. Different values for r can be used in constructing the principal subspace, but as a trade off between reduced dimensionality and truncated energy, we suggest the r value = 5 for all

authors. Using this value of r, we have 99.43 percent of the signature energy compressed into the five left singular vector of the data matrix A. This will significantly reduce the required storage space for enrollment as well as the computational time for matching. To verify the effectiveness to 5 as the r value, an experiment was conducted where the value of r changes from 3, 4, 5 and 6, respectively. For this experiment, 100 data sets, each containing 110 genuine signatures from one signature contributor, are obtained. The first 10 genuine signatures are used to find the reference signature of the users and the remaining 100 genuine signatures are matched with it using the SVD-based signature verification technique for verification. On the other hand, 100 data sets, each contains 100 skilled forgeries to an authentic signature are obtained. The forgery signatures in each data set are compared with the reference signature of the writer and 100 similarity factors are obtained. The percentage distribution of the 100×100 similarity factors as a function of the class limits is depicted in Table III. TABLE III. SIMILARITY FACTOR OF GENUINE AND FORGERY SIGNATURES BASED ON THE r VALUES Signature Type of Signature Type r = 3 r =4 r=5 r=6 Similarity Factor (%) G F G F G F G F (91-100)%

99

1

82

1.4

69

0

8

0

(86-90)%

1

2.5

13

1.9

21

0

38

0

(81-85)%

0

3.3

3

2.7

7.5

0

18

0

(76-80)%

0

6.9

2

3.35

2.5

0

18

0

Here, G and F in Table III are defined as Genuine and Forgery, respectively. From experimental point of view, it is apparent from the results depicted in the Table III that the higher values of r produced lower percentage of the False Acceptance Rate (FAR) and higher percentage of the False Rejection Rate (FRR). More specifically, if the threshold of authenticity is set at 75% the proposed technique produced 13.55%, 9.3%, 0% and 0% FAR where the values of r were used as 3, 4, 5 and 6, respectively. Conversely, it produced 0%, 0%, 0% and 18% of FRR where the same sets of r values were used, respectively. Hence, from this experimental results it is noticeable that when r = 5, it revealed reasonably better result compare to the other values of r. H. Experimental Settings We have collected three categories of signature data namely; reference, genuine and forgery using 14-, 10-, 9-, 8-, 7- and 5sensor based glove data sets. To demonstrate frog and hand’s performance of the proposed technique, numerous experiments were conducted and tested with large number of authentic and forgery signatures data sets.

III. RESULTS AND DISCUSSION The summary with the best results obtained from the similarity factors of the genuine signatures and the imposter trials based on the entire data sets is depicted in Table IV. It is noteworthy to briefly highlight the empirical observations obtained from the various experimental results which is reported in Table IV revealed that 14- and most prominent 5-sensor based signature data sets performed remarkably superior performance than rest of the signature data sets. TABLE IV: BEST RESULTS OBTAINED FROM GENUINE AND IMPOSTER TRIALS USING DIFFERENT SIGNATURE DATA SETS Signature Type Genuine Imposter Similarity Factor (%) (75% and above) for 14-sensor based data sets 10- sensor based data sets 9- sensor based data sets 8- sensor based data sets 7- sensor based data sets 5- sensor based data sets

100 93 88 91 94.5 98

0 2.2 2.7 2.9 3.4 2.3

In order to provide a more reliable assessment of our proposed technique, further experiments were conducted to produce ROC curves which provide an empirical assessment of the system performance. For these experiments, entire data sets from 14-, 10-, 9-, 8-, 7- and 5- sensors were used, respectively. The ROC curves resulting from these experiments are shown in Figures 4 to 9, respectively. Based on the performance of our proposed technique for signature verification in terms of FAR and FRR achieved values which is depicted in Table IV, the most promising result obtained from 14-sensor based data sets where it produced zero percentage of FAR and FRR. When we reduced the number of sensors from 14 to 5, the proposed approach produced 2% of FRR and 2.3% of FAR which is also a remarkable level of accuracy and it is promising for further application of online signature verification technique.

Figure 4. ROC Curve Using 14-Sensor Based Data Sets

Figure 6. ROC Curve Using 9-Sensor Based Data Sets

Figure 5. ROC Curve Using 10-Sensor Based Data Sets

Figure 7. ROC Curve Using 8-Sensor Based Data Sets

Figure 8. ROC Curve Using 7-Sensor Based Data Sets

IV.

Figure 9. ROC Curve Using 5-Sensor Based Data Sets

CONCLUSION

An innovative approach to signature verification problem with data glove as input device has been presented. This research is an initial attempt in demonstrating the data glove as an effective high bandwidth data entry device for signature verification. The technique is based on the singular value decomposition in finding a set of singular vectors sensing the maximal energy of the glove based signature. The angles between the different principal subspaces are used for signature classification. The performance of our proposed technique for signature verification in terms of FAR and FRR achieved values where the most promising result obtained from 14-sensor based data sets and it produced zero percentage of FAR and FRR. After reducing the number of sensors from 14 to 5, it produced 2% of FRR and 2.3% of FAR which is truly a significant level of accuracy and it is potential for further application of online signature verification technique. In future, data glove structure can be further simplified by interfacing with the computer wireless technology. REFERENCES [1]

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[2]

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[3]

S. Sayeed, R. Besar, and N. S. Kamel, “Dynamic Signature Verification Using Sensor Based Data Glove,” In proc. 8th International Conference on Signal Processing, pp. 2387-2390, 2006.

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N. S. Kamel, S. Sayeed, and A. E. Grant, “Glove-Based Approach to Online Signature Verification,” IEEE Transactions on Pattern. Analysis and Machine Intelligence, vol. 30, no. 6, pp. 1109-1113, 2008.

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S. Hangai, and T. Higuchi, “Writer Identification Using Finger-Bend in Writing Signature”. Lecture Notes in Computer Science. 3087, 229237, 2004.