Virtual Reality Based Dynamic Signature Verification Using Data glove

International Conference on Intelligent and Advanced Systems 2007

Virtual Reality Based Dynamic Signature Verification Using Data glove Shohel Sayeed a, Nidal S. Kamel b, Rosli Besar c a

Faculty of Information Science and Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450 Melaka, Malaysia. b Department of Electrical & Electronic Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia. c Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450 Melaka, Malaysia. Email: {shohel.sayeed, rosli}@mmu.edu.my, [email protected]

Abstract– Data glove is a new dimension in the field of virtual reality environments, initially designed to satisfy the stringent requirements of modern motion capture and animation professionals. In this paper we try to shift the implementation of data glove from motion animation towards signature verification problem, making use of the offered multiple degrees of freedom for each finger and for the hand as well. The proposed technique is based on the Singular Value Decomposition (SVD) in finding r singular vectors sensing the maximal energy of glove data matrix A, called principal subspace, and thus account for most of the variation in the original data, so the effective dimensionality of the data can be reduced. Having identified data glove signature through its r-th principal subspace, the authenticity is then can be obtained by calculating the angles between the different subspaces. The SVD-signature verification technique is tested with large number of authentic and forgery signatures and shows remarkable level of accuracy in finding the similarities between genuine samples as well as the differenced between genuineforgery trials.

Keywords: Data glove, Signature verification, Virtual reality, Singular value decomposition I.

INTRODUCTION

People recognition by means of biometrics [1–3] can be split into two main categories: Physiological biometrics: It is based on direct measurements of a part of the human body. Fingerprint, face, iris and hand-scan recognition belong to this group. Behavioral biometrics: It is based on measurements and data derived from an action performed by the user, and thus indirectly measure some characteristics of the human body. However, this classification is quite artificial. For instance, the speech signal depends on behavioral traits such as semantics, diction, pronunciation, idiosyncrasy, etc. (related to socioeconomic status, education, place of birth, etc.) [4]. However, it also depends on the speaker’s physiology, such as the shape of the vocal tract. On the other hand, physiological traits are also influenced by user behavior, such as the manner in which

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a user presents a finger, looks at a camera, etc. Signature recognition belongs to this last category, and according to market share reports [5] it is the second most important within this group, just behind speech recognition, and over keystroke, gait, gesture, etc. This paper is organized as follows: Section II summarizes signature recognition techniques. Section III is focused on dynamic signature recognition by means of template matching and proposes a signature verification methodology based on Singular Value Decomposition. Section IV provides experimental results, and Section V summarizes the conclusions of this work. II.

SIGNATURE RECOGNITION

Signature recognition can be split into two categories: Static: In this mode, users write their signature on paper, digitize it through an optical scanner or a camera, and the biometric system recognizes the signature analyzing its shape. This group is also known as “off-line”. Dynamic: In this mode, users write their signature in a digitizing tablet such as the device [6], which acquires the signature in real time. Another possibility is the acquisition by means of stylus-operated PDAs. Dynamic recognition is also known as “on-line”. For a signature verification system, depending on testing conditions and environment, three types of forgeries can be established [7]: 1. “Simple” forgery: where the forger makes no attempt to simulate or trace a genuine signature. 2. “Random” forgery: where the forger uses his/her own signature as a forgery. 3. “Skilled” forgery: where the forger tries and practices imitating as closely as possible the static and dynamic information of the signature to be forged. Dynamic signature verification: Taking into account the highest security levels, which can be achieved by dynamic systems, most of the efforts of the international scientific community are addressed toward this group. This paper will be

1-4244-1355-9/07/$25.00 @2007 IEEE


mainly devoted to dynamic signature verification [8–9], also known as authentication. In dynamic signature verification system involves i) data acquisition ii) feature extraction iii) matching and iv) decision. Data Acquisition: For dynamic signature verification system digitizing tablet or pen tablet or smart pen is used to acquire the signature data. Feature Extraction: Static or dynamic features are extracted for verification process. Static features are extracted from the whole process of signing, such as maximum, minimum and average of writing speed, curvature measurements, etc. On the contrary, the dynamic features are the evolution of a given parameter as function of time f(t). Examples are position x(t), y(t), velocity v(t), acceleration a(t), pressure p(t), tangential acceleration ta(t), curvature radius r(t), normal acceleration na(t), etc. These features are also named functions. Matching: Consists of measuring the similarity between the claimed identity model and the input features. When using dynamic features, some kind of length normalization must be done, because different repetitions of a signature from a given person will last differently. Decision: Once a similarity (probability) measure, also known as opinion and score, is obtained, the decision implies the computation of a decision threshold. If the similarity is greater than a threshold, the decision is accepted as genuine; otherwise it is rejected as forgery. Contrarily, if the matching block produces a distance (dissimilarity) measure, the person is accepted if the score is smaller than the threshold, and otherwise it is rejected.

III.

PROPOSED METHOD

In the past some researchers have worked on simple or random forgeries while others have dealt with the signature verification of skilled forgeries. Our present work deals with the signature verification of skilled forgeries using data glove along with the Singular Value Decomposition (SVD) based technique.

In our dynamic signature verification system (see fig 1), the users are first enrolled by providing signature samples (reference signatures). Then, when a user present a signature (test signature) claiming to be a particular individual, this test signature is compared with the reference signatures for that individual. If the dissimilarity is above a certain threshold, the user is rejected. During verification, the test signature is compared to all the signatures in the reference set, resulting in several distance values. One then has to choose a method to combine these distance values into a single value representing the dissimilarity of the test signature to the reference set, and compare it to a threshold to make a decision. A. Data Glove Data glove is a new dimension in the field of signature verification and forgery detection [10-11]. The glove signature is a virtual-reality- based environment to support the signing process. Most input devices offer one, two, or three degrees of freedom, the data glove is unique in that it offers multiple degrees of freedom for each finger and for the hand as well. This permits a user to communicate to the computer a far richer picture of his or her intentions than most other input devices. The dynamic features of the data glove provide information on: 1. Patterns distinctive to an individuals’ signature and hand size. 2. Time elapsed during the signing process. 3. Hand trajectory dependent rolling. In this research, we used a 5DT Data Glove 14 Ultra model hand glove shown in Fig. 2 with 14 fully enclosed fiber optic bend sensors spread two per finger as well as abduction between fingers [12]. The Data Glove interfaces with the computer 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.

Fig. 2. Sensor mappings for 5DT data glove 14 ultra Fig. 1. Glove-based dynamic signature verification system

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D. SVD for Dynamic 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 exist a real factorization:

A = U ⋅ S ⋅V T

m×m m×n n×n

,

(1)

SUr = span [u1, u2, … ,

ur] is called the r-th left principal subspace. In a similar way, the r-th right singular subspace is defined. E. 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 i2

(2) m

∀q ∈ UB: if q = ¦ γ i ⋅ ui , then i =1

m

Eq [ A ] = ¦ γ ⋅ σ 2 i

2 i

(3)

i =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: r

1. max Q ⊂ R EQ [ A] = ES [ A] = ¦ σ i2 m

r

r U

2. min Q ⊂ R EQ [ A] = E S r

m

r

(

m− r U

,

(4)

i =1

)

⊥

[ A] =

m

¦

σ i2 ,

(5)

i = m − r +1

where ‘max’ and ‘min’ denote operators, maximizing or r minimizing over all r-dimensional subspaces Q of the

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subspace

of

matrix

A

while

(S )

m−r ⊥ U m− r

r-dimensional orthogonal complement of SU

denotes

the

.

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 dynamic signature verification, when signature data are taken using data glove.

Now, having identified each signature through its r-th r

principal subspace SU , the authenticity of the tried signature can be obtained by calculating the Euclidean distance between its principal subspace and the genuine reference. The Euclidian distance for every genuine or forged signature X i ∈ {x1 , x 2 ,..., x k } with the reference signature

Yi ∈ {y1 , y 2 ,..., y k } is calculated by given equation:

§ k Dis t an ce ( X i , Y i ) = ¨ ¦ X i − Y i ¨ i =1 © G. Reference signatures

2

· ¸ ¸ ¹

1

2

(6)

During the enrollment stage, 15 sample signatures from each writer to be enrolled are collected and pairwise angles between their principal subspaces are computed. Based on these angles, a reference signature is selected as the one that presents minimal overall angle to the others. The value of 15 sample signatures is chosen in determining the reference signature, because it gives the best performance for the SVD-based signature verification technique in term of receiver operating characteristic (ROC) curves. Summary of our Dynamic Signature Verification Technique: i. From the data glove output form data matrix A (m× n) ii. Compute the SVD of matrix A

Proof: Trivial from theorem 1.

r

r

F. Distance Measurement for Signature data sets

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

m

ambient range space R . SU is the r-dimensional principal

A = U ⋅ S ⋅V T m×m m×n n×n

iii. From the smallest singular values estimate the rank (r) of matrix A iv. From matrix U extract the first r left singular vectors r

and form the principal subspace SU v. Find the similarity factor by calculating the Euclidean distances between r-the principal subspaces of the different signatures.


IV.

EXPERIMENTAL RESULTS AND DISCUSSION 80

It is quit clear form the results in Fig. 3 that the threshold of authenticity can be set at 75% or slightly lower. With this threshold value the proposed technique would be able to recognize genuine signatures with false rejection rate (FRR) 2.5%. The 75% value for the similarity factor is called the threshold of authenticity because signatures that are producing higher values when compared with their reference signatures would be recognized as genuine.

FAR FRR

70 60 50 Error Rat e [% ]

In the first experiment the threshold for authentic signatures is sought. 100 data sets, each contains 25 genuine signatures from one signature contributor, are obtained. The first 15 genuine signatures are used to find the reference signature of each user. The remaining 10 genuine signatures are run with the SVD-based signature verification technique for verification. The percentage distribution of the 100×10 similarity factors as a function of the class limits is depicted in Figure 3.

40 30

EER = 2.46%

20 10 0 -10

0

0.1

0.2

0.3 0.4 Threshold

0.5

0.6

0.7

Fig 4. FRR and FAR as a function of the classification threshold

In the second experiment, 100 data sets, each contains 10 skilled forgeries to an authentic signature are obtained. It is worth mentioned here that each forger contributes total 100 skilled forgeries against 10 genuine signatures. The forgery signatures in each data set are compared with the reference signature of the writer The percentage distribution of the 100×10x10 similarity factors as a function of the class limits is depicted in Figure 3.

For further evaluating the performance of a signature verification system, we adopt the equal error rate (EER), that is the error rate when the false rejection rate (FRR) of genuine signatures and the false acceptance rate (FAR) of forgery signatures assume the same value; it can be adopted as a unique measure for characterizing the security level of a biometric system. Figure 4 shows that the EER of our proposed technique. The FAR and FRR are calculated for the normalized threshold values ranging from 0 to 1. FAR and FRR are calculated by

It is quit clear form the results in Fig. 3 that if the threshold of forgery is set at 75%, the proposed technique will be able to recognize forgery signatures with false acceptance rate (FAR) 1.2%.

FAR =

From the results in Figure 3 and Figure 4, it becomes quit reasonable to set the decision threshold of the proposed technique at 75%. With this value of the decision threshold, we have both FAR and FRR of low enough values to fulfill the requirements of most of on-line signature verification applications. 60

Imposter

Total number of accepted forgeries X 100 Total number of tested forgeries

FRR =

Total number of genuine rejected Total number of tested genuines

(7)

X 100 (8)

Our proposed technique achieved accuracy with 2.46% of EER, which is comparable with other dynamic signature verification techniques and it is promising for future applications of dynamic signature verification techniques.

Genuine

50

40

Samples (%)

V.

30

20

10

0 91-100

86-90

81-85

76-80

71-75

66-70

61-65

51-60

> 75%. In the second experiment, 10 forgery samples per writer are collected and the similarity factors with authentic ones are calculated. The SVD-signature verification technique developed similarity factors