J. Cent. South Univ. Technol. (2007)04-0563-05

DOI: 10.1007/s11771-007-0108-y

Authentication based on feature of hand-written signature

ZHU Shu-ren(朱树人)^1,2

(1. School of Information Science, Guangdong University of Business Studies, Guangzhou 510320，China;

2. School of Computer, Beijing University of Aeronautics and Astronautics, Beijing 100083, China）

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Abstract: The typical features of the coordinate and the curvature as well as the recorded time information were analyzed in the hand-written signatures. In the hand-written signature process 10 biometric features were summarized: the amount of zero speed in direction x and direction y, the amount of zero acceleration in direction x and direction y, the total time of the hand-written signatures, the total distance of the pen traveling in the hand-written process, the frequency for lifting the pen, the time for lifting the pen, the amount of the pressure higher or lower than the threshold values. The formulae of biometric features extraction were summarized. The Gauss function was used to draw the typical information from the above-mentioned biometric features, with which to establish the hidden Markov mode and to train it. The frame of double authentication was proposed by combing the signature with the digital signature. Web service technology was applied in the system to ensure the security of data transmission. The training practice indicates that the hand-written signature verification can satisfy the needs from the office automation systems.

Key words: behavioral biostatistics feature; hand-written signature; hidden Markov mode; signature verification

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1 Introduction

Personal authentication is becoming necessary in more and more fields. The traditional personal authentication methods cannot keep up with the development of the society because of their inherent defects. Under such circumstance, biometrics emerged as the time requires. Biometrics is the technologies that analyze human characteristics for automated personal authentication. Online handwritten signature verification is an important branch of biometrics. Handwritten signature has been a human behavior characteristic and been widely applied since ancient times^[1-3]. It represents the user’s intrinsic and unique traits, and is also related to the specific biomechanical system^[4-8]. The behavioral biostatistics^[6] is expressed by the long-term behavioral characteristics(the hand-written signatures, the contrail of pivotal strokes)^[9]. The hand-written signature verification is based on the concepts that everyone’s signature conveys his unique understanding and the mode of writing conforms to the behavioral biostatistics^[10]. The hand-written signature verification system has become a hot topic of identity verification technology^[11] .

Some researchers considered common issues with extraction of identification data from various types of biometrics, and protection of such data against conceivable attacks^[12-18]. They aimed at facilitating reliable biometrics authentication by improving authentication preciseness and providing counter- measures against attacks to an authentication system. In this article, the typical features of the coordinate and the curvature as well as the time information recorded in the hand-written signatures were analysed, the 10 biometric features involving in the hand-written signature process were obtained. The Gauss function was used to draw the typical information from the above-mentioned biometric features, with which to establish the hidden markov mode(HMM) and to train it.

2 Modeling of hand-written signature verification system

2.1 Potential features

The feature extraction is the key step in the recognition of the on-line hand-written Chinese characters^[10], the quality of the feature extraction can directly affect the  recognition performance. The coordinate feature extraction and the curvature feature extraction were used in the paper. The coordinate feature extraction regards the coordinate at the special spots as the strokes’ features, it takes position information at the special spots into consideration and expresses the directional information at the special spots in the strokes. The curvature feature extraction regards the curvature at the special spots as the strokes’ features; it focuses on the movement information of the strokes’ figure. According to the features of the coordinate and the curvature, and the recorded time information, a series of biological features of the signatures recognized were obtained by system. 10 primary biometric features were summarized as follows:

1) N_vx is the amount of zero speed in direction x;

2) N_vy is the amount of zero speed in direction y (the absolute zero is spanless, so the zero is replaced by a speed value that is a little lsmaller than peak value);

3) N_ax is the amount of zero acceleration in direction x;

4) N_ay is the amount of zero acceleration in direction y(the amount of zero expresses the movement of speedup to speed-down or speed-down to speedup);

5) t_w is the total time of the hand-written signature;

6) D is total distance of the pen travelled on the hand-written, namely the Euclid distance of all the points:

, i=0, 1,…, N-1     (1)

where  x_i is the coordinate in direction x and y_i is the coordinate in direction y;

7) N_w is the frequency of lifting the pen;

8) t_n is the total time of lifting the pen(namely the total time from the beginning to the ending of the writing);

9) N_max is the amount of pressure higher than the threshold value T_max (according to the hardware features of the hand-written pen);

10) N_min is the amount of pressure lower than the threshold value T_­min(according to the hardware features of the hand-written pen).

2.2 Feature extraction

The system draws such features as the total time, the total length of the strokes and the amount of zero speed from the signatures, and then constructs a model for these features with the Gauss function that can compute the probability density, namely through density function it can estimate all the parameters of the features from the signature swatches. In the estimation process   it obtains the corresponding average and variance of the features, and regards them as the unique signs of the signature.

In the process of designation and realization of the system, it is discovered that the signature is closely connected with the user’s psychology. And the signature has a great difference in different surroundings and time; and some other factors can also exert great influences on it. For example, the total time, the length of the strokes, the time for lifting the pen can be different for the same user’s different signatures. These features oscillate about the average and variance which can symbolize one person’s biometric features^[19-21]. Therefore it can be considered as a proper choice to describe these features through the distribution of a certain kind of signatures and to verify these features through experiments with the Gauss function.

The following part offers a detail illustration to these formulae how to draw the features.

Speed v_x and v_y  express the functions of time, which can be calculated with the following  formulae：

     (2)

where  m is the serial number, m=0, 1, …, N-1; x_m is the coordinate in direction x; y_m is the coordinate in direction y; t_m is the time of movement; v_x is the speed at point t_m in direction x; v_y is the speed at point t_m in direction y.

Acceleration a_x and a_y can be calculated with different speeds, the acceleration at point t_m in directions x and y can be expressed in the following formulae:

       (3)

where  a_x is the acceleration at point t_m in direction x, a_y is the acceleration at point t_m in direction y.

The average describes the general of the recorded data collectivity; the variance describes the distributing pattern of each group in the feature space. The N groups of signature swatches can deduce N values of one feature, through the Gauss function these values can supply the average estimate and variance estimate that can show the distribution of parameterized definitions. The 10 biological features can be deduced by the formulae in the following analysis.

The agonic estimate(μ_k) of the average can be illustrated in this way:

              (4)

where   x_i shows the 10 biological features.

The agonic estimate(V_k) of the variance can be illustrated in this way:

       (5)

where  x_i shows the above-mentioned 10 biological features, μ_k expresses the agonic estimate of  the divided difference; k is the amount of features, which means that V_k is the value of k features. Therefore,(μ_k, V_k) can describe the feature of each user. The system that collects the 10 features can deduce the following figures like （μ₁,V₁）,（μ₂,V₂）,…, (μ₁₀,V₁₀). The referred signature template of each signatory that is used for authentication can be built with those vectors.

If the user has four signature swatches, only two of them are taken into consideration in the following patterns: the total time of the hand-written signature and the frequency to lift the pen.  Signature 1: 4.234 s, 5 times; Signature 2: 4.623 s, 6 times; Signature 3: 4.555 s, 4 times; Signature 4: 4.772 s, 5 times. For the total time, the average is 4.546 s, the variance is 0.051 477; for the frequency to lift the pen, the average is 5, the variance is 0.666. So the extracted features of the four signature swatches are (4.546, 0.051 477), (5, 0.66 6).

The signature can be regarded as a two-dimensional curve that takes (x₁, y₂)=(0, 0) as the beginning and (x_N, y_N) = (n_x, n_y) as the end, the shortest of the length is:

   (6)

where  D is the shortest length of the curve, x_k is the coordinate in direction x, y_k is the coordinate in direction y.

The information of special points x and y obtained from the above control can be used to modulate the above-mentioned formulae; then the following formula can be deduced:

     (7)

where  D_t is the total length of the curve.

2.3 Signature verification

2.3.1 Hidden Markov model

Hidden Markov model(HMM) includes a Markov chain X={x_t:T+1>t>0} and an observed stochastic process Y={y_t:T+1>t>0}, wherein the Markov chain is unobservable, but can only be recognized through an observed stochastic process^[10-12]. The parameter set of one HMM is as follows.

1) The model state collection is S={S₁, S₂ , …, S_N};

2) The observation state collection V={V₁, V₂, …, V_M}, for the successional observed quantities the collection is infinitudes;

3) The initial probability is П={π_i}, therein π_i=    P (q₁=S_i), 1≤i≤N；

4) The transfer probability is A={a_ij}, wherein a_ij= P(q_t+1=S_j|q_t=S_i) ,1≤i , j≤N；

5) In state j the visible probability distribution of the sign is B={b_j(k)}, therein b_j(k)=P(at  time point t the sign is V_k|q_t=S_j) , 1≤j≤N ,1≤k≤M.

2.3.2 Hidden Markov classifier

In the signature verification process the HMM is used as a feature classifier. The scattered HMM is expressed by 5 parameters: model state, observation sign, initial probability, transfer probability and emission probability. The model state and observation sign are different in accordance with their application. The scattered HMM classifier is built for each signature, and is composed of strokes type classifier HMM1 and strokes position classifier HMM2 .

In strokes type classier HMM1, the number of the elements in the observation set expresses the amount of the signature strokes; each observed sign shows one kind biological features, for the 10 kinds biological features the amount of observed signs is 10; the amount of model states is 20. The imput of HMM is the biological features obtained from the initial feature values, the signature is modeled in accordance with the types of strokes .

In strokes position classifier HMM2, the margin between the number of the elements in the observation set and the amount of signature strokes is 1, each observed sign expresses one kind of strokes’ position, for 9 kinds of strokes’ position the amount of observed signs is 9; the amount of elements in the model state set is 20; the position connection is determined by the direction vector that points are from the ending spot (E) to the beginning spot (S). Two categories are classified in accordance with the coincidence of E and S. If there is no coincidence between E and S, 8 strokes’ positions can be deduced：1(East), 2(East north), 3(North), 4(West north), 5(West), 6(West south), 7(South), 8(East south); if there is a coincidence between E and S, there only one strokes’ position can be deduced.

HMM combines HMM1 with HMM2, the number of elements in each model’s observation set refers to the amount of signature strokes; each observed sign expresses one kind of  biological feature or one kind of strokes’ position: the amount of observed signs is 19,  the number of elements in model state set is 20.

2.4 Verification model

The signature verification system could certainly be inserted into some applicational system conveniently and efficiently, so it plays its role completely^[13-15]. In order to provide a more agile and convenient method with the combination of every office automation(OA) system, the portion of signature verification can be supplied through activeX(OCX) control and dynamic link library(DLL) file, and its interface and security policy can be affected in accordance with the specific conditions. Through open database connectivity(ODBC) the verification server can be connected with each kind of popular database server conveniently. Our platform chose security socket layer(SSL) and remote authentication dial in user service(RADIUS) for the protocol to transfer biometrics data between the agent and the authentication client, and the authentication client and the authentication server, respectively, SSL can adequately protect biometrics data sent over a network by a standard encryption algorithm, As for RADIUS, it only supports encryption of passwords that are much shorter than usual biometrics data. Our platform enhanced RADIUS by adding encrypted transfer of multiple types of large identification data, including user ID to suit for multi-biometrics.

The system’s working process is shown in Fig.1. The general register process is as follows: The new user firstly needs to write 20 signature swatches on the hand-written board in relaxation, and then the system draws the user’s behavioral features with the Gauss function, forms the sole string and then saves it as a template. When one wants to register with his identity: firstly he needs to write his name on the control, and then the system draws the behavioral features from this signature; HMM classifier recognizes them and compares with the template; if this signature is real, then this comparison process will obtain a higher similarity, otherwise the similarity will be lower.

Fig.1 Working process of signature verification system

1) Imput the signature information obtained from hand-written board into the control; 2) Draw 10 potential biological features;

3) Obtain feature values and feature vectors; 4) Match the above 10 features in the DB.

3 Experiment and analysis

When a new user registers in the system he should write 5 signatures (the more the better), the hand-written pen driver will report x-y coordinate at each spot. The system draws the feature value with the control, when all the features have been drawn it obtains 5 vectors containing 10 feature elements as listed in Table 1.

Table 1 Values of feature elements

According to formulae, the average and variance of the 10 feature vectors are listed in Table 2.

Table 2 Average and variance of feature elements

5 signatures can deduce  feature values, and also 8 groups of features N_vx(8, 0.5), N_vy(9, 0.5), N_ax(16, 0), N_ay(16, 0), t_w(4.4898, 0.544), D(224.2, 47.5), N_w(4.8, 0.7), t_n(13.4, 0.3). This group of vectors can create each user’s signature template, the template is stored in the signature template DB and used as threshold value that can judge true and false of the signature.

In the verification process, through HMM classifier the features of the signature are matched to the referenced feature value, and the true and false of the signature can be judged by the threshold value. If the match is successful, the signature is true; otherwise, the signature is false.

4 Conclusions

1) Through the potential feature extraction method that combines the curvature feature extraction with that of the coordinate, the system obtains behavioral biostatistics features that can clearly convey the stokes’ features; on this basis, the system draws the feature information from the behavioral biostatistics features with the Gauss function and train HMM with the data of behavioral biostatistics features. 

2) This hand-written signature verification system uses VB6.0 in the development and has been applied in the documents management system successfully through transferring WindowsGUI.  It has mainly two effects, one is verification of the identity, the other is printing the signature of the report form. The verification enhances the system security. Printing the signature of the report  form has two advantages. Firstly it lets the users realize the document reliability, step up the efficiency in the examination and approval of the documents; secondly it enhances the non-repudiation of the signature, when necessary the actual signature can be appraised by hand-written analysis expert.

3) Through testing, the result indicates that after training the hand-written signature verification model can satisfy the application in OA system. Under limited experiment conditions, the testing and formal application only use the simple signature imitation instead of the signature of skillful copyist. In the process of building the user’s templates the system needs signature swatches as many as possible, which makes the features distribute in a normal manner and brings about a larger initial workload; further researches in the field covers how to synthesize the features and to filtrate yawp.

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Foundation item: Project(03JJY3102) supported by the Natural Science Foundation of Hunan Province, China

Received date: 2006-12-24; Accepted date: 2007-03-27

Corresponding author: ZHU Shu-ren, PhD, Professor; Tel: +86-15913137689; E-mail: zhusr@gdcc.edu.cn

(Edited by YANG Hua)