FIR signature verification system characterizing dynamics of handwriting features
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Abstract
This paper proposes an online signature verification method based on the finite impulse response (FIR) system characterizing timefrequency characteristics of dynamic handwriting features. First, the barycenter determined from both the center point of signature and two adjacent penpoint positions in the signing process, instead of one penpoint position, is used to reduce the fluctuation of handwriting motion. In this paper, among the available dynamic handwriting features, motion pressure and area pressure are employed to investigate handwriting behavior. Thus, the stable dynamic handwriting features can be described by the relation of the timefrequency characteristics of the dynamic handwriting features. In this study, the aforesaid relation can be represented by the FIR system with the wavelet coefficients of the dynamic handwriting features as both input and output of the system. The impulse response of the FIR system is used as the individual feature for a particular signature. In short, the signature can be verified by evaluating the difference between the impulse responses of the FIR systems for a reference signature and the signature to be verified. The signature verification experiments in this paper were conducted using the SUBCORPUS MCYT100 signature database consisting of 5,000 signatures from 100 signers. The proposed method yielded equal error rate (EER) of 3.21% on skilled forgeries.
Keywords
Impulse Response Wavelet Coefficient Finite Impulse Response Area Pressure Signature Verification1 Introduction
Now the need for biometric authentication systems is on the rise because of the ease of use without a password or keycard required. Signature verification is one of the biometrics based on handwriting behavior. In several parts of the world, a signature is the customary way to verify an individual in daily activities, such as withdrawing cash from a bank account and entering a contract. Although visual examination is a popular method for signature verification, it usually takes a long time to process and there are occasions in which examiners make mistakes. To effectively verify the signature, an automatic system for signature verification is required. Signature verification methods are largely classified into two classes: One is the offline method based only on static visual information, and the other is the online method based on the dynamics of handwriting process with a major advantage over the first method in that it is very difficult to forge or copy the dynamics which are invisible. It is well known that handwriting is a highly individual entry depending on such many factors as country, age, habits, psychological or mental state, physical, and practical conditions[1]. For instance, size of scripts, location of scripts, shape of scripts, and duration time in handwriting process of scripts written by the same writer are never precisely the same due to the fluctuation of handwriting. Although the handwriting has many fluctuations described above, it is necessary to extract the feature of handwriting which is more consistent and not likely to be changed, for online signature verification. Such a feature is considered as a stable feature of handwriting. Hence, the preprocessing and feature extraction are very important for online signature verification. Furthermore, in the signature verification, the registration requirement of a large number of signatures of one same individual is impractical. Therefore, to extract the stable handwriting feature from the limited number of signatures is one of the important problems of online signature verification. The issues, i.e., unstable handwriting features and large number of signatures required in the registration process, make the development of online signature verification complicated. Moreover, it is desirable that the feature of handwriting should carry only the essential information of a particular signature and the size of the handwriting feature should be as minimal as possible.
2 Preprocessing
In this paper, signatures are written on a graphical tablet. The horizontal component, vertical component, and pen pressure of penpoint position at a time, t = n τ(≡ t_{ n }), in the signing process are represented as x(t_{ n }), y(t_{ n }), and p(t_{ n }) respectively, where τ is a constant sampling rate. In order to reduce the fluctuation of handwriting, three types of normalization with respect to size, location, and duration time in the signing process are performed with the details described in the following subsections.
2.1 Normalization of size
and N is the total number of sampled points of penpoint positions.
2.2 Normalization of location
2.3 Trajectory of barycenter
3 Feature extraction
3.1 Dynamic handwriting features
It is assumed here that the individual signing feature can be described by the following eight features:

Horizontal direction r_{ x }(t_{ n }) of the barycenter trajectory in signing process.

Vertical direction r_{ y }(t_{ n }) of the barycenter trajectory in signing process.
 Areal velocity a_{ v }(t_{ n }), which is the area swept out per unit time by the penpoint moving along the barycenter trajectory of handwriting script. The a_{ v }(t_{ n }) is computed from$\begin{array}{l}{a}_{v}({t}_{n})=\frac{1}{2}\left\begin{array}{cc}{r}_{x}({t}_{n1})& {r}_{y}({t}_{n1})\\ {r}_{x}({t}_{n})& {r}_{y}({t}_{n})\end{array}\right,\\ \phantom{\rule{5.3em}{0ex}}(n=1,2,\dots ,N1)\end{array}$(5)
 Displacement s(t_{ n }), which is the distance from the center of signature to barycenter trajectory at time t_{ n }. The s(t_{ n }) can be calculated as$\begin{array}{l}s({t}_{n})=\sqrt{{r}_{x}{({t}_{n})}^{2}+{r}_{y}{({t}_{n})}^{2}},\\ \phantom{\rule{2.5em}{0ex}}(n=0,1,2,\dots ,N1)\end{array}$(6)
 Magnitude of velocity v(t_{ n }) of the barycenter trajectory. The v(t_{ n }) is computed from$\begin{array}{l}v({t}_{n})=\sqrt{{(\mathrm{\Delta}x({t}_{n}))}^{2}+{(\mathrm{\Delta}y({t}_{n}))}^{2}},\\ \phantom{\rule{3.95em}{0ex}}(n=0,1,2,\dots ,N1)\end{array}$(7)where$\begin{array}{l}\mathrm{\Delta}x({t}_{n})={r}_{x}({t}_{n+1}){r}_{x}({t}_{n}),\\ \mathrm{\Delta}y({t}_{n})={r}_{y}({t}_{n+1}){r}_{y}({t}_{n})\end{array}$
 The direction change θ(t_{ n }) of the barycenter trajectory. The θ(t_{ n }) can be calculated by$\begin{array}{l}\theta ({t}_{n})={tan}^{1}\left(\frac{{r}_{y}({t}_{n+1}){r}_{y}({t}_{n})}{{r}_{x}({t}_{n+1}){r}_{x}({t}_{n})}\right),\\ \phantom{\rule{6em}{0ex}}(n=0,1,2,\dots ,N1)\end{array}$(8)
It is known that the pen pressure is one of the important features for signature verification. In this paper, two features related to the pen pressure are introduced as follows:
 Area pressure a_{ p }(t_{ n }) as shown in Figure5b, which is the area of triangle consisting of pen pressure, penpoint position, and center of signature in the signing process. The a_{ p }(t_{ n }) is computed from$\begin{array}{l}{a}_{p}({t}_{n})=\frac{1}{2}\times \widehat{p}({t}_{n})\times \sqrt{\stackrel{~}{x}{({t}_{n})}^{2}+\stackrel{~}{y}{({t}_{n})}^{2}},\\ \phantom{\rule{8em}{0ex}}(n=0,1,2,\dots ,N1)\end{array}$(9)
 Motion pressure m_{ p }(t_{ n }) as shown in Figure5b, which is distance of the diagonal between two adjacent penpoint positions and the pen pressure. The m_{ p }(t_{ n }) is computed from${m}_{p}({t}_{n})=\sqrt{\widehat{p}{({t}_{n})}^{2}+S{({t}_{n})}^{2}},$(10)where$\begin{array}{l}\mathrm{\Delta}x({t}_{n})=\widehat{x}({t}_{n+1})\widehat{x}({t}_{n}),\\ \mathrm{\Delta}y({t}_{n})=\u0177({t}_{n+1})\u0177({t}_{n}),\\ \mathrm{\Delta}p({t}_{n})=\stackrel{~}{p}({t}_{n+1})\stackrel{~}{p}({t}_{n}),\\ \phantom{\rule{.85em}{0ex}}S({t}_{n})=\sqrt{{(\mathrm{\Delta}x({t}_{n}))}^{2}+(\mathrm{\Delta}y{({t}_{n})}^{2})+(\mathrm{\Delta}p{({t}_{n})}^{2})}\end{array}$
Figure5 shows the area pressure a_{ p }(t_{ n }) and the motion pressure m_{ p }(t_{ n }) in the signing process determined by using Equations 9 and 10.
3.2 Timefrequency characteristic of the dynamic handwriting features
3.3 FIR system characterizing the dynamics of handwriting features
The FIR system is designed as follows:
4 Signature verification
In this section, the impulse responses obtained in the preceding section are used to verify signature. The algorithm is given as follows.
4.1 Training process
The following are the steps in the training process:

First, the member register their name and sign their signatures five times used for reference data and training process.

Second, the obtained signatures are preprocessed using method in Section 2.

Third, the eight dynamic handwriting features as described in Section 3.1 are calculated.

Fourth, after normalization of duration time, they are expanded into wavelet series to determine the timefrequency characteristics of their features. In this step, the suitable level of the timefrequency characteristics which represent the stability of their handwriting feature is determined by using the standard deviation of each level. We select the level of their standard deviations less than the predetermined threshold values as the stable handwriting feature. Therefore, these parameters are the individual features for a particular person.
 Fifth, the obtained timefrequency characteristics of the eight features are used to determine the handwriting system using the FIR systems as described in Section 3.3. In this case, the order of the FIR systems (M) for each particular person can be determined by using standard deviation of the impulse responses. We choose the maximum value of the parameter M that its standard deviation is less than the predetermined threshold value. Then, the obtained impulse responses are combined as$\begin{array}{r}\phantom{\rule{.5em}{0ex}}{\mathbf{h}}_{i,j}^{{(z)}^{\text{(ref)}}}=[{\mathbf{h}}_{i,j}^{{({a}_{z})}^{\mathrm{T}}}{\mathbf{h}}_{i,j}^{{({d}_{z})}^{\mathrm{T}}}],\\ (i={r}_{x},{a}_{v},\theta ,{a}_{p};j={r}_{y},s,v,{m}_{p}).\end{array}$(29)
The obtained feature vector (${\mathbf{h}}_{z}^{\text{(ref)}}$), level of the timefrequency characteristics, and order of the FIR system are used as the individual feature for signature verification for a particular person.
4.2 Testing process
In the testing process, the following steps must be undertaken:

First, test persons put their registered name and sign their signatures.

Second, the test signature is preprocessed using the method in Section 2.

Third, after normalization of duration time and using the registered name corresponding to the test name, the number level of the registered person is used to determine the timefrequency characteristics of their features.
 Fourth, the obtained timefrequency characteristics of the eight features are used to determine the handwriting system using the FIR systems as described in Section 3.3. In this case, the order of the FIR systems (M) of the registered name corresponding to the test name is used to calculate the impulse responses. Then the obtained impulse responses are combined as$\begin{array}{r}{\mathbf{h}}_{i,j}^{{(z)}^{\text{(test)}}}=[{\mathbf{h}}_{i,j}^{{({a}_{z})}^{\mathrm{T}}}{\mathbf{h}}_{i,j}^{{({d}_{z})}^{\mathrm{T}}}],\\ (i={r}_{x},{a}_{v},\theta ,{a}_{p};j={r}_{y},s,v,{m}_{p}).\end{array}$(31)
where ∥·∥ is Euclidean norm, and η is a predetermined threshold value determined by using the experiments with the training data for a particular signature.
5 Experimental result
6 Conclusions
In this paper, we proposed an online signature verification method based on the FIR system characterizing the timefrequency characteristics of dynamic handwriting features. The stable timefrequency characteristics of the dynamic feature were determined by selecting the suitable level of wavelet coefficients. The FIR system was realized by considering the selected wavelet coefficients of the dynamic features as the input and output of the system, respectively. The obtained impulse response was used as the individual feature for signature verification. It was found from our experiments that the proposed method is useful for online signature verification. In this research, a graphical tablet was used as the data acquisition system. Thus, the penpoint position was used to describe the handwriting feature in signing process. However, the graphical tablet can acquire such features as pen pressure and pen inclination. As such, the incorporation of such features into signature verification remains our future work.
Notes
Acknowledgements
This research was in part supported by the Thailand Research Fund (TRF) and the Commission on Higher Education (CHE) for research no. MRG5080378. The authors would like to express profound appreciation to J. OrtegaGarcia et al. for sharing the MCYT100 public database and to W. Surakampontorn and P. Sooraksa for their kind and useful suggestions.
Supplementary material
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