On-line Signature Verification Based on Altitude and Direction of Pen Movement Seiichiro Hangai
Shinji Yamanaka
Takayuki Hamamoto
Department of Electrical Engineering Science University of Tokyo
[email protected]
Signature is widely used to authorize who issued the document. However, signature has ambiguity, and it is difficult to distinguish the authentic signature from the mimicked signature only by bit mapped patterns. On the other hand, altitude and direction of gripped pen under signing depends on the shape of writer's hand and the habit of writing. In this paper, we propose a new on-line signature verification method, which uses the pen movement. From experimental results with 24 writers, verification rate of 92% is obtained.
Off-line verification method uses the feature (1) of signature which has already been written. Therefore, it shows the weakness against mimicry. On the other hand, on-line verification method considers the process of writing the signature. Most of conventional on-line methods use the feature (1), (2) and (3). It is expected to have high verification rate compared to off-line method [2]. We have been investigating an on-line signature verification method by using pen movement. Altitude and direction of the pen during writing a signature is relatively stable and such data include obviously the individuality of the person who writes the signature.
1. Introduction
2.1. Tablet and acquisition data
In issuing official documents or purchasing items, signature is widely used to show the authenticity. However, the signature varies every time, and a few people subjectively verify such signatures with no a priori knowledge. In considering electrical media distribution, it is strongly requested not only to protect a bit mapped documents or pictures from the forgery but also to make the new signature stamp. We have been investigating the individuality included in the signature itself and altitude and direction variation of pen movement [1]. The former gives the visible pattern and is easy to mimic. The later, altitude and direction of pen movement, depends on the shape of writer's hand and the habit of writing and is difficult to mimic. In this paper, we describe a new signature verification method by using the individuality extracted from the altitude and direction of the pen.
Figure 1 shows a tablet and a pen, and acquired data. Output data obtained by the tablet are x, y position x(t) and y(t), pen pressure p(t), pen direction θ (t), and altitude φ (t).
Abstract
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2. Writer identification It is well known that signatures, which are written by the identical person, have the following features, (1) Shape similarity (2) Writing speed similarity (3) Writing pressure similarity
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Figure 1：Data from tablet and Pen
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Figure 2:Example data (1) of genuine signature
2.2. Example data of genuine and spurious signatures Figure 2 and Figure 3 show signature data of an identical person in different time, and Figure 4 shows the mimicked data by the other person. From these figures, it is found that x, y position and pen pressure pattern show similar shapes even if the signature is the authorized one or the mimicked one. On the other hand, the pen direction pattern and the pen altitude pattern show visible difference between the authorized one and the mimicked one. It appeared that the direction and the altitude pattern of pen includes the writer's individuality very much.
3. Signature verification method 3.1. Signature data set All signature data obtained by the tablet are preprocessed. They are normalized by the length of writing duration, which is decided by magnitude of the pen pressure. In the following experiments, we use three data sets, they are pen movement, shape of signature and writing pressure.
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Figure 3 :Example data (2) of genuine signature
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sin θ ( t ) cos φ ( t ) − cos θ ( t ) cos φ ( t ) = ( ) V t sin φ ( t )
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Pen movement data V (t ) is defined by using direction θ (t) and altitude φ (t) as the following 3D vector.
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The difference between a reference data and an input data is estimated by integration of d(t) which is defined as
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A Shape of signature The starting position of pen-tip movement is adjusted to the origin of x, y coordinates. The difference between two shapes is evaluated by integration of Euclid distance of xy space at the sampled points. B Writing pressure The similarity of writing pressure p(t) is simply estimated by integration of the absolute difference of the reference and input data.
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where V r (t ) is the vector of the reference data and V i (t ) is the vector of the input data. Figure 5, Figure 6 and Figure 7 show the example vector of pen movement. It appears that two data of the genuine signatures are very similar compared to the spurious signature.
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Figure 6: Pen movement (2) of genuine signature
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Signature data for the experiments are written by 24 subjects. They write their genuine signatures 20 times and the 5 forgeries for the other persons after training. The forgeries of 5 persons are selected randomly for the experiments. The writing area on the tablet is 95.8mm x 17mm. In general, there is some fluctuations of the data set in the time-axis when a person writes his signatures. In this paper, the dynamic programming (DP) matching method [2] is adopted in order to reduce such fluctuations. In the experiments, we compare the results of normal linear matching method and the DP matching method.
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t[msec] Figure 7: Pen movement of spurious signature The following three methods are applied to the signature verification. In each method, the correct verification rate is independently evaluated by using each of three data sets which are pen movement, shape of signature and writing pressure. The correct verification rate is decided by the point where the accepted percentage
Method A: One data of the genuine signatures is utilized for each reference data.
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of genuine signatures and the rejected percentage of mimicked signatures are balanced.
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4. Verification results Figure 8, Figure 9 and Figure 10 shows the evaluation of similarity of pen movement, signature shape and writing pressure after DP matching. In these figures, the thin line means the distance between a genuine data and a mimicked data, the thick line means the distance between two genuine data. It appears that the two lines of pen movement are much different. The difference is very stable compared to the other parameters. Therefore, it shows that the pen movement is very effective for signature verification. Table 1 shows the verification results obtained by method A, method B and method C. The pen movement has better results in each method. Although the method B is rather simple, the method B has best rate 92.6% among all results. From the results of the experiments, it appears that the pen movement with DP matching is very effective compared to the other parameters.
5. Conclusion In this paper, we describe a new on-line signature verification method. We adopt altitude and direction variation of pen movement as parameter to extract the individuality of signatures. We show the results of the experiments by three methods. Although most of conventional signature verification methods utilize the signature shape and writing pressure, it is verified that the pen movement with DP matching is very effective compared to such parameters.
Figure 8: Evaluation of similarity (pen movement)
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Method C: The reference data is defined of the average of five genuine data after the DP matching. The dispersion d v (t) is calculated between the reference data and the five genuine data at every sampled point. If d v (t1) is lager than a threshold, the sampled point t1 is skipped for evaluation of the difference between the reference data and the input data.
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Figure 9: Evaluation of similarity (signature shape) 200 100 0
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Method B: Three data sets of the genuine signatures are utilized for the reference data. The final difference are evaluated by the average of three difference between each reference data and the input data.
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Figure 10: Evaluation of similarity (writing pressure)
Table 1: Verification results
A B C
Linear DP Linear DP DP
Correct verification rate[％] Pen Signature Writing movement shape pressure 90.3 72.4 77.0 91.3 73.2 79.9 92.4 79.9 83.5 92.6 80.7 86.3 92.5 87.0 85.3
[1] S.Nakajima, T.Hamamoto and S.Hangai, “On-line Signature Verification using Pen Inclination”, PRMU, 97-242 , pp. 15-22, 1997.(in Japanese) [2] P.Zhao, A.Higachi, Y.Sato, “On-line Signature Verification by adaptively weighted DP mathing”, IEICE Trans. Inf. & Syst., vol.E79-D, No.5, pp.535-541, 1996.
