On-Line Signature Verification by Exploiting Inter-Feature Dependencies M. Khalid Khan1 , M. Aurangzeb Khan2 Dept. of Electrical Engg. CIIT, Islamabad, Pakistan 1 khalid
[email protected] 2 aurangzeb
[email protected]
Abstract The traditional on-line signature verification process involves use of various dynamic features such as velocity, pressure, acceleration, angles, etc. The idea is to device a composite vector structure combining more than one feature where each feature is treated independently. Our proposed research work is an attempt to exploit the interfeature dependencies by employing a higher dimensional vector approach. The strategy adopted here is to obtain pressure strokes with respect to various velocity bands. The strokes thus obtained are found to portray a reasonably accurate basis for discriminating genuine vs forgery class. The simulation results validate our assumptions and show improvements in the discriminating index.
1. Introduction The on-line signature verification systems make use of time-evolution of signatures that are captured by pressure sensitive tablets and are widely used in real time applications like credit card transaction or resource access [4]. The on-line signatures provide protection against forgery since these involve dynamic characteristics like velocity, pressure, etc. in addition to the morphological characteristics like shape [8]. A survey of literature indicates that the velocity has been extensively employed in on-line signature verification [2]. In some cases, it is used as a stand-alone discriminating feature [3] whereas in most other cases, it is combined with other dynamic features for verification purposes [1]. A well documented example in this regard is shown in [6], where velocity is combined with pressure to get reasonably accurate results. The major drawback of the composite approach is that it uses each of the available features independently ∗ Part of the research described here is funded by the NSERC - Canada and HEC - Pakistan.
Mohammad A. U. Khan3 , Imran Ahmad4∗ 3 Dept. of Computer Engg. Kyung Hee University, Korea mohammad a
[email protected] 4 School of Computer Science, University of Windsor, Canada
[email protected] instead of using a higher dimensional approach [5]. As a result, composite approach does not exploit the relationship that may exist among various dynamic features. In this paper, we propose an alternative simple strategy to form a higher dimensional composite feature vector with the aim to exploit the inter-dependencies among the shape, pressure and velocity. More specifically, in this proposed method, shape and pressure are decomposed into strokes while satisfying the velocity constraints. Figure 1 shows an array of pictures depicting genuine as well as skilledforgery strokes. The first row in this figure illustrates the velocity-based shape strokes whereas the second row indicates the pressure-based shape strokes. It is evident in both the cases that the forgeries are quite similar to their genuine counterparts. This allows us to observe small discriminating powers attached to these scenarios. The third row illustrates the velocity-based pressure strokes which are found to be highly discriminative in nature because they are quite dissimilar from each other. This result is significant since it allows us to strengthen the on-line signature verification process by utilizing the velocity-based pressure strokes in addition to the conventional shape strokes. This observation is the basis of our motivation to exploit inter-dependencies between the velocity and pressure signals. In our scheme, we divided the verification process into two steps: in the first step, shapes of signatures are compared on the basis of Euclidean distance and only if the input signature successfully passes the shape-test, it is tested for proper velocity-based pressure signals in the second step. Therefore, the input signature has to pass both the steps before it can be declared genuine. Rest of the paper is organized as follows: Sections 2, 3 and 4 deal with the signature data acquisition process, preprocessing steps and details about partitioning of velocity profile respectively whereas Sections 5, 6 and 7 present methods for stroke extraction, template generation and the verification process. Finally, some of the experimental results are presented and discussed in Section 8.
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(a)
(b)
(c)
(d)
signer may differ in angle, position, width and even in size. This may cause problem if we wish to compare the shapes of the signatures. The widely accepted norm is simply to transform the signature to a standard size and orientation. Signatures are made rotation-invariant by rotating each signature from 0 to 360 degrees in steps and calculating the cross-correlation at each angle with the base-signature. Angle at which cross-correlation value is maximum is utilized to make the signature rotation-invariant. After rotation-invariance, next step is to adjust the size of the signatures. We achieved this by scaling x and y coordinate of each signature separately. First y coordinate is linearly scaled between the range of 0 and 1 and then x coordinate is scaled in such a way so that the ratio between x and y coordinate do not change. To do so, we calculate the ratio between the two coordinates and then scale the x coordinate between the range of 0 and that ratio.
4. Partitioning of Velocity Profile
(e)
(f)
Figure 1. a) and b) show spatial areas corresponding to velocity, whereas c) and d) show spatial areas corresponding to pressure of genuine and forgery; e) and f) show areas of pressure for genuine and forgery respectively corresponding to a specific velocity band.
2. Signature Data Acquisition To capture signatures, we used a Wacom’s Graphire2 tablet. It is a pressure sensitive tablet that can sample data at about 100 samples per second and allows to capture and record the (x, y) coordinates of the signature’s trajectory and pressure and velocity at each sampling point. Base-signature is a signature among the genuine signature database of a signer whose average Euclidean distance from the rest of his/her genuine signatures is minimum. Rest of the preprocessing steps involve reference to the base-signature. The velocity profile corresponding to the base-signature is termed as the base-velocity.
3. Preprocessing One of the difficulties faced by a signature verification system is the fact that different signatures by the same
Once all the signatures of a signer i are preprocessed and aligned, the next job is to segment horizontal trajectory xik , vertical trajectory yki and pressure profile pik of each of his/her signature on the basis of base-velocity vbi , where k represents the signature number. Before decomposing xik , yki and pik on the basis of vbi , dynamic time-warping is performed between vbi and velocity profiles vki of all signatures of a signer as described in [3]. Subsequently, one-to-many relationship present in warping path is eliminated so that the length of warping path becomes equal to the length of the vector vbi . It can be accomplished by discarding all of the repeated values in the warping path of vbi . Now the corresponding time-points are used to retrieve xik , yki and pik for all signatures. After establishing correspondences of all signatures with the base-signature, we partition base-velocity vbi into three partitions: low, medium and high. On the basis of these velocity partitions, we segment xik , yki and pik of all signatures into strokes. Reason for creating these three partitions is that the distribution of vbi resembles that of the Gaussian distribution. As Gaussian distributions are mainly characterized by their mean and standard deviation, we can use mean mvbi and standard deviation svbi of vbi for creating partitions. Velocities are declared low velocities if and only if vbi is less than or equal to (mvbi − svbi ). Velocities which are greater than low velocities but smaller than (mvbi +svbi ) are named as medium velocities whereas all remaining velocities are termed as high velocities. Three partitions created in vbi are depicted in Figure 2. Due to this type of partitioning, resulting strokes are simpler and almost linear. We limited our self to three partitions due to the fact that having large number of partitions will result in isolated time-points rather than continuous strokes.
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After creating partitions in vbi , next step is to check spatial areas of signatures corresponding to all of the three partitions for minimum intra-class variation (less variation among genuine signatures). The partition that gives minimum intra-class variation is used for stroke-extraction and verification purposes. Empirical results on our database show that the spatial areas corresponding to medium velocities have lesser variations and are more stable as compared to the low and high velocities.
6. Template Generation After stroke-extraction, next step is the template generation process. Respective strokes of all genuine signatures for the ith signer are averaged together to get the template strokes for the shape and pressure. Mathematically, these template strokes can be represented as: N N ssi psi (1) tsi = k=1 jk , tpi = k=1 jk , j
tsij
N
tpij
j
N
th
and represent j template stroke for the where shape and pressure respectively, and N is the total number of genuine signature for the ith signer. After completion of template generation, two threshold values T si and T pi for shape and pressure, respectively, are estimated. These thresholds are used during the verification process for judging a test signature as genuine or forgery. For selecting threshold, we calculate the Euclidean distances between the strokes of a signer i with his/her respective template strokes as:
Figure 2. Partition map of velocity profile for base signature.
5. Stroke-extraction When medium velocity-partition is selected, next task is to segment xik , yki and pik on the basis of this partition. For this purpose, vbi is scanned for medium velocities. The moment we get first velocity value satisfying the medium velocity criterion, an index vector A is created which keeps the index of this value. Subsequently, the next value in vbi is scanned and if it also satisfies the medium velocity condition, its index is also stacked in A. This process is continued unless a value other than the medium velocity is found. Whenever a velocity other than the medium velocity is found, warping path is used to find corresponding indices in all velocity vectors which are associated with A. After corresponding indices of all velocity vectors are established, horizontal trajectory xik , vertical trajectory yki , and pressure pik of all signatures are segmented on the basis of the corresponding indices. These segmented trajectories are declared as first shape-stroke ssi1k and the segment of pressure profile pik is named as first the pressure-stroke psi1 . After the generation of first stroke, vector A is reset. Scanning of rest of vbi is again carried out, and in the same way, rest of the strokes (ssijk and psijk , where j = 1, 2, · · · , J is the stroke number) are generated. Strokes having length less than or equal to two points are discarded to avoid isolated points to be considered as strokes. Strokes produced in this manner are simpler and have less loop-backs. This in turn reduces the stress on the template matching process.
dsijk =
i (tsj − ssijk )2 , dpijk = (tpij − psijk )2 .
(2) Consequently, for each genuine signature, all dsijk are averaged together to produce a single measure dsik for the shape and all dpijk are averaged to form dpik . The maximum average Euclidean distances from all genuine signatures is declared as thresholds for discrimination purpose and can be computed as: T si = M ax(dsik ), i
T pi = M ax(dpik ),
(3)
i
where T s and T p are the desired threshold values for the ith signer and k = 1, · · · , N is the signature number.
7. Verification Process In verification process, an input test signature is verified as the genuine signature or forgery on the basis of previously calculated thresholds. In the proposed method, verification process is divided into two tests: (i) the shape-test and (ii) the pressure-test. An input test signature must pass both the tests to qualify as genuine. After necessary preprocessing, test signature is decomposed into shape-strokes and pressure-strokes as discussed earlier and is subjected to these tests as described in the subsequent subsections.
7.1. Shape-test Here Euclidean distance between the shape-strokes of the test signature and the template shape-strokes are obtained. Mathematically it can be given as: (tsij − ttsij )2 , (4) dtsij =
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where ttsij represents the j th shape-stroke of the test signature. These Euclidean distances are averaged together to get a single Euclidean distance for the test signature: J i
DT s =
j=1
dtsij
, (5) J where DT si is the total distance of the shape of the test signature, and J is the total number of strokes in that signature. Now DT si is compared with the threshold distance T si according to the following criteria: T est Signature ∈
P ressure − test if DT si ≤ T si F orgery otherwise. (6)
(a)
(b)
Figure 3. ROC curves for two out of 40 signers. It is obvious from (a) and (b) that FAR and FRR depicted in (a) are relatively lesser as compared to curve shown in (b).
7.2. Pressure-test
9. Conclusion
For this purpose, total distance DT pi for the pressure of test signature is calculated in the same way as for DT si , described in previous section. Finally, a decision about the test signature is taken according to the following condition:
The improved performance of our system is due to better exploitation of inter-dependencies among velocity, pressure and shape signals of a given signer where a forger has to imitate shape and pressure with certain velocity.
T est Signature ∈
Genuine F orgery
if DT pi ≤ T pi otherwise.
(7)
8. Experimental Results and Discussion We have collected signatures from 40 different signers. 5 of these were women whereas 7 were left-handed. Each signer provided a total of nearly 600 signatures over a period of 3-months. In these experiments, we also considered skilled forgeries. For skilled forgeries, the forger was provided with the simulation of genuine signatures from where the forger could easily acquire information like total signature time, sequence of strokes, signature velocity, etc. A total of 275 skilled forged signatures were acquired for each genuine signer. The performance of a verification system is mainly judged by the Receiver Operating Characteristics (ROC) curve and the Equal Error Rate (EER). ROC curve plots the False Acceptance Rate (FAR) against the False Rejection Rate (FRR), where FAR represents the probability that a false match may occur while FRR represents the probability that a false rejection may occur. Basically ROC depicts the trade-off between FAR and FRR at various thresholds. Due to space constraints, Figure 3 shows ROC curves for only 2 of the 40 signers in the database. Mainly the signature verification systems are compared through EER, which represents the point on ROC where FAR is equal to FRR. The average EER for our database of 40 signers is 0.022 whereas average EER in [7] and [8] is 0.059 and .061. The improvement in average EER as compared to the system proposed in [7] is 3.7% and in case of [8] is 3.9%.
References [1] F. Alonso-Fernandez, J. Fierrez-Aguilar, F. Del-Valle, and J. Ortega-Garcia. On-line signature verification using tablet pc. In 4th International Symposium on Image and Signal Processing and Analysis, pages 245–250, Sept. 2005. [2] G. Dimauro, S. Impedovo, M. G. Luccchese, R. Modugno, and G. Pirlo. Recent advancement in automatic signature verification. In IEEE. 9th International Workshop on Frontiers in Handwriting Recognition, pages 179–184, Oct. 2004. [3] T. Hastie, E. Kishon, M. Clark, and J. Fan. A model for signature verification. In IEEE International Conference on Systems, Man and Cybernetics, volume 1, pages 600–604, July 1991. [4] B. Li, K. Wang, and D. Zhang. On-line signature verification for e-finance and e-commerce security system. In 2nd International Conference of Machine Learning and Cybernetics, pages 3002–3007, Nov. 2003. [5] R. Martens and L. Claesen. On-line signature verification by dynamic time-warping. In 13th International Conference on Pattern Recognition, volume 3, pages 38–42, Aug. 1996. [6] T. Qu, A. E. Saddik, and A. Adler. A stroke based algorithm for dynamic signature verification. In Canadian Conference on Electrical and Computer Engineering, volume 1, pages 461–464, May 2004. [7] M. Wrioutius, J. Y. Ramel, and N. Vincent. Selection of points for on-line signature comparison. In Ninth International Workshop on Frontiers in Handwriting Recognition, pages 503–508, Oct. 2004. [8] J. Yi, C. Lee, and J. Kim. Online signature verification using temporal shift estimated by phase of gabor filter. IEEE. Trans. on Signal Processing, 53:776–783, Feb. 2005.
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