ON AN OFFLINE SIGNATURE VERIFICATION SYSTEM Ben Herbst Department of Applied Mathematics, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa, Email:
[email protected] Hanno Coetzer Department of Mathematics and Applied Mathematics, University of the Orange Free State, Private Bag 339, Bloemfontein 9300, South Africa, Email:
[email protected]
Abstract
On the other hand, in an application like the automatic clearing of checks by commercial banks, the above mentioned dynamic approach is not available{o line systems rely only on directly accessible geometric information. The accuracy of o line systems is therefore not comparable to that of online systems. Since commercial banks for example, pay little attention to verifying signatures on checks{mainly due to the number of checks that are processed{systems capable of screening casual forgeries should already prove bene cial. The fact that commercial banks screen the written amount on check very carefully, opens the possibility for human intervention in the case of rejected signatures. The pressure on a low rejection rate is therefore not quite as severe as in the case of online applications. Previous techniques used for o line signature veri cation, include backpropagation learning algorithms [5], synthetic discriminant functions [8] and neural networks [7], see also [5, 6] for additional techniques. In paper [5] a false rejection rate (FRR) of 1% with a false acceptance rate (FAR) of 4% is reported. An EER of 4% is reported in paper [8] and a EER of 3% in paper [7]. However, it should be noted that these results were obtained using only casual forgeries in the test test. In addition a very small database was used. Since the results tend to deteriorate when the size of the database is increased (see e.g. [9]), the gures quoted above should be used with caution. In the next section we describe our database in some detail, before we give a brief outline of our algorithm.
We investigate the feasibility of using the Radon transform and a dynamic programming algorithm to authenticate handwritten signatures on checks. Since there no dynamic information is available as in the case of the online problem where signatures are typically captured by means of a digitising tablet, the oine problem poses serious challenges. Our present system achieves an equal error rate of approximately 23% when only very high quality forgeries (skilled forgeries) are considered and an equal error rate of approximately 10% in the case of only casual forgeries.
1 Introduction Although handwritten signatures are by no means the most reliable means of personal identi cation, it remains one of the most widely acceptable means of personal identi cation. It is also non intrusive, inexpensive and one of the most commonly used personal identi cation systems. . A number of reasonably reliable online signature veri cation systems exist, see for example [9, 2]. These systems nd particular applications, for instance to verify the identity of a purchase card, including credit card, holder. In this case the person will be required to sign on an electronic device, typically a digitizing tablet. The test signature is veri ed by comparing it with a template in a database which may take the form of a reference signature or a vector of parameters describing the features of the signature. In this context a template will consist of geometric and dynamic data extracted from a set of sample signatures supplied by the individual at the time of registration. 1
2 Database Our database consists of the signatures of twenty-three individuals, all students of roughly the same age. For each individual a reference signature was constructed, using ten sample (training) signatures registered at a single contact session. Thirty-two test signatures (twenty genuine signatures, six skilled forgeries and six casual forgeries) were then obtained over a period of two weeks (at three di erent contact sessions). The rst and second set of ten genuine test signatures were supplied by the same individuals during contact sessions one week and two weeks after the initial session. The casual forgeries were obtained by supplying only the names of the individual to the forgers{the casual forgers did not have any access tot he actual genuine signature. The skilled forgeries were obtained by providing sample genuine signatures to the forgers which were then allowed ample opportunity to practice their forgeries. A group of six di erent forgers then provided one forgery each for the genuine signatures in the test set. Note that none of the forgeries was used for training. It should also be pointed out that the genuine signatures were produced using di erent pens and that the forgeries were produced using the same pens as used for the genuine signatures. Only `perfect' signatures were considered, i.e. no deterioration of the signatures such as the introduction of smears, scratches, etc., was allowed. Each signature in the database was scanned into a 512x512 binary image. The database therefore consists of 966 images in total. Figure 1 shows typical examples of the signatures in the database. (a)
(b)
3 Preprocessing 3.1 The Radon transform
Continuous model: The Radon transform of a function, f (x; y), consists of projections (shadows) of that function obtained at di erent angles. In the Cartesian coordinate system, (x; y), it is assumed that f (x; y) is nonzero only in a nite region around the origin. The Radon transform is obtained by considering another coordinate system, (s; t), which is rotated by degrees with respect to the (x; y)-system. Data collection is done along sets of lines parallel to the t-axis. The set of all line integrals along such a set of parallel lines, is a projection of the function. The Radon transform, p(s; ), consists of all the projections for all angles , where 2 [0; ] and s indicates the perpendicular distance from the origin to the line in question. The Radon transform is therefore given by p(s;
Z 1 )=
?1
f (c s
? s t; s s + c t)dt
The function p(s; ) is often displayed as a grey-scale image, which is called a sinogram because of the sinusoidal patterns appearing in the image. Discrete model: For the purposes of signature veri cation the function in question is an image (matrix) consisting of say N pixels (in our application N = 5122). We assume that the intensity of the ith pixel is fi and that the sinogram is generated using M non-overlapping beams (with an equal number of beams per angle) and that the cumulative intensity of the pixels within the j th beam is pj (the j th beamsum). In discrete form the Radon transform can therefore be expressed as follows pj
=
X N
i=1
wij fi ;
j
= 1; 2; : : : ; M;
where wij indicates the contribution of the ith pixel to the j th beam sum (Figure 2). The value of wij is determined by interpolation. The accuracy of the sinogram calculated will be determined by the number of angles considered, the number of beams used per angle and the accuracy of the interpolation method used to calculate wij . In this application we use 128 angles and 512 beams per angle to generate a sinogram. The sinogram (Radon transform) of each signature will therefore be a 128x512 grey-scale image. Figure 1: (a) Sample signature (b) Genuine test signa- These sinograms contain the same information as the ture (c) Skilled forgery (d) Casual forgery signature itself and signatures can be reconstructed from their sinograms by using the inverse Radon transform, see e.g. [1, 4]). (c)
(d)
@@@@ ith pixel @ @@@ @?@? @@@@ @@@? @ @@@@@@@ @@@ 6 j th
beam
Figure 2: Discrete model for the Radon transform. wij 0:9
3.2 Translation, rotation and size invariance Translational invariance: During preprocessing the
`center of mass' of the signatures are located at pixel coordinates [256 256]T . Rotational invariance: Although the Radon transform itself is rotational invariant, it is nevertheless essential that signatures are compared in the same orientation. For this reason the signatures are aligned along their rst principle axes. Scale invariance: During preprocessing signatures are scaled linearly, preserving their aspect ratios. Nonlinear adjustments are ensured by the dynamic programming algorithm.
4 Veri cation 4.1 Dynamic programming algorithm The accumulated search distance (ASD) necessary to warp a projection of one signature (sample vector) onto the corresponding projection of another signature (reference vector) will depict the dissimilarity of the two projections in question. The dynamic programming algorithm is as follows: (1) A grid is constructed where each grid point relates a speci c component of the reference vector with a speci c component of the sample vector. Grid point (x; y) will e.g. relate the xth component of the reference vector to the yth component of the sample vector. (2) For every grid point, the absolute value of the difference between the reference and sample components, associated with that point, is calculated. We shall call it the dissimilarity value of the grid point in question.
(3) Each grid point is assumed to have a maximum of three preceding points, i.e. the point diagonally underneath it to its left, the point directly underneath it and the point horizontally to its left. (4) Each grid point is now considered in a left-to-right, bottom-to-top fashion: The rst grid point is assigned a partial accumulated search distance (PASD) equal to its dissimilarity value. For every other grid point, its PASD is taken to be the sum of its dissimilarity value and the PASD of its preceding grid point with the smallest PASD assigned to it during one of the previous iterations. This grid point is referred to as its preferred preceding grid point (PPGP). Should two or three of these preceding grid points have the same PASD the diagonal grid point is preferred, followed by the vertical one. For every grid point, its PASD as well as its PPGP are stored. (5) The shortest search path is found by starting with the last grid point and connecting it with its PPGP. This preceding grid point is now considered, and connected with its PPGP. The process is repeated until the second last PPGP is connected with the rst grid point. (6) The PASD associated with the last grid point is the ASD necessary to warp the two vectors onto each other and will depict the dissimilarity between them. (a)
(b)
(c)
(d)
Figure 3: Search paths when comparing the rst projections of the signatures in Figure 1 with the rst projection of the signature in Figure 1 (a). Dissimilarity values (ASD's) are as follows: (a) 0 (b) 650 (c) 3479 (d) 3888 In Figure 3 the search paths are shown on a grid when the rst projections of the signatures in Figure 1 are
compared to one another. In each case the rst projection of Figure 1 (a) serves as the reference vector. The sample vectors are the rst projections of: (a) Figure 1 (a), (b) Figure 1 (b), (c) Figure 1 (c) and (d) Figure 1 (d).
larity values are used to assign a con dence value to every possible test dissimilarity value. This con dence value is scaled between 0 and 100. A simple threshold is then used to either accept or reject a test signature. 100
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FRR (%)
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0
(a)
(b)
(c)
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Figure 4: Test dissimilarity values for (a) Genuine test signatures obtained during the rst week (b) Genuine test signatures obtained during the second week (c) Skilled forgeries (d) Casual forgeries
4.2 Veri cation strategy In order to compare two signatures, their corresponding projections (rows of their sinograms) are used as input for the non-linear warping algorithm discussed in the previous section. The average dissimilarity of these corresponding projections depicts the dissimilarity between the signatures in question. A reference signature is constructed from the ten sample signatures. It will consist of the sinogram of the most representative (best) sample signature as well as the dissimilarities of the nine other sample signatures with respect to this best signature. We therefore have nine sample dissimilarity values. The most representative test signature is obtained by calculating the average dissimilarity of each of the sample signatures with respect to the other nine. The signature of which this average dissimilarity is the lowest is deemed the most representative. A test signature (genuine or forged) is evaluated by comparing it to the most representative sample signature, hence obtaining a test dissimilarity value. In Figure 4 the dissimilarity values for the di erent types of test signatures are compared. All these signatures are for the same individual, of which the signatures in Figure 1 are examples. The statistical properties of the nine sample dissimi-
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50 Threshold
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Figure 5: Solid lines indicate FAR and FRR for di erent threshold values as percentages, when all the forgeries are considered. Small dotted lines indicate FAR when only skilled forgeries are considered. The larger dotted lines indicate FAR when only casual forgeries are considered
5 Discussion When only skilled forgeries are considered, an EER of approximately 23% is obtained (Figure 5) as compared with an EER of approximately 10% when only casual forgeries are considered. Note that these numbers do not in uence the FRR. Figure 5 therefore demonstrate the most serious shortcoming of the present system|a sharp increase in the FRR for very low values of the decision boundary. This means that the false acceptance rate increases sharply{to about 41.3% for a FRR of about 5.2%{if the FRR is reduced. This should be compared with the a priori probability of a forgery. Although no data is available (to us) on the extent of signature forgeries, gures for serious crime in South Africa is typically in the order of 30 per 100 000 of the population, i.e. about 0.03%. If this gure is accepted as representative, it implies that that the present system where banks do not verify any signatures, i.e. where all forgeries are accepted, is actually very reliable. However, this does not imply that o line (or even online) signature veri cation systems are not viable with current technology. It does imply that the design and implementation of a signature veri cation system, which include issues such as the choice of decision boundary, value of the checks, human in-
tervention, etc., become of paramount importance see e.g. [3] where some of these issues are addressed in more detail).
References [1] Brooks, A. and Di Chiro, G. Principals of Computer Assisted Tomography (CAT) in Radiographic and Radio isotopic Imaging. Physics in Medicine and Biology, 21, pp.658-731 (1976). [2] Dol ng, JGA. Handwriting recognition and veri cation. A hidden Markov approach. PhD Thesis, Eindhoven University of Technology (1998). [3] Herbst, B. and Richards, D. On an automated signature veri cation system. In Proceedings IEEE International Symposium on Industrial Electronics, pp 600{604. Pretoria (1998). [4] Lewitt R.M. Reconstruction algorithms: Transform Methods. Proceedings of the IEEE, 71, pp. 390-408 (1983). [5] Mighell, D.A., Wilkinson, T.S., and Goodman, J.W. Backpropagation and its Application To Handwritten Signature Veri cation. Advances in Neural Information Processing Systems 1, Morgan Kaufman Publishers, pp. 340-347, 1989. [6] Wilkinson, T.S. Novel Techniques for Handwritten Signature Veri cation. PhD Dissertation, Stanford University, California (1990). [7] Pender, D.A. Neural Networks and Handwritten Signature Veri cation. PhD Dissertation, Stanford University, California (1991). [8] Wilkinson, T.S., Pender, D.A. and Goodman, J.W. Use of synthetic discriminant functions for handwritten signature veri cation. Applied Optics, 30, pp. 3345-3353 (1991). [9] Gupta, J and McCabe, A. A Review of Dynamic Handwritten Signature Veri cation. James Cook University, Australia (1997).
