Improved wavelet-based online signature verification scheme considering pen scenario information

Improved wavelet-based online signature verification scheme considering penscenario information

Mohammad Reza Nilchiyan*Universiti Teknologi Malaysia,

Centre for Artificial Intelligence and Robotics (CAIRO),Skudai 81310, Malaysia

[email protected]

Rubiyah Bte YusofUniversiti Teknologi Malaysia,

Centre for Artificial Intelligence and Robotics (CAIRO),Kuala Lumpur, Malaysia

Abstract—Although signature verification is safer biotypesin terms of criminal, it has more risk on business safety. Inthis paper we address important challenge of on-line signatureverification, which is the high dimensionality of the signaturefeatures dataset. This issue can make the verification procedurecomputationally costly. In this regard, we take advantage ofwavelet transform along with a feature selection scheme tointroduce a new set of features. The experimental results onSVC 2004 database suggest that using this set of features,we can verify the signature with 3.5% EER while havingsignificantly lower dimension data set in comparison with thestate-of-the-art techniques.

Keywords-SignatureVerification, Feature Extraction, WaveletTransform, Feature Selection;

I. INTRODUCTION

Over the past few decades, there have been many attemptsto develop and strengthen the security of authenticationsystems [1]–[4]. Signature verification and identification isthe challenging issues in the new biometric research area.The widely usage of signature due to the social and legalacceptance, has opened the new research on it.

The nature of the input data makes the two types ofautomatic signature authentication, offline and online mode.Digital image of the signature on the document has beenused for offline mode [5]–[7] and on the contrary, the onlinesignature system cares to use the dynamic signing process[8]–[10]. The key point of the handwritten signature is thatconsidering the dynamic properties beside the static shapeof the signature that can makes highly unique characteristic.

Designing a fast and reliable signature verification sys-tem is the main direction of this paper. Any application-dependent signature verification system must be designedregard to features that characterize spatial and temporalaspects of that signature. Deriving a proper model forthe signature with introduced features is a main step inmodifying a signature corroboration system.

Feature extraction and feature selection are the two im-portant methodologies′part of on-line signature verification.These two parts have the direct effect on the verificationsystems dimension, which has effect on the speed and

performance of the system. In fact, all features set inverification process are time consuming whereas, not allfeatures are acceptable. Finding the set of expedient featuresis a prerequisite to do a fast processing and achievingreasonable performance. There are several feature extractionand selection methodology like geometric, topologic anddynamic schemes [11]–[14].The contributions of this paper are summarized as follows:

1) Formulation of a discretization scheme for the signa-ture features using B-spline functions.

2) Proposal of a new set of features based on wavelettransform along with the consideration of the statisticsof the coefficients to reduce the dimension of inputfeatures.

3) Proposal of a feature selection scheme using threedifferent metrics.

4) Validation of the proposed verification scheme by itsapplication on SVC2004 database.

The remainder of the paper is organized as follows: InSection II, we review the general steps toward the online sig-nature verification procedure. In Section III, we describe thediscretization scheme of time-dependent signature featuresusing B-spline functions. Also, in this section we propose anew set of wavelet-based features for a signature. A featureselection scheme is considered in Section IV. We evaluatethe proposed verification scheme in Section V. In Section VIwe summarize and conclude the paper finally.

II. PROCEDURE OF PROCESS

Recent research in the online signature modality has beenevaluated more safety than offline even include of skilledforgery signatures. Online dynamic signature verificationsystem categorises to four steps in its implementation. Dataacquisition, preprocessing, feature scheme, and decision-making [8]–[10].

A. Data acquisitionThe digital form of the signature with respect to time

was obtained from hardware system. There are severaldata bank include the Signature verification Competition

2013 First International Conference on Artificial Intelligence, Modelling & Simulation

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Figure 1. To find the direction of the signature (a), One way is consideredthe whole signature and turn in the opposite direction of the estimated angle(b), but it couldn’t estimate the direction correctly. The other way is usinga specific region around the centre of mass of the signature (c).

SVC2004, the BioSecure Multimodal Evaluation CampaignBMEC2007,International Conference on Frontiers in Hand-writing Recognition ICFHR2012 and more recently theInternational Conference on Document Analysis and Recog-nition ICDAR2009-2013. In this case we examined oursuggestions on SVC2004. This database introduced 1600signature of 40 users with 20 genuine and 20 skilledforgeries for each one [15].

B. Preprocessing

Differences in handwriting conditions make the unfaircomparison between signatures. Typically, the two signa-tures of one person may not be the same because of thesigner′s psychological and hardware′s physical conditions.Preprocessing is the first step for resampling, smoothing thedata and filtering out noise. In this case, Preprocessing hasbeen done on centre of signature due to the fact that startand end of the signature could be changed with respect todifferent writing conditions.

In order to normalize the signature direction as a function,the eigenvector of the momentum matrix determines thedirection of the signature. The formula of momentum matrixis

M =

[x2 xyxy y2

], (1)

withxy =

1

N − 1

∑

i∈Z(x[i]− x)(y[i]− y) ,

where x2 and y2 are the empirical variance of the variables xand y, respectively and N is the number of sampled points.Therefore, we rotate the signature with the determineddirection with negative sign. After that we normalize thescale by making the variance along each direction to unit(see Fig. 1).

C. Feature ShemeThere are several numbers of features which can be

presented for each signature; e.g. pen pressure, signatureshape, orientation of the pen, pen inclination, number ofloops, velocity and etc. The mission of extracted featuresis describing the characteristics of a signature that presentsreliable and effective feature selection algorithm. In theother side, existence of the number of instances for eachas the input of signature could be confronted with the highdimensionality. In fact, In spite of advantages by usingmore features, the process will be faced some problemslike complex designing of network, difficult computing inits algorithm, decreasing the speed and increasing the usagememory of the system. In order to overcome to these issues,we do it in two step by, 1) extracting and introducing newset of features and 2) proposing a feature selection schemeto choose a subset of the given features.

The final step is decision making that we explains morein Section V.

III. FEATURE EXTRACTION

A. B-spline representationWe assume that x = [x1, x2, ..., xN ] is a time-dependent

feature where N is the number of samples that are taken bythe specified device along the time dimension. For example,it can be pen pressure, position of the pen and speed alongdifferent directions.

In order to compute some features, it is required to applysome continuous operator on the measured features, e.g.,the given data can be the position of the pen, therefore inorder to compute the velocity, it is required to computeits derivative. In this regard, one way is to approximatethe derivative as a finite difference in the discrete domainthat can introduce inaccuracy in the verification procedure.In order to overcome this, we take advantage of general-ized sampling and represent the time dependent feature onthe space V {φ} =

{f(t) =

∑k∈Z ckφ(t− k) : c ∈ l2(Z2)

}

where φ(t) is a proper Riesz basis generating function.Therefore, we have

x(t) =∑

k∈Zckφ(t− k) (2)

where x(t) with x(k) = xk, ∀k = 1, 2, ..., N .We choose cubic B-spline function as the generating

function which is a proper trade off between cost andquality [16], [17]. In order to compute the coefficients c,we use the recursive scheme presented in [16] that itscomputational cost is o(1). It is possible to show that thederivative of x(t) in the specified point k is

∂x

∂t(k) = ck−1 − ck+1 . (3)

It suggests that the computation cost is as cheap as finitedifference but with an accurate and rigorous formulation.

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B. Wavelet-Based Features extraction

Basically, in this paper, a new set of features based on thestatistics of the wavelet decomposition of the time-dependentdata regard to the assumed problem is proposed. In fact,when the wavelet transform is applied, it is more commonthat many coefficients vanish for the real data. This principleis called transform coding that provides information aboutthe time and the frequency. Therefore, the huge number ofdata that could make the complexity in the system withspecial properties of the wavelet transform could be emitted.For instance, Fig. 2 shows the pen position of the signatureof one user along one direction and also represents it on thebasis function 1) Daubechies orthogonal wavelets D6 and2) Haar wavelet. It shows that the wavelet coefficients aresparse in comparison with the x representation in the timedomain (see the histogram as shown in Fig. 2).

The critical issue is that the number of non zero waveletcoefficients and their positions are completely dependent onthe input function. By analyzing the wavelet coefficientsin different scales, we observe that the distribution of thecoefficients is close to the Gaussian distribution except thefirst channel as shown in Fig. 3. Owing to the fact that itis sufficient to know the mean and the variance to specify aGaussian function, we consider their values for the waveletcoefficients in different scales as features of interest. Inaddition, we consider higher moments for the coefficients ofthe first channel. Algorithm 1 describes the feature extractionstep.

The given input data from the tablet is the following time-dependent features

1) x,y: pen position2) p: pen pressure3) ψ,φ: the azimuth and the altitude of the pen

where the size of each of them is denoted by N . Fur-thermore, we append to the set the velocity and accel-eration along two different directions. In order to com-pute them from the information of pen position, wetake advantage of (3). Therefore, the time series data is(x,y,vx,vy,v, ax, ay, a,p,ψ,φ) that contains 11 ∗ Nnumbers where the average value of N is around 300 forSVC2004. After, we use Algorithm 1 to extract the proposedmulti-scale features with k = 3. So, the number of featuresthat we consider is 11 ∗ 9 = 99-dimension data that hassignificantly lower diminution in comparison with the wholetime sequence data. In order to show the advantage of theproposed features, we illustrate 20 genuine signatures and20 forged ones of each user in SVC2004.

IV. FEATURE SELECTION

The main idea of feature selection methods was to find arepresentation of the data that was more suitable for learning

Input: x: the data vector given by the measurementdevice with length N

Output: wavelet-based features extracted from xif the feature of interest is ∂x

∂t thencompute cubic B-spline coefficients c n;forall m=1:N do

xm ← cm−1 − cm+1 with mirror boundarycondition;

endendset k the number of scales;initialization i = 1;while i <= k do

compute wavelet coefficients xlow and xhigh whoselengths are N/2i;µi =

∑Nm=1 xm/N ;

σ2i =

∑Nm=1 (xm − µi)2/N ;

if i=1 thenm(3)

i =∑N

m=1 (xm − µi)3/N ;endx← xlow;i← i+ 1;

endreturn µ,σ,m(3)

Algorithm 1: WAVELET-BASED FEATURE EXTRACTION

Figure 4. 20 genuine signatures and 20 forgery signature of one user inSVC 2004. This figure shows that how well the three features classifiedforgeries and genuine ones.

and improving classification accuracy while reducing mem-ory requirements [18]–[20]. We reduced the dimension ofthe set of features by factor eighteen (11 ∗ 160/(11 ∗ 9))by using Algorithm 1. In order to push the limits further,we introduce a feature selection scheme to filter the mostinformative features from the data set. In this regard, itis required to introduce a set of metrics to measure howinformative one feature is. Moreover, the selected featuresshould be the same for all the signers that needs a well-defined algorithm.

We consider two different types of measures for the

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Figure 2. (a) x in time domain. (b) Coefficients of x in the Daubechies wavelet domain. (b) Coefficients of x in the Haar wavelet domain. (e), (f) and(g) are their histogram, respectively.

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Figure 3. Wavelet coefficients of the azimuth angle of pen scenario in different channels (scales) and their distribution.

selection scheme. First category takes into account how wellthe feature separates the genuine signatures from the forgedones. We introduce Fischer metric for this case which is

FM{x,y} =|µx − µy|σx + σy

(4)

where x and y are feature vectors corresponds to genuineand forgery ones, respectively.

Second category is the one which measures how much onefeature is dispersed among the existing signatures of oneuser. We consider Arithmetic Mean and Geometric Mean(AMGM) and Mean Absolute Distance (MAD) from thiscategory. AMGM is defined as:

AMGM(x) =1n

∑Ni=1 exp(xi)

(∏n

i=1 exp(xi))1n

, (5)

where xi is the feature x related to i-th sample of the

signature of one user. The MAD metric is defined as

MAD(x) =1

N

N∑

i=1

|xi − x̄| , (6)

where x̄ is the mean of the feature x.In order to select a unique set of features for all the

signers, 1) we set the measure m, 2) we compute thismeasure for the given features for all the signatures of eachuser, 3) we sort them from the most informative features foreach user to the least one. We put them in matrix A

A =

⎛

⎜⎜⎜⎝

a1,1 a1,2 · · · a1,La2,1 a2,2 · · · a2,L

......

. . ....

aJ,1 aJ,2 · · · aJ,L

⎞

⎟⎟⎟⎠(7)

with its entries are feature numbers where J is the totalnumber of signers and L is the number of features.

99911111111

In order to pick the K most informative features, wecount how many times each feature is repeated in the firstK column of matrix A. Finally, the K most frequent onesare selected as the most informative features. Algorithm 2summarize the proposed feature selection algorithm.

Input: m: measure of how informative one feature isOutput: selected featuresset K the number of features that you are interested in;forall signers (i = 1 : J) do

forall signatures (j = 1 : L) docompute measure mi,j ;

endsort the measures from the highest to the lowestvalue, and put the corresponding features in thei-th row of matrix A;

endB ← K columns of matrix A;F ← how many times each feature repeated in matrixB, sort them;return the first K elements of F

Algorithm 2: FEATURE SELECTION SCHEME

V. EXPERIMENTAL RESULTS

In order to validate the importance of the proposedfeatures and the feature selection scheme, we test them onthe signature verification competition (SVC) 2004 database.There are two different types of data in this database. Oneconsists of only the information of the pen position, but theother one in addition includes the information of the penpressure and its direction. Each one contains signatures of 40different users which divided into 20 genuine signatures and20 forged ones. As we aim at considering the pen scenario,we apply our method on the second one. We compute falseacceptance rate (FAR) and false rejection rate (FRR) to showwhich algorithm outperforms the others.

We use multi-perceptron neural network (NN) with oneintermediary layer for the decision making. In the proposedverification scheme, there are several terms that play roles,e.g. the measure used for the selection scheme, number ofnode in the intermediary layer of NN. We consider all ofthem by experiments in this part.

For training of NN, we choose 15 signatures from thegenuine ones and 15 signatures from the forged ones.The rests, we use for the test. We adjust the number ofinformative feature K to 20. Figure 5 shows the performanceof the verification system while using 1 or 3 nodes for theintermediary layer. It suggests that 3 intermediary nodes per-forms better than NN with 1 intermediary node. Moreover,it illustrates that FM performs poorly in comparison withthe other two metrics. Moreover, MAD metric has the bestperformance. In contrary to FM, it should be noted thatMAD does not require any forged signature.

The performance of the proposed verification procedure iscompared with the other techniques which they used SVC2004 as their database (shown in Table I). It shows thatwe improve the performance of the verification proceduresignificantly while using less number of features.

Table IPERFORMANCE COMPARISON

Methods Number of FAR FRR EERfeatures

SVM [21] > 200 6.84% 6.84% 6.84%

HMM [22] > 1000 6.90% 6.90% 6.90%

DTW [23] > 900 6.96% 6.96% 6.96%

WP [24] > 2000 6.65% 6.65% 6.65%

Total Wavelet-Based 99 5% 5% 5%

FeaturesInformative Features 20 3.5% 3% < 3.5%

(MAD)

VI. CONCLUSION

Signature verification plays an important role in the hu-man society because it is wildly used in daily life as a bio-metric for the security. Most of the proposed techniques forthe verification are based on machine learning philosophy.The complexity of the learning procedure is proportionalto the size of the system. In order to reduce this size, oneway is to decrease the number of features to specify onesignature. In this paper, we proposed a new set of featuresbased on wavelet transform along with fusion techniques thatconsidered the statistics of the wavelet coefficients. In orderto push the limit further, we presented the feature selectionalgorithm. The proposed verification procedure was tastedon SVC 2004 considering the pen scenario. Finally, thismethod performs better than other art-techniques which hasused significantly less features.

ACKNOWLEDGMENT

This work was supported in part by the Ministry of HigherEducation Scholarship Division, Malaysia(MIS).

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Improved wavelet-based online signature verification scheme considering pen scenario information

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