velocity and pressure-based partitions of horizontal and vertical trajectories for on-line signature...

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Pattern Recognition 43 (2010) 2817–2832

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Pattern Recognition

0031-32

doi:10.1

� Corr

E-m

aurangz

sats.edu

jinnah.e

journal homepage: www.elsevier.com/locate/pr

Velocity and pressure-based partitions of horizontal and vertical trajectoriesfor on-line signature verification

Muhammad Talal Ibrahim a,�, M. Aurangzeb Khan b, Khurram Saleem Alimgeer b, M. Khalid Khan c,Imtiaz A. Taj d, Ling Guan a

a Ryerson Multimedia Research Lab, Ryerson University, Toronto, Canadab Department of Electrical Engineering, COMSATS Institute of Information Technology, Islamabad, Pakistanc Centre for Image Analysis, Uppsala University, Uppsala, Swedend Department of Electronics Engineering, Mohammad Ali Jinnah University, Islamabad, Pakistan

a r t i c l e i n f o

Article history:

Received 28 July 2008

Received in revised form

3 February 2010

Accepted 11 February 2010

Keywords:

Signature verification

Horizontal and vertical trajectories

Velocity profile

Pressure profile

Partitions

Discriminating features

03/$ - see front matter & 2010 Elsevier Ltd. A

016/j.patcog.2010.02.011

esponding author. Tel.: +1 416 979 5000�61

ail addresses: muhammadtalal.ibrahi@ryerson

[email protected] (M. Aurangzeb K

.pk (K. Saleem Alimgeer), [email protected] (

du.pk (I.A. Taj), [email protected] (L. Guan

a b s t r a c t

In general, shape of an on-line signature is used as a single discriminating feature. Sometimes shape of

signature is used alone for verification purposes and sometimes it is used in combination with some

other dynamic features such as velocity, pressure and acceleration. The shape of an on-line signature is

basically formed due to the wrist and fingers movements where the wrist movement is represented by

the horizontal trajectory and the movement of the fingers is represented by vertical trajectory. As the

on-line signature is formed due to the combination of two movements that are essentially independent

of each other, it will be more effective to use them as two separate discriminating features. Based on

this observation, we propose to use these trajectories in isolation by first decomposing the pressure and

velocity profiles into two partitions and then extracting the underlying horizontal and vertical

trajectories. So the overall process can be thought as the process which exploits the inter-feature

dependencies by decomposing signature trajectories depending upon pressure and velocity information

and performs verification on each partition separately. As a result, we are able to extract eight

discriminating features and among them the most stable discriminating feature is used in verification

process. Further Principal Component Analysis (PCA) has been proposed to make the signatures rotation

invariant. Experimental results demonstrate superiority of our approach in on-line signature

verification in comparison with other techniques.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Signature verification is a process used to verify whether anindividual hand-written signature is a forgery or a genuine. Theprimary advantage that signature verification systems have overother types of biometric technologies is that signatures arealready accepted as the common method of identity verification.This history of trust means that people are willing to accept asignature based verification system.

Usually, signature verification systems can be classified intotwo categories off-line signature verification and on-line signature

verification. There is a significant difference between off-lineand on-line signature verification. Off-line signature verificationsystems mainly deal with the shape of the signature. The

ll rights reserved.

06.

.ca (M.T. Ibrahim),

han), khurram_saleem@com

M. Khalid Khan), imtiaztaj@

).

shape-related features include x�y coordinates, height-to-widthratio, direction histogram, and curvature [1]. The main applicationof off-line signature verification systems is in automatic verificationof signatures found on bank cheques and documents.

On the other hand, on-line signature verification systems areperceived more reliable, because in on-line signature verification,it is not only the shape that matters but also the changes indynamic features such as velocity, acceleration and pressure[2–4]. The shape of a signature is represented by the horizontaland vertical trajectories where normally the horizontaltrajectories are formed due to the movement of wrist and thevertical trajectories are due to motion of fingers during thesigning process [5]. Moreover total signature time, RMS speed,instantaneous velocity at sampling points are also considered asdynamic features [6]. It is widely believed that shape anddynamics of a given signature play somewhat complementaryroles in distinguishing genuine signature from forgeries.The reason being that it must be more difficult for forgers toimitate both the shape and dynamics of the original signaturesimultaneously as compare to imitating either of the two aspects

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M.T. Ibrahim et al. / Pattern Recognition 43 (2010) 2817–28322818

in isolation. Only the genuine signer can recreate the samedynamics. It is easy for an expert forger to forge what a signaturelooks like in shape, but it is almost impossible to forge thedynamic changes as discussed in Section 3.1.1.

In on-line signature verification systems, shape of a signatureis a parametric representation of two features, i.e. horizontal andvertical trajectories of a signer as shown in Fig. 1. Normallyon-line signature verification systems use signature shape asa single feature during verification process. Recently in [7] Khanet al. proposed an approach that decomposes the velocity profileof a signature into three bands and further decomposes thesignature shape into strokes based on these velocity bands. Butthe experimental results revealed that horizontal and verticaltrajectories in isolation played an important role in theverification process instead of using them as single feature(shape).

In this paper, we present a novel approach which decomposesthe shape (horizontal and vertical trajectories) of a signature on thebasis of pressure and velocity profiles, and uses horizontal andvertical trajectories as separate features during verification.Pressure and velocity profiles are partitioned into low andhigh regions, and underlying horizontal and vertical trajectoriesare extracted on the basis of these subsets. So the overallprocess can be thought of as the process which exploits theinter-feature dependencies by decomposing signature trajectoriesdepending upon pressure information as well as the velocityinformation and performs verification on each partitionseparately. Principal Component Analysis (PCA) has been usedto make signatures rotation invariant whose details are discussedin Section 2.2.3 while in [7] cross-correlation was used tomake signatures rotation invariant which is much morecomputationally expensive than our proposed rotation invariant

Fig. 1. Sample signature, (a), (b) are the horizontal and vertical trajectories of the signat

horizontal trajectory against the vertical trajectory.

technique. For the first time, pressure profile has been partitionedinto two subsets based on base-pressure (i.e. the pressure profileof the base-signature) and dynamic time warping was alsoperformed on pressure profile. Our experimental results revealthe fact that every signer has at least one stable feature and can beused independently for verification purpose.

The paper is organized as follows. Section 2 deals with theacquisition of signature data and preprocessing steps. Section 3describes the design and structure of our proposed system. Theexperimental results are presented and discussed in Section 4.Conclusions are drawn in the last section.

2. Data acquisition and preprocessing

2.1. Data acquisition

Signature samples analyzed in this study were collected fromthe students and faculty members of COMSATS Institute ofInformation Technology, Islamabad, Pakistan, over a period ofthree months at different time and in different situationsto capture the different moods of a signer. Our database consistsof 15 000 genuine signatures by 25 different signers: 600signatures per signer. All of these were real signatures of thesigners. Among these 25 signers, four are female and two are left-handed. In order to obtain a signature template, which can reflectthe long-term manner of a user’s signing process, signers wereasked to practice the signing process until they feel they canrecreate their signature easily and comfortably on the digitizer.

Skilled forgers were hired for obtaining 250 skilled forgeriesagainst each signer. To facilitate the forgers, a signing simulationmodule was added to our system. Simulation module animates the

ure, respectively, whereas (c) is the shape of the signature obtained by plotting the

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M.T. Ibrahim et al. / Pattern Recognition 43 (2010) 2817–2832 2819

signing process of a signature so that forger is able to see not only thesignature shape but also the signing dynamics (speed andacceleration) as well. Signature simulation module animatessignature dynamics according to the time stamps of signature’strajectory points. Forgers had a chance to see the animation severaltimes and practice tracing over the signature image a few timesbefore forging it. All signers were properly guided in signing theirsignatures in the center of the tablet and in up right position. Fig. 2shows some genuine signatures along with their respective skilledforgeries.

In our proposed system, signatures were captured using Wacom’sGraphire2 which is a pressure sensitive tablet with physical size of216.1 �218 �26.3 mm and with active area of 127.6 �92.8 mm. Itis capable of sampling the data at about 100 samples per second: ateach sample point, the (x,y) coordinates of the signature’s trajectory,pressure and the time stamp are recorded.

2.2. Preprocessing

Despite the supervised data acquisition, there is a significantintra-class deformation and variation in orientation of signatures.So there is always a need of preprocessing module which canremove these intra-class variations. For this purpose, all signa-tures of i th signer are preprocessed with reference to a singlestandard signature called base-signature. Base-signature ib is agenuine signature of the i th signer whose average Euclideandistance from rest of genuine signatures of that signer isminimum. Our preprocessing module can be further divided intothe following steps:

(1)
smoothing by cubic-spline; (2) translation invariance; (3) rotation invariance; (4) scale invariance; (5) zero pressure removal.
2.2.1. Smoothing through cubic-spline

Tablet used in our system has a low sampling rate, i.e.100 samples/s which results in jagged signature trajectories.Verification process based on jagged trajectories leads to poorsystem performance. Cubic spline is used to smoothen out thejagged trajectories as discussed in [7]. Signature is a parametricfunction of time, which provides the liberty to smooth x and y

coordinate curve in isolation and then combining them in the endas shown in Fig. 3.

Fig. 4 shows two sample signatures before and after smoothingthrough cubic splines. As the first derivative of cubic spline is velocityso after smoothing the signatures, we have also obtained the velocitysignal for each signature that do have one-to-one correspondencewith the shape signal. Pressure signal is also smoothed by cubic-spline in order to have one-to-one correspondence with thesmoothed shape signal as well as with the velocity signal. Fromnow onwards, whenever we refer to signature signal we will bereferring to velocity, pressure as well as shape signal.

2.2.2. Translation invariance

As the active area of the digitizer used in our system is 127.6�92.8 mm which allows each signer to sign at different locationson his different trials, there is a need to make all the signaturestranslation invariant. For this purpose we shifted the mean of allthe signatures to zero, so that all signatures have their meantranslated to the origin. This is performed by subtracting themean of the jth signature of the ith signer from horizontaltrajectories xi

j and vertical trajectories yij.

2.2.3. Rotation invariance and scale invariance

After making all the signatures translation invariant, the next stepis to make the signatures rotation invariant as different signatures arecaptured at different angles. This may cause problem if we wish tocompare the shape of the signature. The widely accepted way issimply to transform the signature to a standard orientation. So, wehave introduced a method that can make all the signatures rotationinvariant with respect to the base-signatures ib. This is performed bythe conventional Principal Component Analysis (PCA) which is notonly used for dimensionality reduction but also to make theimages rotation invariant [8]. It is a rotation transformation thataligns the data with the eigenvectors that corresponds to largesteigenvalues of the scatter matrix. Fig. 5(a) shows a base signatureand Fig. 5(b) shows two signatures superimposed on each other,signature in solid-line is the original signature and signature in doted-line is after rotating the original into the direction of the base-signature.

For scale invariance, horizontal and vertical trajectories of thesignature are separately scaled in such a way that their aspectratio remains same [7]. In the process of rotation and scaleinvariance only shape signal has been disturbed while velocityand pressure profiles remain unchanged.

2.2.4. Zero pressure removal

The last preprocessing step is to remove spatial areas of asignature which have falsely became part of signature. In fact,these areas are generated due to the high sensitivity of the tablets,which is capable of capturing the data even when pen tip is closeto surface of the tablet as shown in Fig. 6(a) and (c). The spatialareas and velocities of signature corresponding to such regionsare termed as zero pressure regions. At these zero pressureregions, the pressure profile is not exactly zero but close to zero.So, there is need of a threshold that can help us in removing thesefalse spatial areas. Experimentally, we selected a threshold valuetij based on the pressure profile of each signature of ith signer and

the spatial areas and velocities corresponding to the pressureprofile below this threshold value were considered as zeropressure region and hence they were removed. Mathematicallythis threshold value can be calculated as

tij ¼

1

M

XMm ¼ 1

zijðmÞ�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

M

XMm ¼ 1

zijðmÞ�

1

M

XMm ¼ 1

zijðmÞ

!2vuut , ð1Þ

where M is the total number of samples in a pressure profile zij of j

th signature of i th signer. The result of this step is shown inFig. 6(b) and (d). The threshold ti

j helps to remove the false spatialareas between pen-up and pen-down that were captured due tothe high sensitivity of the tablet.

3. Design and structure of proposed system

Fig. 7 shows the block diagram of our proposed system whichconsists of two phases:

(1)
training phase; (2) verification phase.
In the training phase feature selection based on velocity andpressure is performed and based on selected feature, templatesare generated. In the verification phase, any test signature isverified on the basis of stable selected features. The followingsubsections deal with each phase in detail.

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Fig. 2. Sample signatures, (a), (c), (e) and (g) are genuine signatures whereas (b), (d), (f), and (h) are forgeries. Here we see that skilled forgeries are quite closer in shape to

their genuine counterparts. The need of dynamic features like velocity and pressure are evident for proper discrimination.


3.1. Training phase

Training phase deals with training of the system with thegenuine signatures only. Schematic diagram shown in Fig. 8depicts main processes involved in training phase. The details aregiven in subsequent sections.

3.1.1. Partitioning of signatures

The first and foremost task performed in the training phase isto partition all signatures of signer i. Usually, signatures arepartitioned into small strokes on basis of one or more dynamicfeatures, namely velocity, pressure, acceleration, pen angle, etc.The critical question here is: which one to choose and why; and

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Fig. 3. Sample signature after smoothing, (a), (b) are the horizontal and vertical trajectories of the signature after smoothing whereas (c) is the shape of the signature

obtained by plotting the smoothed horizontal trajectory against the smoothed vertical trajectory.

Fig. 4. Signatures (a) and (c) before smoothing (b) and (d) after smoothing.


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Fig. 5. (a) Base signature, (b) signature in dotted-line is original test signature and solid-line represents test signature after rotation, whereas in both (a) and (b) straight

lines represent largest eigenvector corresponding to its respective signature. It is obvious from the (b) that after rotation eigenvectors of base-signature and test are at same

angle.

Fig. 6. Signatures (a) and (c) before zero pressure removal, (b) and (d) after zero pressure removal.

Fig. 7. Block diagram of our proposed system.


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how to use it more conveniently and efficiently? The authors in[9] provided a comparative study on signature verification. Theyused regional correlation, dynamic time warping, and tree

Fig. 8. Schematic diagram of training phase.

Fig. 9. (a), (c) and (e) are shape, velocity and pressure profiles of genuine signature, whe

from the figure that decision on basis of only shape can be misleading, but a composite

can lead us to more reliable decision.

matching algorithms to compute type-I, and type-II errorsfor the above mentioned dynamic features. Afterwards, theycalculated the total error (type-I plus type-II) for each dynamicfeature, averaged over the three algorithms. Their analysisrevealed that velocity feature has provided less overall total erroras compare to other dynamic features. Following this study,researchers employed velocity alone as the discriminating featurefor few years [10,11,7]. In [4], a stroke based algorithm wasproposed in which strokes were identified by finding the decreasein pen tip pressure, decrease in pen velocity and whenever thereis a rapid change in pen angle. In [12], inter-feature dependencieswere exploited by partitioning velocity into partitions and furtheron the basis of these velocity partitions, horizontal, vertical andpressure profiles were segmented into strokes and verificationwas performed based on the distance between strokes whereas a

reas (b), (d) and (f) are shape, velocity and pressure profiles of forgery. It is obvious

feature set containing shape along with dynamic features (velocity and pressure)

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combination of different dynamic features such as writing order,initial and final point of signature, velocity change in horizontaland vertical trajectories, etc. were used in [13] for verification

Fig. 10. Warping path between (a) genuine test signature and base signature velocities

and base signature pressure, (d) forged test signature and base signature pressure.

Fig. 11. DTW processing compensate phase removal. Two velocity signals (a) genuine a

(c) genuine against base signature and (d) forgery against base signature.

purpose. In [14] velocity profile was segmented into strokes basedon local minima and the signature was then broken down intomore easily analyzed sub-components. In [15], relationship

, (b) forged test signature and base signature velocities, (c) genuine test signature

gainst base signature and (b) forgery against base signature. Two pressure signals

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between shape and dynamic features was exploited to develop ahighly discriminative feature set for classification purpose and avelocity based directional decomposition was introduced for theexploitation of inter-feature dependencies. It is clear from Fig. 9that if velocity is combined with other dynamic features it willperform better than having a verification system only dependenton velocity and also it is hard for the forger to reproduce thedynamic features by just looking at the shape of the signature[16,17]. In our proposed system, we used velocity as well aspressure to form a higher dimensional discriminating feature setwhich facilitates the verification phase more than using velocityalone. To accomplish this task, we will divide the horizontal xi

j and

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.10.20.30.40.50.60.70.80.9

1

Medium Horizontal Trajectory

Med

ium

Ver

tical

Tra

ject

ory

Fig. 12. (a) Partition map of velocity profile of base signature as proposed in [7], (b), (c)

velocities as proposed in [7].

Fig. 13. (a), (b) proposed partition map of velocity an

vertical yij trajectories independently into two partitions on the

basis of velocity. The same procedure will be performed on thebasis of the pressure profile as well.

3.1.2. Velocity and pressure based partitioning

The first step involved in partitioning the horizontal xij and

vertical yij trajectories on the basis of the base-velocity vi

b (velocityprofile of base-signature) and base-pressure zi

b (pressure profile ofbase-signature) is to develop the one-to-one correspondencebetween the base-signature ib and all the signatures includinggenuine and forgeries of the i th signer. For this purpose dynamic

0 0.5 1 1.5 2 2.5 3 3.5 40

0.10.20.30.40.50.60.70.80.9

1

Low Horizontal TrajectoryLo

w V

ertic

al T

raje

ctor

y

0 0.5 1 1.5 2 2.5 3 3.50.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

High Horizontal Trajectory

Hig

h V

ertic

al T

raje

ctor

y

and (d) are spatial areas of base signature corresponding to low, medium and high

d pressure profile of base signature, respectively.

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time-warping (DTW) is used between vib and velocity profiles vi

j ofall the signatures of signer i as described in [10]. The purpose ofDTW transformation in a signature verification system is toreduce the intra-class variation while preserving the inter-classvariability. If DTW is performed directly to actual signature datathen this transformation artificially makes two signatures almostidentical and reduces inter-class variability. So direct applicationof DTW to shape signal of signature data is not recommended insignature verification [10]. The remedy of this problem lies infinding a time function which directly corresponds to signaturebut has no concern with the overall shape of the signature.Velocity, pressure and acceleration can fit the bill because theyhave direct one-to-one correspondence with the signature time-index. We employed velocity signal for time warping and creatingcorrespondences among signatures of the same person and thesame idea was used for the pressure signal. Now, we will have

Fig. 14. (a) and (c) are spatial areas of genuine signatures corresponding to low velo

velocities, (e) is the spatial areas of forgery corresponding to low velocities and (f) is the

among the genuine signature areas, whereas forgery signature areas are quite differen

two sets of horizontal and vertical trajectories having one-to-onecorrespondence with vi

b and zib, respectively.

Fig. 10(a) and (c) shows the matching of genuine velocityprofile and genuine pressure profile against vi

b and zib,

respectively. Note that how close the warping function remainsto the diagonal. Fig. 10(b) and (d) shows the warping path ofvelocity profile and pressure profile belonging to forged signaturewith vi

b and zib, respectively, and the deviation of path from

diagonal is obvious from the figure. If one now plots vib and vi

j

against their re-parameterized time points and zib and zi

j againsttheir re-parameterized, Fig. 11 shows how the different peaks arenow perfectly aligned.

After accomplishing DTW transformation, one-to-manyrelationship present in warping path is eliminated [7], so thatlength of warping path becomes equal to the length of basevectors(vbi, zbi). It is performed by discarding all the repeated

cities, (b) and (d) are spatial areas of genuine signatures corresponding to high

spatial areas of forgery corresponding to high velocities. We see a lot of similarity

t from genuine.

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values in the warping path of vib and zi

b. Now the correspondingtime-points are used to retrieve xi

j and yij for all signatures of the i

th signer.After establishing correspondences of all signatures with

base-signature, we divide vib and zi

b into two partitions; low andhigh and then on the basis of these partitions, we segment xi

j andyi

j. As the partitioning procedure for both vib and zi

b is identical, soin the later part of this section, we will partition the signature onthe basis of vi

b and the same procedure will be followed for zib. In

[7], authors proposed a partitioning method in which theydecomposed the xi

j and yij firstly into three subsets on the basis

of low, medium and high vib and then by claiming that low and

high velocity subsets have little spatial consequences and will notplay any major role in verification, they removed these twopartitions and then further decomposed the medium-velocity intolow-medium and high-medium velocity sub-partitions as shown

Fig. 15. (a) and (c) are spatial areas of genuine signatures corresponding to low pressure

(e) is the spatial areas of forgery corresponding to low pressure and (f) is the spatial are

genuine signature areas, whereas forgery signature areas are quite different from genu

in Fig. 12. But, there is always a possibility of losing someimportant spatial information that can be effective in verificationprocess as shown in Fig. 12(b) and (d). To eliminate this possibleerror, we have included these spatial regions in our proposedpartitioning method as well. Velocities are declared low velocities

vlib if and only if vib is less than or equal to mean velocity mvi

b ofthe base-signature. And velocities which are greater than lowvelocities are declared as high velocities vhi

b. Similarly, the pressureprofile of the base-signature is decomposed into low pressure zliband high pressure zhi

b based on the mean pressure mzib of the

base-signature. Proposed velocity and pressure partitions areshown in Fig. 13(a) and (b), respectively. Then for each signer i,DTW correspondences helped us to pick spatial areas (xi

j,yij) of

signature corresponding to vlib, vhib, zlib and zhi

b. Spatial areas ofgenuine and forged signatures corresponding to our proposedpartitions are shown in Figs. 14 and 15, respectively.

, (b) and (d) are spatial areas of genuine signatures corresponding to high pressure,

as of forgery corresponding to high pressure. We see a lot of similarity among the

ine.

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It is clear from both figures that our proposed partitioningmethod correspond to same spatial areas in case of genuinesignatures while there is a significant difference in forgeries incase of both velocity and pressure. Four spatial areas correspond-ing to velocity and pressure for j th signature of signer i can begiven as:

1.

Figsma

low-velocity spatial areas svlij ¼ ðxvlij,yvlijÞ;

2.
high-velocity spatial areas svhij ¼ ðxvhi
j,yvhijÞ;

3.
low-pressure spatial areas szlij ¼ ðxzlij,yzlijÞ;
4.
high-pressure spatial areas szhij ¼ ðxzhi
j,yzhijÞ.

3.1.3. Discriminating feature selection

After partitioning the signatures, next task of our proposedtraining phase is to select a single stable discriminating featurewhich will be from above mentioned four spatial areas. We haveachieved it using following proposed algorithm:

1.
In first step, we generate eight templates temabci one for each
trajectory as given below:

temiabc ¼

1

T

XT

t ¼ 1

abcit , ð2Þ

where aAfhorizontal,verticalg, bAfvelocity,pressureg, cAflow,highg

and T represents total number of signatures used for trainingof ith signer.

. 16. (a), (b), (c) and (d) are 2D dissimilarity spaces where (d) is declared as most stab

ller than other three dissimilarity spaces.

2.

le f

Now we will calculate the Euclidean distance of abcit from its

respective template temabci :

di,tabc ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXJ

j ¼ 1

ðtemi,jabc�abci,j

t Þ2

vuut , t¼ 1,2, . . . ,T: ð3Þ

where J represents the number of samples in each partition of i

th signer.
3. In this step, four two dimensional (2D) spaces are created by
plotting distances corresponding to all horizontal trajectoriesagainst their respective distances of vertical trajectories asshown in Fig. 16. We did not use horizontal and verticaltrajectories together in calculating the Euclidean distances(i.e. distance of signature shape against shape) because of theradial nature of Euclidean distance [8]. Now we calculate thedistances of vectors (di

abct) plotted on each two dimensional

space, and find out the maximum from each of the four abovementioned 2D spaces as given below:

mdibc ¼maxf

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðdi

xbctÞ2þðdi

ybctÞ2

q,t¼ 1,2,3, . . . ,Tg: ð4Þ

As a result of this step, we will have four maximum distances(mdvl

i , mdvhi , mdzl

i , and mdzhi ), each of which will represent the

maximum scatter of training data set corresponding to i thsigner in each of the above mentioned 2D spaces.

4.
Finally, we will calculate the minimum of four distances(mdvl
i , mdvhi , mdzl

i , and mdzhi ), and the partition corresponding to

that minimum distance is considered as most stablepartition, e.g. the stable partition in case of Fig. 16 is ‘d’. Afterselecting stable partition we need two dissimilarity measureswhich will be used for selecting decision boundary

eature because the maximum separation (4.8533) among genuine signatures is

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Fig(f)

pre

bet


during verification process. Distances calculated in Eq. (3)corresponding to stable partition will serve as dissimilaritymeasures, represented by dxsi

t and dysit, where s stands for

0 1 2−1

−0.50

0.51

1.52

2.53

3.54

Euclidean DistanHorizontal Trajectories i

Euc

lidea

n D

ista

nces

of V

ertic

al

Traj

ecto

ries

in H

igh

velo

city

. 17. 2D dissimilarity spaces with decision boundaries after spreading testing data. (a), (b

represent the poor discrimination power of shape (horizontal and vertical trajectories) i

ssure regions were not removed. It is evident that dissimilarity space (d) which was decl

ween genuine and forgeries and the zero-pressure removal plays an important role in t

stable partition and t represents signature number of i thsigner used in training phase. Further details are given in thenext subsection.

3 4 5ces of

n High velocity

c = 1.95

), (c) and (d) are same dissimilarity spaces as shown in Fig. 16 whereas (e) and

n the verification process, (g) is the dissimilarity space same as (d) but zero-

are as the most stable partition in case of Fig. 16 gives the optimum separation

he verification process.

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3.2. Verification phase

Table 1Equal error rates (EER) for 25 signers belonging to our signature database.

Signer no. EER of [7] EER of proposed system

1 0.090 0.000

2 0.015 0.000

3 0.020 0.007

In verification phase, a test signature of the ith signer isdeclared as ‘‘genuine’’ or ‘‘forgery’’. For this purpose, first testsignature (testi) is passed through all necessary preprocessingsteps, then its horizontal and vertical trajectories are decomposedon the basis of most stable feature selected during the trainingphase for the i th signer as shown in Fig. 7.

To decide whether testi is genuine or forged, a decisionboundary is needed. Due to absence of a priori information aboutpossible forgeries, the decision boundary is computed by exploitingthe consistency of dissimilarity measures in signatures participat-ing in the training phase (see also [7]). The decision boundary isestablished as a straight line on a two-dimensional dissimilarityspace whose axes are Euclidean distances dxsi

t and dysit for signer i,

as in Fig. 17. The parameters for the decision boundary arecomputed by using the means and variances of the dissimilarities(Euclidean distances) shown in the following equations:

midxs ¼

1

T

XT

t ¼ 1

dxsit , ð5Þ

midys ¼

1

T

XT

t ¼ 1

dysit , ð6Þ

sidxs ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

T�1

XT

t ¼ 1

ðdxsit�mi

dxsÞ2

vuut , ð7Þ

sidys ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

T�1

XT

t ¼ 1

ðdysit�mi

dysÞ2

vuut , ð8Þ

where T represents total number of genuine signatures present inthe database for a given signer i. The decision boundary is

computed with these four values, in the way that sidxs and si

dys

decide the slope of the decision boundary and midxs and mi

dys decide

the position of the decision boundary, and is given by

dysi¼�

sidys

sidxs

ðdxsi�c � mi

dxsÞþc � midys: ð9Þ

In this equation, c is the independent constant to adjust theposition of the decision line. By adjusting the c value, we canbalance the false rejection against false acceptance errors. With asmall c value, the false rejection error increases while falseacceptance error decreases and with a large c value vice versahappens.

4 0.018 0.011

5 0.025 0.014

6 0.013 0.009

7 0.015 0.011

8 0.013 0.002

9 0.029 0.015

10 0.023 0.000

11 0.019 0.007

12 0.030 0.000

13 0.022 0.012

14 0.027 0.010

15 0.019 0.000

16 0.012 0.009

17 0.015 0.004

18 0.024 0.000

19 0.026 0.000

20 0.019 0.005

21 0.017 0.003

22 0.022 0.008

23 0.026 0.015

24 0.029 0.004

25 0.030 0.000

4. Experiments and results

To ensure the robustness of our proposed system, we haveexperimented with our own database of 25 signers containing21 250 signatures (15 000 genuine+6250 forgeries). Among 600genuine signatures of each signer, we have used 200 signaturesfor training purpose, whereas remaining 400 genuine signaturesand 250 skilled forgeries for a single signer are used for testingpurpose. The decision of declaring a test signature as ‘‘genuine’’ oras ‘‘forgery’’ is made by throwing the dissimilarity measure of thatsignature on two-dimensional space of dxsi and dysi, and if it fallsabove the decision boundary it is declared as ‘‘forgery’’ else as‘‘genuine’’.

Largely verification systems are compared through equal errorrate (EER), which represents the point on receiver operatingcharacteristics (ROC) where false acceptance rate (FAR) is equal tofalse rejection rate (FRR). FAR represents the probability that a

false match occurs, while FRR represents the probability that afalse rejection occurs. Table 1 shows EER for the signers belongingto our database. The average EER for our proposed system is0.0058, where as average EER in [12,7,18,2] are 0.0220, 0.0239,0.0590 and 0.0610, respectively, while using our own database.All of the above referred algorithms were tested on our owndatabase under same testing conditions. Researchers of on-linesignature verification are trying to improve the performanceunder the constraint that only a few genuine signatures areavailable for training. In order to show the validity of ourproposed algorithm, same experiments was also performed onthe subset of our database containing 25 signers and for eachsigner 25 genuine and 25 forgeries were selected. In thisexperiment, training was done by using only three and fivegenuine signatures. The results are given in Table 2. However, inorder to compare the performance with other algorithms, we haveevaluated the performance of our proposed algorithm using bothprivate (our own database) and public (MCYT) database. We haveused one of the most famous public database MCYT-SignatureDatabase [19]. This database contains 100 different signers andfor each signer, there is 25 genuine and 25 forgery signatures.These forgery signatures have been made up by the fivesubsequent users, who were able to get a static image of thesignature to imitate and trying until they feel confident, hence,there are skilled forgeries signature. The results of our proposedsystem on the MCYT database while using only three and fivegenuine signatures for the training of our purposed system areshown in Table 3.

It is clear from the results that our proposed system performsbetter even if training is done by using only three and five genuinesignatures. The results on the MCYT database are also satisfactorywhere we have achieved the EER of 0.0340 when only threegenuine signatures were used for training and EER of 0.0109 whenonly five genuine signatures were used, where as average EER in[20,21] are 0.0120, 0.0375, respectively, while using only fivegenuine signatures for training. It has been found experimentallythat the spatial areas corresponding to high velocity and lowpressure regions are more stable and they give better verificationresults.

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Table 2Avg. equal error rates (EER) for signers belonging to our signature database.

No. of training

signatures

Avg. EER of [12] Avg. EER of [7] Avg. EER of [18] Avg. EER of [2] Avg. EER of

our system

3 0.0320 0.0140 0.0680 0.0770 0.0042

5 0.0157 0.0094 0.0186 0.0193 0.0012

Table 3Avg. equal error rates (EER) for 100 signers belonging to MCYT signature database.

No. of

training signatures

Avg. EER of [12] Avg. EER of [7] Avg. EER of [18] Avg. EER of [2] Avg. EER of

our system

3 0.1470 0.0868 0.1622 0.2100 0.0340

5 0.1253 0.0820 0.1327 0.1582 0.0109


5. Conclusions

This paper substantially extended the work presented in [7].The proposed method decomposes an on-line signature intopartitions and then selecting an appropriate and the most stablepartition for verification purpose. These partitions are created onbasis of base-velocity and base-pressure profiles, PCA has beenused as a rotation invariance method in on-line signatureverification, further DTW was also performed on pressure andprofile. We believe that the reason for improved performance liesin the better exploitation of inter-dependencies between dynamicfeatures (velocity and pressure) and signature trajectories(horizontal and vertical). By employing dynamic features (velocityand pressure) and extracting signature trajectories of a givensigner, it is made impossible for a forger to maintain shape withina certain velocity and pressure partition at a given time.

References

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About the Author—MUHAMMAD TALAL IBRAHIM received the MS degree in Digital Image Processing from Center for Advanced Studies in Engineering, Islamabad,Pakistan, in year 2007. He is currently pursuing his Ph.D. degree at Ryerson University, Toronto, Canada, under the supervision of Prof. Ling Guan. His research interestsinclude biometrics, pattern recognition, image processing, and computer vision applications.

About the Author—M. AURANGZEB KHAN received his BSc degree in Computer Science and MS degree in Digital Image Processing from International Islamic University,Islamabad, Pakistan, in 2001 and 2004, respectively. He is with Department of Electrical Engineering as Assistant Professor at COMSATS Institute of InformationTechnology, Islamabad, Pakistan. He is currently pursuing his research in Signature Verification. Decimation-free directional filter banks, image enhancement andsegmentation, face recognition, fingerprint identification, iris verification are his areas of interest.

About the Author—KHURRAM SALEEM ALIMGEER did his Bachelors degree in IT in 2002 and completed his MS in Telecommunications (Gold Medal) in 2006. He has beenwith Department of Electrical Engineering, Comsats Institute of Information Technology (CIIT) since 2003. He is active researcher and supervising extensive research workat Bachelors and Masters Level. Currently, he is Assistant Professor at CIIT and is also working as doctoral researcher. He has published research papers in the field ofWireless Communications, Image Processing and Antenna Design.

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About the Author—M. KHALID KHAN received the MS degree in Image Processinpursuing his PhD in Image Processing from Centre for Image Analysis at Uppsa

g from International Islamic University, Islamabad, Pakistan, in 2004. He is currentlyla University, Sweden. His current interests include stochastic optimization, image

registration and feature extraction.

About the Author—IMTIAZ A. TAJ is currently Professor in Electronics Engineering Department of Muhammad Ali Jinnah University (MAJU), Islamabad. He completed hisBachelors in Electrical Engineering from University of Engineering and Technology (UET), Peshawar in 1993. He did his Masters and PhD in Electronics and InformationEngineering from Hokkaido University, Japan, in 1998 and 2001, respectively. After his PhD he joined Communication Enabling Technologies, Islamabad and worked as amember of VLSI hardware design group till 2003. In 2003, he joined CARE (Center for Advance Research in Engineering) Pvt. Ltd. as Senior Member Technical and led theMachine Vision Group of the company and successfully completed some very important projects related to Vision based navigation system development. In parallel he alsoworked as Faculty Member in the CASE (Center for Advance Studies in Engineering) in its Graduate Program of Computer Engineering.

Since June 2007, he has been associated with Mohammad Ali Jinnah University, Islamabad, Pakistan, and is supervising the Vision and Pattern Recognition Systems(VisPRS) Research Group (www.visprs.com), comprising of more than 15 members including six PhD and four Masters research students. His group is currently working ontwo R&D projects funded by Ministry of IT and Telecom, Pakistan, related to Biometrics and Video Encoding, respectively. His main areas of research interests includebiometrics, vision based tracking and navigation, video processing and encoding, medical diagnostics based on ECG and EEG patterns and optics. He has authored or co-authored 30+ international research papers including 14 papers in journals of international repute.

About the Author—LING GUAN is Tier I Canada Research Chair in Multimedia and Computer Technology, and Professor of Electrical and Computer Engineering at RyersonUniversity, Toronto, Canada. He received his Bachelors degree from Tianjin University, China, Masters degree from University of Waterloo and PhD degree from Universityof British Columbia. Dr. Guan has been working on image, video and multimedia signal processing and published extensively in the field. He currently serves on theeditorial boards of IEEE Transactions on Circuits and Systems for Video Technology and numerous other international journals. He chaired the 2006 IEEE InternationalConference on Multimedia and Expo in Toronto, and co-chaired the 2008 ACM International Conference on Image and Video Retrieval in Niagara Falls. Dr. Guan is Fellow ofthe IEEE, Fellow of Engineering Institute of Canada, IEEE Distinguished Lecturer (2010–2011) and a recipient of the 2005 IEEE Transactions on Circuits and Systems forVideo Technology Best Paper Award.

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