online signature veriﬁcation based on kolmogorov-smirnov distribution distance

8/10/2019 Online Signature Verification Based on Kolmogorov-Smirnov Distribution Distance

1/5

Online Signature Verification based on

Kolmogorov-Smirnov Distribution Distance

Erika Griechisch

MTA-SZTE Research Group on Artificial Intelligence

Hungarian Academy of Sciences and University of Szeged

[email protected]

Muhammad Imran Malik and Marcus Liwicki

German Research Center for

Artificial Intelligence (DFKI GmbH)

{muhammad_imran.malik, marcus.liwicki}@dfki.de

AbstractOnline signature verification methods examine thedynamics of the handwriting process to decide whether a sig-nature is probably genuine or forged. Most of the previouslyproposed methods for online signature verification apply NeuralNetworks, Dynamic Time Warping, or Hidden Markov Modelfor classification and they consider several aspects, like planarcoordinates, pressure, velocity, and acceleration with respectto time. Here we apply a non-parametric statistical test for a

comparison of features and the verification of signatures.

I. INTRODUCTION

Despite the spread of digital signatures and documents,handwriting and signature analysis is still an important area ofpattern recognition. In some areas only handwritten signaturesare accepted and in some sectors, this attitude is changingslowly, though it is still necessary to develop more effectivemethods.

In signature analysis we have two main ways of capturingand examining signatures: the offline and the online way.Offline signature verification is based on the image of thesignature and methods consider the shape of the signature in

several ways. In this case, the signatures are written down onpaper and then scanned with a high resolution scanner.

Online signature verification has to take into account thedynamics of the handwriting. The signatures can be capturedwith different tablets or pens fitted with sensors. Severalfeatures can be recorded: the most common ones being thex, y coordinates, pressure value (usually denoted by p or z),and slant. Velocity or acceleration can be derived from thecoordinates. Sensors (accelerometer or gyroscope) can alsomeasure acceleration or angular velocity.

Here we present an online signature verification approachbased on the Kolmogorov-Smirnov distribution metric. Dif-ferent feature distributions are compared in order to performclassification and distinguish between forged and genuinesignatures. Section II contains the related work of this area,while Section III describes our proposed algorithm for onlinesignature verification. Lastly, in Section IV we draw someconclusions and suggest further directions for future study.

II. RELATED WORK

Over the past few decades, several online signature ver-ification methods have been proposed. Researchers reviewedthe different methods of signature verification, like Plamon-don et al. in 1989 [1], 1994 [2], 2000 [3] and 2008 [4].

These surveys described the studies concerning handwritingrecognition, including handwriting interpretation, handwritingidentification, and signature verification. Besides these surveys,special survey were published in the past few years, such asthe verification survey by Sanmorino et al. [5], and paperson online signature verification, by Zhang et al. [6] and El-Henawy et al. [7].

In online signature verification several devices are usedto capture the dynamics of the handwriting process. Recentlydifferent types of WACOM tablets [8][10] and Anoto pens[11] appeared in several studies. Some other pens with sensorsembedded [12] or attached [13], [14] have been developed aswell. These special pens were developed for research purposes,hence usually only a few prototypes exist.

We can distinguish several verification approaches.Function-based approaches compare one-dimension discretetime functions (e.g. x, y coordinates, velocity ) and are usuallybased on the elastic matching called Dynamic Time Warping(DTW) [15][19] or Hidden Markov Models (HMMs) [20][23]. DTW measures the distance between two vectors withdifferent sizes. It aligns two time functions and finds a distance

between them. HMM is a statistical Markov Model wherethe probability distribution of the features are used to builda model for each author. Neural Networks are widely used aswell [24][26]. Another commonly used classifier is the Sup-port Vector Machine (SVM) [27], [28], which is a supervisedclassifier and it measures the similarity between two signaturesby using different kernel functions.

The winning system of the first signature verificationcompetition [8] was based on the DTW approach combinedwith statistics [9]. An offline signature verification methodbased on high pressure polar distribution was proposed in [29].Shrinivasan et al. [30] proposed an offline signature verificationalgorithm based on Kolmogorov-Smirnov statistics. We havenot found any online signature verification analysis or method

which is based on statistical data, hence we decided to carryout studies in this direction.

We considered the relevance of the Kolmogorov-Smirnovstatistics in online signature verification and here we evaluatea method based on the distribution distance determined byapplying the Kolmogorov-Smirnov test.

III. ALGORITHM

Every signature verification method consists of preprocess-ing, feature extraction, and classification steps (see Figure 1).

2014 14th International Conference on Frontiers in Handwriting Recognition

2167-6445/14 $31.00 2014 IEEE

DOI 10.1109/ICFHR.2014.129

738


2/5

Fig. 1. Typical steps in signature verification

During the training phase, based on the training set we deter-mine parameters. In the evaluation phase we use the evaluationdataset which includes the reference signature and questionedsignatures for each author. First, we perform preprocessing,then we extract the features, and as a last step we decidewhether a questioned signature is most likely a forged or agenuine.

Our idea was to keep the simple, given features withouttoo many transformations. The SigComp2011 database [10]

was used for the evaluation of our method, which containsDutch and Chinese online and offline signatures as well.

We performed the verification on the Dutch online data.The signatures were collected by a WACOM Intuos3 A3Wide USB Pen Tablet with sampling rate of 200Hz, resolution2000 lines/cm and precision of 0.25mm. In the SigComp2011dataset, the (xt, yt, pt) values are captured as x and y coordi-nates of the signature, and pressure p at a given time t.

A. Preprocessing

The WACOM tablet is a large tablet with an active areaof 488mm305mm and it is possible for two signatures fromthe same person to be written on any part of the active area.

Therefore we shifted the x, y coordinate values to the origin,so for each signatures S the minimal x and y values weresubstracted from the original coordinates. Thus, we got

xt = xtmink

(xk) (t= 1, . . . , T S)

yt = ytmink

(yk) (t= 1, . . . , T S)

shifted coordinates, whereTSis the number of sampled valuesof signature S.

B. Feature extraction

In addition to the above-mentioned features (i.e., shiftedx, y, andp), we calculated thev velocity values based on thedifference between the coordinates. The difference between the

coordinates is calculated simply using difference formulas

xt = xt+1xt (t= 1, . . . , T S 1)

yt = yt+1yt (t= 1, . . . , T S 1).

and the velocity values are calculated in the following way:

vt=

x2t + y2t =

xt+1xt

t

2+

yt+1yt

t

2.

0

0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000 2500

Cumm

ulativeprobability

y

1301301182013

Fig. 2. Plots of two empirical distribution functions, the black arrow denotingthe two-sample KS distance

C. Classification

The classification is based in the distribution of the differentfeatures, especially the pressure and velocity values of the

signatures.

In order to compare two distribution functions, theKolmogorov-Smirnov test was used which calculates the maxi-mal difference between the cummulative distribution functions.IfFx = f(X < x) and Gx = g(X < x) are the two distri-butions, then the Kolmogorov-Smirnov distance (KS-distance)between the two distribution functions is

D (f, g) = supx

|FxGx| .

Figure 2 shows two empirical distribution functions andthe arrow indicates the KS-distance of these distributions.

During the verification process the KS-distance was calcu-lated pairwise between each reference signature for the sameauthor and the questioned signature and the references for allthe features. Dutch evaluation data set usually contains 12reference signatures and 24 questioned ones for each author.All together there are 36 signatures per person. The KS-distance is always in the[0, 1] interval so we can represent thedistance matrices as a greyscale image. Examples are shown onFigure 3. The figure depicts the KS-distance values belongingto the author denoted by id 022. Each column representsdifferent features (i.e., x ,y,p,v) and contain three subfigures.The first row shows the distance matrix which shows thedistance between the reference signatures. The diagonal is

black (whose colour is assigned to zero) because there isno difference between identical distributions (the KS-distancebetween identical signatures is zero). The second row showsthe distance values between the questioned forged signatures.Each row in the image contains 12 pixels which representthe 12 distances between the corresponding forged, questionedsignature and the reference signatures. The third row shows thedistances between questioned genuine and reference signaturesin the same way as the forged ones: each row in the imagerepresents the distances between the corresponding questionedgenuine signature and the reference signatures.

739


3/5

distance between the reference signatures and . . .

reference signatures

questioned forged signatures

questioned genuine signatures

x y p v

Fig. 3. KS-distance matrix of the coordinates, pressure and velocity features of author 022 from the evaluation set of the SigComp2011 dataset

1) Training: Based on the reference signatures of a par-ticular author, the reference distance was calculated basedon each author. First, the KS-distance between each pairs ofreference signatures was calculated for an arbitrary featureand the reference distance was determined by taking theaverage, maximum or minimum of these distances. During thetesting phase, this reference distance was used for comparisonpurposes.

2) Evaluation: For each questioned signature the KS-distance from each corresponding reference signature was cal-culated and the KS-distance of the given questioned signature

was defined as the average, maximum or minimum of theseKS-distances.

Algorithm 1 shows the verification steps. From the sec-ond to seventh line, the distances for the reference set arecalculated, while lines 8-10 calculate the distances for thecorresponding questioned signature. On line 11 we see thedecision is based on the duration of the signature. On line14, the main constraint for the (minimal, maximal or average)distance of the questioned signature from the references istaken into account.

Another constraint impact was tested too. We added asignature duration constraint, the duration of the signaturewriting process being tested first. If the questioned signatureduration was greater than 1.5 times the maximal duration ofthe reference signatures, and the same hold for the pen downduration (whenpi> 0), the questioned signature was rejected.

First the constraints of the different features were taken toointo account separately (for x,y, p and v and for maximum,minimum and average distance it means 43 = 12 differentcases, if the time duration and maximal reference constraintsare taken into account it makes412 = 48cases). For example,if the minimal KS-distance of the pressure values fulfilled theconstraint in the line 14, hence if min /average(dist, p) 111.5 max(duration(references)) then

return forgery12else13

ifmax / min /avg(dist)< c max / min /avg(distRef)14then

return genuine15else16

return forgery17end18

end19

was accepted as a genuine signature (certainly the durationconstraint was take into account), otherwise it was rejected.Thec threshold was varied from 0 to 7.

In the next step these constraints were combined in severalways: the constraints regarded to the x and y coordinates werecombined with AND () and OR (), the p pressure and vvelocity the same way. The pressure was combined with thex, y coordinates as well, as shown below.

740


4/5

With time constraint Without time constraint

x

average

12. 27% /12 .19 % 2 9. 62% /2 9. 01%y 11. 13% /11 .27 % 3 0. 28% /3 0. 56%p 9.66%/9.57% 19.97%/19.91%v 11. 13% /11 .11 % 2 7. 66% /2 7. 78%xy 10. 47% /10 .34 % 2 6. 19% /2 5. 15%xy 12. 44% /12 .50 % 2 9. 79% /2 9. 01%pv 7.86%/8.02% 15.55%/15.74%pv 10. 31% /10 .19 % 2 6. 35% /2 6. 54%

(xy)p 8.02%/7.72% 16.04%/16. 05%(xy)p 10. 80% /10 .96 % 2 1. 93% /2 2. 22%

x

max

11. 95% /12 .04 % 3 1. 75% /3 3. 95%y 11. 29% /11 .42 % 3 2. 90% /3 0. 71%p 9.66%/9.88% 23.73%/23.61%v 10. 97% /10 .49 % 2 6. 35% /2 7. 31%xy 10. 64% /10 .34 % 3 0. 93% /3 1. 02%xy 10. 31% /11 .73 % 3 2. 24% /3 3. 64%pv 7.86%/8.02% 16.69%/16.67%pv 11. 46% /11 .73 % 2 7. 00% /2 6. 85%

(xy)p 8.84%/9.26% 19.97%/20. 06%(xy)p 12. 44% /11 .73 % 2 5. 37% /2 6. 23%

x

min

11. 78% /11 .88 % 2 7. 82% /2 7. 62%y 10. 97% /10 .96 % 2 7. 99% /2 8. 55%p 9.00%/8.95% 20.13%/20.22%v 4. 42% /50 .46 % 2 1. 11% /5 0. 46%xy 9.82%/9.88% 22.91%/23. 30%xy 11. 29% /11 .27 % 2 6. 35% /2 5. 93%pv 2. 13% /52 .01 % 1 0. 64% /5 2. 01%

pv 9.49%/9.41% 19.31%/19. 44%(xy)p 8.67%/8.64% 17.02%/17.13%(xy)p 10. 47% /10 .49 % 2 0. 13% /1 9. 75%

DTW distance

paverage

13. 75% /13 .89 % 3 8. 13% /3 8. 89%v 14. 08% /14 .04 % 3 3. 06% /3 3. 18%

pmax

13. 91% /14 .04 % 3 0. 44% /3 0. 86%v 14. 57% /14 .66 % 2 9. 95% /3 0. 09%

pmin

8 . 67% /62 .19 % 4 9. 75% /6 2. 04%v 6. 87% /74 .54 % 2 5. 86% /7 4. 54%

TABLE I . FA R/ FRR VALUES

ID FAR FRR

4 3.76 3.70

5 3.44 3.867 6.87 7.251 7.69 7.56KS 7.86 8.026 8.02 8.339 11.27 11.11

TABLE II. RESULTS (FAR A ND F RR VALUES) O FS IG COMP 2011DUTCH ONLINE COMPETITION

IV. RESULTS

Table I lists the false acceptance and false rejection rates(FAR/FRR) on the Dutch dataset ofSigComp2011 based onthe proposed method. The rows show which feature (x, y

coordinates, pressure p or velocity v ) and which distance wasused (average, maximum, minimum). The columns show twoscenarios. In scenario I the duration constraint was used (line11 in Algorithm 1), while in scenario II this constraint wasnot applied. In addition we tested two scenarios (with andwithout time constraints): in those we excluded the referencesignature which differed the most from the other referencesignatures, so it was not used during the decision process here.These experiments that negligibly worsened both the accuracyand equal error rates (by approximately0.5 1.0%) producedresults which were not included here.

For comparison purposes, the Dynamic Time Warping(DTW) distance for pressure and velocity features is includedin Table I. Moreover, Table II shows the results of thecompeting systems submitted to the Signature VerificationCompetition in 2011 [10]. Values in bolds indicate the lowestFAR/FRR rates in that section of the table. Also, the differentcombination of constraints are compared when the same type

of statistic is used for comparison (maximum, minimum andaverage distances are compared both on the reference signa-tures and between the references and each questioned). Valuesin italics indicate the lowest FAR/FRR rates when only singlefeatures are considered.

It is evident that the classification scheme based on theKS-distance performed better than the others based on DTWhave a performance comparable to the systems submitted to theSigComp2011 competition. We observe if the time constraintis applied (column with labelwith time constraint), the equalerror rates are roughly less than 13%. If the time constraint isnot applied, the error rates increases by 10 20%.

For almost all constraints the best results were achievedwith a minimum distance. In this case the reference distance

was the minimum distance between the reference signaturesand it was compared with the minimum distance of the ques-tioned signature and the reference signatures. If we comparethe performance of the different single features, we see thesmallest error rates appear in the rows which belongs tothe pressure feature . The minimum KS-distance gives goodresults when the coordinate constraints and pressure are usedtogether (rowx yp) otherwise (in the case of average andmaximum) the constraint for pressure and velocity together(row p v ) gives the lowest equal error rates. Besides theminimum distance, the time constraint improved the resultssignificantly.

V. CONCLUSIONS

An online signature verification method based on simplestatististical test and time constraints was proposed and eval-uated. We tested the x, y coordinates, pressure, and velocityfeatures both separately and combined. The performance wasevaluated on an open Dutch dataset.

In the future we would like to combine the features ina more sophisticated way and apply averaging methods onthe reference signature distribution. We intend to evaluate themethod on different databases and investigate the stability ofthe features.

ACKNOWLEDGMENT

This work was supported by the MTA-SZTE Research

Group on Artificial Intelligence.

REFERENCES

[1] R. Plamondon and G. Lorette, Automatic signature verification andwriter identification - the state of the art, Pattern Recognition, vol. 22,no. 2, pp. 107131, 1989.

[2] F. Leclerc and R. Plamondon, Automatic signature verification: Thestate of the art - 1989-1993, IJPRAI, vol. 8, no. 3, pp. 643660, 1994.

[3] R. Plamondon and S. N. Srihari, On-line and off-line handwritingrecognition: A comprehensive survey,IEEE Trans. Pattern Anal. Mach.

Intell., vol. 22, no. 1, pp. 6384, 2000.

741


5/5

[4] D. Impedovo and G. Pirlo, Automatic signature verification: Thestate of the art, Trans. Sys. Man Cyber Part C, vol. 38, no. 5,pp. 609635, Sep. 2008. [Online]. Available: http://dx.doi.org/10.1109/TSMCC.2008.923866

[5] A. Sanmorino and S. Yazid, A survey for handwritten signatureverification, in 2012 2nd International Conference on Uncertainty

Reasoning and Knowledge Engineering (URKE), 2012, pp. 5457.

[6] Z. Zhang, K. Wang, and Y. Wang, A survey of on-line signature

verification, in Biometric Recognition, ser. Lecture Notes in ComputerScience, Z. Sun, J. Lai, X. Chen, and T. Tan, Eds. SpringerBerlin Heidelberg, 2011, vol. 7098, pp. 141149. [Online]. Available:http://dx.doi.org/10.1007/978-3-642- 25449-9 18

[7] I. El-Henawy, M. Rashad, O. Nomir, and K. Ahmed, Onlinesignature verification: State of the art, INTERNATIONAL JOURNALOF COMPUTERS & TECHNOLOGY, vol. 4, no. 2c, 2013. [Online].Available: http://cirworld.com/index.php/ijct/article/view/1172

[8] D.-Y. Yeung, H. Chang, Y. Xiong, S. George, R. Kashi, T. Matsumoto,and G. Rigoll, Svc2004: First international signature verificationcompetition, in Biometric Authentication, ser. Lecture Notes inComputer Science, D. Zhang and A. Jain, Eds. Springer BerlinHeidelberg, 2004, vol. 3072, pp. 1622. [Online]. Available:http://dx.doi.org/10.1007/978-3-540- 25948-0 3

[9] A. Kholmatov and B. Yanikoglu, Identity authentication usingimproved online signature verification method, Pattern Recognition

Letters, vol. 26, no. 15, pp. 2400 2408, 2005. [Online]. Available:

http://www.sciencedirect.com/science/article/pii/S0167865505001376[10] M. Liwicki, M. I. Malik, C. E. v. d. Heuvel, X. Chen, C. Berger,

R. Stoel, M. Blumenstein, and B. Found, Signature verificationcompetition for online and offline skilled forgeries (sigcomp2011),in Proceedings of the 2011 International Conference on Document

Analysis and Recognition, ser. ICDAR 11. Washington, DC, USA:IEEE Computer Society, 2011, pp. 14801484. [Online]. Available:http://dx.doi.org/10.1109/ICDAR.2011.294

[11] M. I. Malik, S. Ahmed, A. Dengel, and M. Liwicki, A signatureverification framework for digital pen applications, Document AnalysisSystems, IAPR International Workshop on, vol. 0, pp. 419423, 2012.

[12] A. Shastry, R. Burchfield, and S. Venkatesan, Dynamic signatureverification using embedded sensors, in Body Sensor Networks (BSN),2011 International Conference on, 2011, pp. 168173.

[13] N. Wada and S. Hangai, Online signature verification using grippingposition and power, in Intelligent Signal Processing and Communica-tion Systems, 2009. ISPACS 2009. International Symposium on, 2009,pp. 647650.

[14] H. Bunke, J. Csirik, Z. Gingl, and E. Griechisch, Online signatureverification method based on the acceleration signals of handwritingsamples, inProgress in Pattern Recognition, Image Analysis, ComputerVision, and Applications, CIARP. Springer, 2011, pp. 499506.

[15] M. Wirotius, J. Ramel, and N. Vincent, Improving DTW for onlinehandwritten signature verification, in Image Analysis and Recognition,ser. Lecture Notes in Computer Science, A. Campilho and M. Kamel,Eds. Springer Berlin Heidelberg, 2004, vol. 3212, pp. 786793.[Online]. Available: http://dx.doi.org/10.1007/978-3-540-30126- 4 95

[16] Z.-H. Quan and H.-w. Ji, Aligning and segmenting signatures at theircrucial points through DTW, in Advances in Intelligent Computing,ser. Lecture Notes in Computer Science, D.-S. Huang, X.-P. Zhang,and G.-B. Huang, Eds. Springer Berlin Heidelberg, 2005, vol. 3644,pp. 4958. [Online]. Available: http://dx.doi.org/10.1007/11538059 6

[17] D. Cho, Y. Bae, and I. Ko, The modified DTW method for on-line

automatic signature verification, in Network and Parallel Computing,ser. Lecture Notes in Computer Science, H. Jin, D. Reed, and W. Jiang,Eds. Springer Berlin Heidelberg, 2005, vol. 3779, pp. 335342.[Online]. Available: http://dx.doi.org/10.1007/11577188 48

[18] M. Faundez-Zanuy, On-line signature recognition based on vq-DTW, Pattern Recognition, vol. 40, no. 3, pp. 981 992, 2007.[Online]. Available: http://www.sciencedirect.com/science/article/pii/S0031320306002780

[19] J. Putz-Leszczynska and M. Kudelski, Hidden signature for DTWsignature verification in authorizing payment transactions, Journal ofTelecommunications and Information Technology, no. 4, pp. 5967,2010.

[20] L. Yang, B. Widjaja, and R. Prasad, Application of hiddenmarkov models for signature verification, Pattern Recognition,vol. 28, no. 2, pp. 161170, 1995. [Online]. Available: http://www.sciencedirect.com/science/article/pii/003132039400092Z

[21] R. Kashi, J. Hu, W. Nelson, and W. Turin, On-line handwrittensignature verification using hidden markov model features, in Doc-ument Analysis and Recognition, 1997., Proceedings of the Fourth

International Conference on , 1997, vol. 1, pp. 253257 vol.1.

[22] A. McCabe, Markov modelling of simple directional features foreffective and efficient handwriting verification, in Proceedings of the6th Pacific Rim international conference on Artificial intelligence , ser.PRICAI00. Berlin, Heidelberg: Springer-Verlag, 2000, pp. 801801.[Online]. Available: http://dl.acm.org/citation.cfm?id=1764967.1765080

[23] A. Humm, J. Hennebert, and R. Ingold, Hidden MarkovModels for Spoken Signature Verification, in Biometrics: Theory,

Applications, and Systems, 2007. BTAS 2007. First IEEE International

Conference on, September 2007, pp. 16, some of the filesbelow are copyrighted. They are provided for your convenience,yet you may dow nload them only i f you are entit led t odo so by your arrangements with the various publishers.[Online]. Available: http://www.hennebert.org/download/publications/btas-2007-hidden-markov-models-spoken-signature-verification.pdf

[24] A. Szklarzewski and M. Derlatka, On-line signature biometric systemwith employment of single-output multilayer perceptron, Biocybernet-ics and Biomedical Engineering, vol. Vol. 26, no 4, pp. 91102, 2006.

[25] M. Khalid, H. Mokayed, R. Yusof, and O. Ono, Online signatureverification with neural networks classifier and fuzzy inference, inThird Asia International Conference on Modelling Simulation, 2009.

AMS 09., 2009, pp. 236241.

[26] M. Alhaddad, D. Mohamad, and A. Ahsan, Online signature verifica-tion using probablistic modeling and neural network, in Engineeringand Technology (S-CET), 2012 Spring Congress on, 2012, pp. 15.

[27] J. Kour, M. Hanmandlu, and A. Ansari, Online signature verificationusing GA-SVM, in International Conference on Image InformationProcessing (ICIIP), 2011, pp. 14.

[28] M. Parodi, J. C. Gomez, and M. Liwicki, Online signature verificationbased on Legendre series representation: Robustness assessment ofdifferent feature combinations, in 13th International Conference onFrontiers in Handwriting Recognition (ICFHR), 2012, pp. 379384.

[29] J. Fierrez-Aguilar, N. Alonso-Hermira, G. Moreno-Marquez, andJ. Ortega-Garcia, An off-line signature verification system based onfusion of local and global information, in Biometric Authentication.

Springer, 2004, pp. 295306.[30] H. Srinivasan, S. N. Srihari, and M. J. Beal, Signature verification using

kolmogorov-smirnov statistic, in Proc. International GraphonomicsSociety Conference (IGS, 2005, pp. 152156.

742

online signature veriﬁcation based on kolmogorov-smirnov distribution distance

Documents