off-line signature verification based on grey level information using texture features

Pattern Recognition 44 (2011) 375–385

Contents lists available at ScienceDirect

Pattern Recognition

0031-32

doi:10.1

n Corr

E-m

(M.A. F

(J.B. Al

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

Off-line signature verification based on grey level informationusing texture features

J.F. Vargas b,n, M.A. Ferrer a, C.M. Travieso a, J.B. Alonso a

a Instituto para el desarrollo tecnologico y la Innovacion en Comunicaciones (IDeTIC), Universidad de Las Palmas de Gran Canaria, Tafira Campus 35017, Las Palmas, Spainb Electronic Engineering Department,(GEPAR),Universidad de Antioquia, Medellin, Colombia

a r t i c l e i n f o

Article history:

Received 7 April 2010

Received in revised form

11 June 2010

Accepted 29 July 2010

Keywords:

Off-line handwritten signature verification

Pattern recognition

Grey level information

Texture features

Co-occurrence matrix

Local binary pattern

LS-SVM

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

016/j.patcog.2010.07.028

esponding author. Tel.: +34 928 451269; fax

ail addresses: [email protected] (J.F. Varga

errer), [email protected] (C.M. Travieso)

onso).

a b s t r a c t

A method for conducting off-line handwritten signature verification is described. It works at the global

image level and measures the grey level variations in the image using statistical texture features. The

co-occurrence matrix and local binary pattern are analysed and used as features. This method begins

with a proposed background removal. A histogram is also processed to reduce the influence of different

writing ink pens used by signers. Genuine samples and random forgeries have been used to train an

SVM model and random and skilled forgeries have been used for testing it. Results are reasonable

according to the state-of-the-art and approaches that use the same two databases: MCYT-75 and GPDS-

100 Corpuses. The combination of the proposed features and those proposed by other authors, based on

geometric information, also promises improvements in performance.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

The security requirements of today’s society have placedbiometrics at the centre of an ongoing debate concerning its keyrole in a multitude of applications [1–3]. Biometrics measureindividuals’ unique physical or behavioural characteristics with theaim of recognising or authenticating identity. Common physicalbiometrics include fingerprints, hand or palm geometry, retina, iris,or facial characteristics. Behavioural characteristics include signa-ture, voice (which also has a physical component), keystrokepattern, and gait. Signature and voice technologies are examples ofthis class of biometrics and are the most developed [4].

The handwritten signature is recognised as one of the mostwidely accepted personal attributes for identity verification. Thissignature is a symbol of consent and authorisation, especially inthe credit card and bank checks environment, and has been anattractive target for fraud for a long time. There is a growingdemand for the processing of individual identification to be fasterand more accurate, and the design of an automatic signatureverification system is a real challenge. Plamondon and Srihari [5]noted that automatic signature verification systems occupy a very

ll rights reserved.

: +34 928 451243.

s), [email protected]

, [email protected]

specific niche among other automatic identification systems: ‘‘Onthe one hand, they differ from systems based on the possession ofsomething (key, card, etc.) or the knowledge of something(passwords, personal information, etc.), because they rely on aspecific, well learned gesture. On the other hand, they also differfrom systems based on the biometric properties of an individual(fingerprints, voice prints, retinal prints, etc.), because thesignature is still the most socially and legally accepted means ofpersonal identification.’’

A comparison of signature verification with other recognitiontechnologies (fingerprint, face, voice, retina, and iris scanning)reveals that signature verification has several advantages as anidentity verification mechanism. Firstly, signature analysis canonly be applied when the person is/was conscious and willing towrite in the usual manner, although it is possible that individualsmay be forced to submit the handwriting sample. To give acounter example, a fingerprint may also be used when the personis in an unconscious (e.g. drugged) state. Forging a signature isdeemed to be more difficult than forging a fingerprint, given theavailability of sophisticated analyses [6]. Unfortunately, signatureverification is a difficult discrimination problem since a hand-written signature is the result of a complex process depending onthe physical and psychological conditions of the signer, as well asthe conditions of the signing process [7]. The net result is that asignature is a strong variable entity and its verification, even forhuman experts, is not a trivial matter. The scientific challengesand the valuable applications of signature verification have

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J.F. Vargas et al. / Pattern Recognition 44 (2011) 375–385376

attracted many researchers from universities and the privatesector to signature verification. Undoubtedly, automatic signatureverification plays an important role in the set of biometrictechniques for personal verification [8,9].

In the present study, we focus on features based on grey levelinformation from images containing handwritten signatures,especially those providing information about ink distributionalong traces delineating the signature. Textural analysis meth-odologies are included for this purpose since they providerotation and luminance invariance.

The paper is organised as follows: Section 2 presents thebackground to off-line signature verification. Section 3 providesan overview of statistical texture analysis. Section 4 describes theapproach proposed. Section 5 presents details about the database.Section 6 is devoted to the classifiers. Section 7 presents theevaluation protocol and reports the experimental results. Thepaper ends with concluding remarks.

2. Background

There are two major methods of signature verification. Oneis an on-line method to measure sequential data, such ashandwriting speed and pen pressure, with a special device. Theother is an off-line method that uses an optical scanner to obtainhandwriting data written on paper. There are two mainapproaches for off-line signature verification: the static approachand pseudo-dynamic approach. The static one involves geometricmeasures of the signature while the pseudo-dynamic one triesto estimate dynamic information from the static image [10].On-line systems use special input devices such as tablets, whileoff-line approaches are much more difficult because the onlyavailable information is a static two-dimensional image obtainedby scanning pre-written signatures on a paper; the dynamicinformation of the pen-tip (stylus) movement such as pen-tipcoordinates, pressure, velocity, acceleration, and pen-up and pen-down can be captured by a tablet in real time but not by an imagescanner. The off-line method, therefore, needs to apply compleximage processing techniques to segments and analyse signatureshape for feature extraction [11]. Hence, on-line signatureverification is potentially more successful. Nevertheless, off-linesystems have a significant advantage in that they do not requireaccess to special processing devices when the signatures areproduced. In fact, if the accuracy of verification systems isstressed, the off-line method has much more practical applicationareas than that of the on-line one. Consequently, an increase inamount of research has studied feature-extraction methodologyfor off-line signature recognition and verification [12].

It is also true that the track of the pen shows a great deal ofvariability. No two genuine signatures are ever exactly the same.Actually, two identical signatures would constitute legal evidenceof forgery by tracing. The normal variability of signaturesconstitutes the greatest obstacle to be met in achieving automaticverification. Signatures vary in their complexity, duration, andvulnerability to forgery. Signers vary in their coordination andconsistency. Thus, the security of the system varies from user touser. A short, common name is no doubt easier to forge than along, carefully written name, no matter what technique isemployed. Therefore, a system must be capable of ‘‘degrading’’gracefully when supplied with inconsistent signatures, and thesecurity risks must be kept to acceptable levels [13].

Problems of signature verification are addressed by taking intoaccount three different types of forgeries: random forgeries,produced without knowing either the name of the signer nor theshape of its signature; simple forgeries, produced knowing thename of the signer but without having an example of his

signature; and skilled forgeries, produced by people who, afterstudying an original instance of the signature, attempt to imitateit as closely as possible. Clearly, the problem of signatureverification becomes more and more difficult when passing fromrandom to simple and skilled forgeries, the latter being so difficulta task that even human beings make errors in several cases.Indeed, exercises in imitating a signature often allow us toproduce forgeries so similar to the originals that discrimination ispractically impossible; in many cases, the distinction is compli-cated even more by the large variability introduced by somesigners when writing their own signatures [14]. For instance,studies on signature shape found that North American signaturesare typically more stylistic in contrast to the highly personalisedand ‘‘variable in shape’’ European ones [15].

2.1. Off-line signature verification based on pseudo-dynamic

features

Dynamic information cannot be derived directly from staticsignature images. Instead, some features can be derived thatpartly represent dynamic information. These special character-istics are referred to as pseudo-dynamic information. The term‘‘pseudo-dynamic’’ is used to distinguish real dynamic data,recorded during the writing process, from information, whichcan be reconstructed from the static image [15].

There are different approaches to the reconstruction ofdynamic information from static handwriting records. Techniquesfrom the field of forensic document examination are mainly basedon the microscopic inspection of the writing trace and assump-tions about the underlying writing process [16]. Another paperfrom the same author [17] describes their studies on the influenceof physical and bio-mechanical processes on the ink trace andaims at providing a solid foundation for enhanced signatureanalysis procedures. Simulated human handwriting movementsare considered by means of a writing robot to study therelationship between writing process characteristics and inkdeposit on paper. Approaches from the field of image processingand pattern recognition can be divided into: methods forestimating the temporal order of stroke production [18,19];methods inspired by motor control theory, which recovertemporal features on the basis of stroke geometries such ascurvature [20]; and finally, methods analysing stroke thicknessand/or stroke intensity variations [21–25]. An analysis of mainlygrey level distribution, in accordance with methods of the lastgroup, is reported in this paper. A grey level image of a scannedhandwritten signature indicates that some pixels may representshapes written with high pressure, which appear as darker zones.High pressure points (HPPs) can be defined as those signaturepixels which have grey level values greater than a suitablethreshold. The study of high pressure features was proposed byAmmar et al. [21] to indicate regions where more physical effortwas made by the signer. This idea of calculating a threshold tofind the HPP was adopted and developed by others researchers[26,14]. Lv et al. [27] set two thresholds to store only theforeground points and edge points. They analyse only theremaining points whose grey level value is between the twothresholds and divide them into 12 segments. The percentage ofthe points whose grey level value falls in the correspondingsegment is one of the values of the feature vector that reflects thegrey level distribution. Lv and co-workers also consider strokewidth distribution. In order to analyse not only HPPs but also lowpressure points (LPP) a complementary threshold has beenproposed by Mitra et al. [28]. In a previous work, we use a radialand angular partition (RAP) for a local analysis to determine theratio, over each cell, between HPPs and all points conforming the

J.F. Vargas et al. / Pattern Recognition 44 (2011) 375–385 377

binary version of the image [29]. Franke [30] evaluates ink-tracecharacteristics that are affected by the interaction of bio-mechanical writing and physical ink-deposition processes. Theanalysis focused on the ink intensity, which is captured alongthe entire writing trace of a signature. The adaptive segmentationof ink-intensity distributions takes the influences of differentwriting instruments into account and supports the cross-valida-tion of different pen probes. In this way, texture analysis of inktrace appears as an interesting approach to characterise personalwriting for enhanced handwritten signature verification procedures.

3. Statistical texture analysis

Statistical texture analysis requires the computation of texturefeatures from the statistical distribution of observed combina-tions of intensities at specified positions relative to each otherin an image. The number of intensity points (pixels) in eachcombination is identified, leading to the classification of thetexture statistics as first-order, second-order, or higher-order.

Biometric systems based on signature verification, in conjunc-tion with textural analysis, can reveal information about ink-pixels distribution, which reflects personal characteristics fromthe signer, i.e. pen-holding, writing speed, and pressure.

But we do not think that only ink distribution information issufficient for signer identification. So, in the specific case ofsignature strokes, we have also taken into account, for the texturalanalysis, the pixels in the stroke contour. By this we mean thosestroke pixels that are in the signature-background border. Thesepixels will include statistical information about the signatureshape. So this distribution data may be considered as acombination of textural and shape information.

3.1. Statistical features of first order

Statistical features of first order, as represented in a histogram,take into account the individual grey level value of each pixel inan image Iðx,yÞ,1rxrN,1ryrM, but the spatial arrangement isnot considered, i.e. different spatial features can have the samelevel histogram. A classical way of parameterising the histogramis to measure its average and standard deviation.

Obviously, the discriminative ability of first order statistics isreally low for automatic signature verification, especially whenuser and forger use a similar writing instrument. In fact, mostresearchers normalise the histogram, so as to reduce the noise forthe subsequent processing of the signature.

3.2. Grey level co-occurrence matrices

The grey level co-occurrence matrix (GLCM) method is a wayof extracting second order statistical texture features from theimage [31]. This approach has been used in a number ofapplications, including ink type analysis [16], e.g. [32–34].

A GLCM of an image I(x,y) is a matrix Pði,jDx,DyÞ,0r irG�1,0r jrG�1, where the number of rows and columns are equal tothe number of grey levels G. The matrix element P(i, j9Dx, Dy) is therelative frequency with which two pixels with grey levels i and j

occur separated by a pixel distance (Dx, Dy). For simplicity, in the restof the paper, we will denote the GLCM matrix as P(i, j).

For a statistically reliable estimation of the relative frequencywe need a sufficiently large number of occurrences for each event.The reliability of P(i, j) depends on the grey level number G andthe I(x, y) image size. In the case of images containing signatures,instead of image size, this depends on the number of pixels in thesignature strokes. If the statistical reliability is not sufficient, we

need to reduce G to guarantee the minimum number of pixelstransitions per P(i, j) matrix component, despite losing texturedescription accuracy. The grey level number G can be reducedeasily by quantifying the image I(x, y).

The classical feature measures extracted from the GLCMmatrix (see Haralick [32] and Conners and Harlow [31]) are thefollowing:

Texture homogeneity H:

H¼XG�1

i ¼ 0

XG�1

j ¼ 0

fPði,jÞg2 ð1Þ

A homogeneous scene will contain only a few grey levels,giving a GLCM with only a few but relatively high values of P(i, j).Thus, the sum of squares will be high.

Texture contrast C:

C ¼XG�1

n ¼ 0

n2XG�1

i ¼ 0

XG�1

j ¼ 0

Pði,jÞ

8<:

9=;, 9i�j9¼ n ð2Þ

This measure of local intensity variation will favour contribu-tions from P(i, j) away from the diagonal, i.e ia j.

Texture entropy E:

E¼XG�1

i ¼ 0

XG�1

j ¼ 0

Pði,jÞlogfPði,jÞg ð3Þ

Non-homogeneous scenes have low first order entropy, while ahomogeneous scene reveals high entropy.

Texture correlation O:

O¼XG�1

i ¼ 0

XG�1

j ¼ 0

ijPði,jÞ�ðmimjÞ

sisjð4Þ

where mi and si are the mean and standard deviation of P(i, j)rows, and mj and sj the mean and standard deviation of P(i, j)columns, respectively.

Correlation is a measure of grey level linear dependencebetween pixels at the specified positions relative to each other.

3.3. Local binary patterns

The local binary pattern (LBP) operator is defined as a greylevel invariant texture measure, derived from a general definitionof texture in a local neighbourhood, the centre of which is thepixel (x, y). Recent extensions of the LBP operator have shown it tobe a really powerful measure of image texture, producingexcellent results in many empirical studies. LBP has been appliedin biometrics to the specific problem of face recognition [35,36].

The LBP operator can be seen as a unifying approach to thetraditionally divergent statistical and structural models of textureanalysis. Perhaps the most important property of the LBP operatorin real-world applications is its invariance to monotonic grey levelchanges. Equally important is its computational simplicity, whichmakes it possible to analyse images in challenging real-timesettings [37].

The local binary pattern operator describes the surroundingsof the pixel (x, y) by generating a bit-code from the binaryderivatives of a pixel as a complementary measure for local imagecontrast. The original LBP operator takes the eight neighbouringpixels using the centre grey level value I(x, y) as a threshold. Theoperator generates a binary code 1 if the neighbour is greater thanor equal to the central level, otherwise it generates a binary code0. The eight neighbouring binary codes can be represented by an8-bit number. The LBP operator outputs for all the pixels in theimage can be accumulated to form a histogram, which representsa measure of the image texture. Fig. 1 shows an example of a LBPoperator.


The above LBP operator is extended in [38] to a generalisedgrey level and rotation invariant operator. The generalised LBPoperator is derived on the basis of a circularly symmetricneighbour set of P members on a circle of radius R. The parameterP controls the quantisation of the angular space and R determinesthe spatial resolution of the operator. The LBP code of central pixel(x, y) with P neighbours and radius R is defined as

LPBP,Rðx,yÞ ¼XP�1

p ¼ 0

sðgp�gcÞ2p

ð5Þ

where sðlÞ ¼1 lZ0

0 lo0,

(the unit step function, gc the grey level

value of the central pixel: gc¼ I(x, y), and gp the grey level of thepth neighbour, defined as

gp ¼ I xþRsin2pp

P,y�Rcos

2pp

P

� �ð6Þ

If the pth neighbour does not fall exactly in the pixel position,its grey level is estimated by interpolation. An example can beseen in Fig. 2.

In a further step, [38] defines a LBPP,R operator invariant torotation as follows:

LBPriu2P,R ðx,yÞ ¼

XP�1

p ¼ 0

sðgp�gcÞ if Uðx,yÞr2

Pþ1 otherwise

8>><>>: ð7Þ

where

Uðx,yÞ ¼XP

p ¼ 1

sðgp�gcÞ�sðgp�1�gcÞ�� , with gP ¼ g0 ð8Þ

Analysing the above equations, U(x, y) can be calculated asfollows:

(1)

Fig.code

Fig.LPB4

is ob

com

gp ¼ 7

work out the function f ðpÞ ¼ sðgp�gcÞ,0opoP consideringgP¼g0;

(2)
obtain its derivate: f ðpÞ�f ðp�1Þ,1rprP;
1. Working out the LBP code of pixel (x, y). In this case I(x, y)¼3, and its LBP

is LBP(x, y)¼143.

2. The surroundings of I(x, y) central pixel are displayed along with the pth neighbo

,1(x, y) code is obtained by comparing gc¼ I(x, y) with gp¼0¼ I(x, y�1), gp¼1¼ I(x+1, y

tained by comparing gc¼ I(x, y) with gp¼0¼ I(x, y�2), gp¼1¼ I(x+2, y), gp¼2¼ I(x, y+

paring gc¼ I(x, y) with gp¼0¼ I(x, y�2), gp ¼ 1 ¼ Iðxþffiffiffi2p

,y�ffiffiffi2pÞ, gp¼2¼ I(x+2, y), gp ¼

¼ Iðx�ffiffiffi2p

,y�ffiffiffi2pÞ.

(3)

urs, m

), gp

2), a

3 ¼

Fig.{g0,

U(x,

g0 ,g�y)¼

leve

inten

calculate the absolute value: 9f ðpÞ�f ðp�1Þ9,1rprP; andP
(4) obtain U(x, y) as the integration or sum P
P ¼ 1 9f ðpÞ�f ðp�1Þ9.

If the grey levels of the pixel (x, y) neighbours are uniform orsmooth, as in the case of Fig. 3, left, f(p) will be a sequence of ‘‘0’’or ‘‘1’’ with only two transitions. In this case U(x, y) will be zero or

two and the LBPriu2P,R code is worked out as the sum

PP�1p ¼ 0 f ðpÞ.

Conversely, if the surrounding grey levels of pixel (x, y) varyquickly, as in the case of Fig. 3, right, f(p) will be a sequencecontaining several transitions ‘‘0’’–‘‘1’’ or ‘‘1’’–‘‘0’’ and U(x, y) willbe greater than 2. So, in the noisy case, a constant value equal to

P+1 is assigned to LBPriu2P,R making it more robust to noise than

previously defined LBP operators.The rotation invariance property is guaranteed because when

summing the f(p) sequence to obtain the LBPriu2P,R , it is not weighted

by 2p. As f(p) is a sequence of 0 and 1, 0rLBPriu2P,R ðx,yÞrPþ1. As

textural measure, we will use its P+2 histogram bins of LBPriu2P,R ðx,yÞ

codes.From the three LBP codes proposed in this section, LBP, LBPP,R,

and LBPriu2P,R , we will use LBPriu2

P,R in this paper, because of itsproperty of rotational invariance.

4. Textural analysis for signature verification

The analysis of the writing trace in signatures becomes anapplication area of textural analysis. The textural features fromthe grey level image can reveal personal characteristics of thesigner (i.e. pressure and speed changes, pen-holding, etc.)complementing classical features proposed in the literature. Inthis section we describe a basic scheme for using textural analysisin automatic signature verification.

arked with black circles, for different P and R values. Left: P¼4, R¼1, and the

¼2¼ I(x, y+1), and gp¼3¼ I(x�1, y). Centre: P¼4, R¼2, and the LPB4,2(x, y) code

nd gp¼3¼ I(x�2, y). Right: P¼8, R¼2, and the LPB8,2(x, y) code is obtained by

Iðxþffiffiffi2p

,yþffiffiffi2pÞ, gp¼4¼ I(x, y+2), gp ¼ 5 ¼ Iðx�

ffiffiffi2p

,yþffiffiffi2pÞ, gp¼6¼ I(x�2, y), and

3. Calculating the LBPriu2P,R code for two cases, with P¼4 and R¼2. Left: gc¼152,

g1, g2, g3}¼{154, 156, 155, 149}, {f(0), f(1), f(2), f(3), f(4)}¼{1, 1, 1, 0, 1}, and

y)¼0+0+1+1¼2r2, therefore LBPriu2P,R ðx,yÞ ¼ 1þ1þ1þ0¼ 3. Right: gc¼154,

1 ,g2 ,g3

�¼ 155,152,159,148f g, {f(0) ,f(1) ,f(2) ,f(3) ,f(4)}¼{1 ,0, 1, 0, 1}, U(x,

1+1+1+1¼4Z2, and LBPriu2P,R ðx,yÞ ¼ Pþ1¼ 5. (a) Smooth and uniform grey

l change and (b) noisy grey level surroundings. The numbers and the shade

sity represent the grey levels


4.1. Background removal

The features used in our system characterise the grey leveldistribution in an image signature but also require a procedure forbackground elimination. Grey levels corresponding to the back-ground are not discriminating information but adding noise cannegatively affect the characterisation.

In this work, we have used a simple posterisation procedure toavoid background influence. Obviously, any other efficientsegmentation procedure would also be useful. Posterisationoccurs when an image apparent bit depth has been decreasedso much that it has a visual impact. The term ‘‘posterisation’’ isused because it can influence the image in a similar way to thecolour range in a mass-produced poster, where the print processuses a limited number of coloured inks.

Let I(x, y) be a 256-level grey scale image and nL+1 the numberof grey levels considered for posterisation. The posterised imageIP(x, y) is defined as follows:

IPðx,yÞ ¼ round roundIðx,yÞnL

255

� �255

nL

� �ð9Þ

where round(U) rounds the elements to the nearest integers. Theinterior round performs the posterisation operation, and the exteriorround guarantees that the resulting grey level of IP(x, y) is an integer.

In the results presented in this paper, with MCYT and GPDSCorpuses, we have used a value of nL¼3 obtaining a 4-grey levelposterised image, the grey levels being 0, 85, 170, and 255.Perceptually, valid values can be nL¼3 or 4. With values ofnL ¼ 1 or 2 the signature is half erased and this is not a validsegmentation. With a value of nL¼3 the signature strokes are wellpreserved and the background appears nearly clean. With valuesof nL43, mainly in the MCYT Corpus, more and more salt andpepper noise appears in the background. In order to avoidposterior image processing and eliminate the salt and peppernoise, a value of nL¼3 was selected.

The images from both corpuses consist of dark strokes against awhite background. In the posterised image the background appearswhite (grey level equal to 255) and the signature strokes appeardarker (grey levels equal to 0, 85, or 170). Therefore, to obtain theIbw(x, y) binarised signature (black strokes and white background)we apply a simple thresholding operation, as follows:

Ibwðx,yÞ ¼255 if IPðx,yÞ ¼ 255

0 otherwise

�ð10Þ

The black and white Ibw(x, y) image is used as a mask tosegment the original signature and the segmented signature isobtained as

ISðx,yÞ ¼255 if Ibwðx,yÞ ¼ 255

Iðx,yÞ otherwise

(ð11Þ

Fig. 4. Posterisation procedure: (a) original image I(x, y) with 256 grey levels, (b) post

segmented image Is(x, y): original signature with the background converted to white (

At this point, a complete segmentation between backgroundand foreground is achieved. An example of the above describedprocedure can be seen in Fig. 4.

4.2. Histogram displacement

This section is aimed at reducing the influence of the differentwriting ink pens on the segmented signature. We achieve this bydisplacing the histogram of the signature pixels toward zero,keeping the background white with grey level equal to 255.Assuring that the grey level value of the darkest signature pixel isalways 0, the dynamic range will reflect features only of thewriting style. This can be carried out by subtracting the minimumgrey level value in the image from the signature pixels, as follows:

IGðx,yÞ ¼ISðx,yÞ if ISðx,yÞ ¼ 255

ISðx,yÞ�minfISðx,yÞg otherwise

(ð12Þ

where IG(x, y) is the segmented image histogram displaced towardzero. Fig. 5 illustrates the effect of this displacement.

4.3. Feature extraction

After the segmentation and signature histogram displacement,the image is cropped to fix the signature size and it is resized toN¼512 and M¼512. The aim of these adjustments is to improvethe scale invariance. As an interpolation method, we use thenearest neighbour. This is in order to keep the ink texture asinvariant as possible.

4.3.1. GLCM features

To calculate GLCM features, we have to assume the statisticsignificance of the Pði,j9Dx,DyÞ,0r i,jrG�1 GLCM matrix estima-tion. If we follow the rule of 3 [39], which supposes anindependent, identical distribution, a 1% estimation error with a95% of confidence limit will require at least 300 samples percomponent. As P(i, j) contains G2 components, the number of pixeltransitions that we will need for a reliable estimation of all theP(i, j) components will be 300 �G2.

The number of signature pixels for each signature in our databaseshas been worked out in its histogram, depicted in Fig. 6. To guaranteestatistical significance at the 98% level for the signatures in thedatabases, we work out the 2nd percentile that corresponds to 23,155pixels. Then, the number of grey levels should be

23,1554300 G2-Goffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi23,155=300

p¼ 8:78 ð13Þ

We need to take into account that the number of grey levels G

is an integer. So, in order to obtain a reliable estimation of theGLCM matrix, the signature images will be quantified to G¼8 greylevels to calculate the P(i, j) matrix, despite losing textureresolution. Experiments with 16 and 32 grey levels have also

erised image IP(x, y) with nL¼3: 4 grey levels, (c) binarised image Ibwðx,yÞ, and (d)

grey level equal to 255).

Fig. 5. Histogram preprocessing. Upper: histogram and signature detail of image IS(x, y), lower: histogram and signature detail of IG(x, y), which is darker than IS(x, y). Note

that IS(x, y) histogram finishes abruptly at grey level 213 because of the posterisation process with nL¼3: as roundð212nL=255Þ ¼ 2, pixels with grey level 212 remain within

the signature stroke, and as roundð213nL=255Þ ¼ 3, pixels with grey level 213 go to the background.

Fig. 6. Number of signature pixel histograms for both databases considered in this

paper.


been performed and the resulting final equal error rate hasconfirmed that it is preferable to have a reliable GLCM matrixestimation than to increase the texture resolution. The quantifiedimage IQ(x, y) is obtained from IG(x, y) as follows:

IQ ðx,yÞ ¼ round fixIGðx,yÞG

255

� �255

G

� �ð14Þ

where fix rounds toward zero, and the exterior round is toguarantee integer grey levels in the IQ(x, y) image.

Once the signature image with G¼8 grey levels has beenquantified, four GLCM matrices of size G� G¼ 8� 8¼ 64 areworked out: P1 ¼ Pði,j9Dx ¼ 1,Dy ¼ 0Þ, P2 ¼ Pði,j9Dx ¼ 1,Dy ¼ 1Þ,P3 ¼ Pði,j9Dx ¼ 0,Dy ¼ 1Þ, and P4 ¼ Pði,j9Dx ¼�1,Dy ¼ 1Þ. TheseGLCM matrices correspond to joint probability matrices thatrelate the grey level of the central pixel (x, y) with the pixel on its

right (x+1, y), right and above (x+1, y+1), above (x, y+1), and leftand above (x�1, y+1). We do not need to work out more GLCM

matrices because, for instance, the relation of pixel (x, y) withpixel (x�1, y�1) is taken into account when the central pixel is at(x�1, y�1).

The textural measures obtained for each GLCM matrix are thefollowing: homogeneity, contrast, entropy, and correlation, all ofwhich are defined in Section 3. So we have 16 textural measures(4 measures of 4 different matrices) to calculate. These arereduced to 8, following the suggestion of Haralick [32].

Suppose that Hi,Ci,Ei, and Oi are the homogeneity, contrast,entropy, and correlation textural measures, respectively, ofPi,1r ir4. We define the 4-element vector M containing theaverage of each textural measure as

M¼ mean1r ir4

Hi, mean1r ir4

Ci, mean1r ir4

Ei, mean1r ir4

Oi

� ð15Þ

where the ‘‘mean’’ of the vector is

mean1r ir4

Hi ¼1

4

X4

i ¼ 1

Hi ð16Þ

and the four-component vector R, containing the range of eachtextural measure, is

R¼ range1r ir4

Hi, range1r ir4

Ci, range1r ir4

Ei, range1r ir4

Oi

( )ð17Þ

where the ‘‘range’’ is the difference between the maximum andthe minimum values, i.e.

range1r ir4

Hi ¼ max1r ir4

Hi� min1r ir4

Hi ð18Þ

The eight-components feature vector is obtained by concate-nating the M and R vectors:

GLCM Feature Vector¼ fM,Rg ð19Þ


4.3.2. LBP features

To extract the feature set of the signature image IG(x, y) basedon LBP, we have chosen the rotation invariant operator LBPriu2

P,R

defined in Section 3. We have studied two cases. For the first casewe consider P¼8 and R¼1, which obtain the LBPriu2

8,1 ðx,yÞ code,thresholding each pixel with the 8 neighbouring pixels. Theproposed feature vector is the normalized histogram ofLBPriu2

8,1 ðx,yÞ. As 0rLBPriu28,1 ðx,yÞrPþ1¼ 9, the histogram is calcu-

lated with 10 bins as follows:

hisLBP8,1ðx,yÞðlÞ ¼#nðx,yÞ LBPriu2

8,1 ðx,yÞ ¼ l�� o 1rxrN¼ 512

1ryrM¼ 512

0r lrPþ1¼ 9

ð20Þ

where # means ‘‘number of times’’. The normalized histogram isobtained from

hisLBP8,1Feature VectorðlÞ ¼

hisLBP8,1ðx,yÞðlÞPPþ1l ¼ 0 hisLBP8,1ðx,yÞðlÞ

, 0r lrPþ1¼ 9

ð21Þ

For the second case analysed, the feature vector is obtained

from the rotation invariant LBPriu2P,R code with P¼16 and R¼2. In

this case LBPriu216,2ðx,yÞ, we consider the second ring around the (x, y)

pixel. As 0rLBPriu216,2ðx,yÞrPþ1¼ 17, the normalized histogram

will contain 18 bins, and the feature vector will be

LBPriu216,2 Feature Vector ðlÞ ¼

hisLBP16,2ðx,yÞðlÞPPþ1l ¼ 0 hisLBP16,2ðx,yÞðlÞ

, 0r lrPþ1¼ 17

ð22Þ

It should be noted that by including the pixels in the border ofthe signature in the GLCM and LBPriu2

P,R matrices, both matrices willinclude a statistical measure of the signature shape. This meanshow many pixels in the signature border are oriented north, northwest, etc. This results from the background having a grey levelequal to 255 (224 in the case of GLCM because of the quantisationwith G¼8).

5. Database

We have used two databases for testing the proposed greylevel based features. Both have been scanned at 600 dpi, whichguarantees a sufficient grey texture representation. The maindifferences between them are the pens used. In the MCYTdatabase all the signers, genuine, and forger are signed with thesame pen on the same surface. Instead, in the GPDS database, allthe users signed with their own pens on different surfaces. So,similar results with both databases will point to a measure of inkindependence of the proposed features.

5.1. GPDS-100 Corpus

The GPDS-100 signature corpus contains 24 genuine signa-tures and 24 forgeries of 100 individuals [25], producing100�24¼2400 genuine signatures and the same for forgeries.The genuine signatures were taken in just one session to avoidscheduling difficulties. The repetitions of each genuine signatureand forgery specimen were collected using each participant’s ownpen on white A4 sheets of paper, featuring two different box sizes:the first box is 5 cm wide and 1.8 cm high and the second box is4.5 cm wide and 2.5 cm high. Half of the genuine and forgedspecimens were written in each size of box. The forgeries werecollected on a form with 15 boxes. Each forger form shows 5images of different genuine signatures chosen randomly. Theforger imitated each one 3 times for all 5 signatures. Forgers weregiven unlimited time to learn the signatures and perform the

forgeries. The complete signing process was supervised by anoperator.

Once the signature forms were collected, each form wasscanned with a Canon device using 256-level grey scale and600 dpi resolution. All the signature images were saved in PNGformat.

5.2. MCYT Corpus

The off-line subcorpus of the MCYT signature database [10]was used. The whole corpus comprises fingerprint and on-linesignature data for 330 contributors from 4 different Spanish sites.Skilled forgeries are also available in the case of signature data.Forgers are given the signature images of clients to be forged and,after training, they are asked to imitate the shape. Signature datawere always acquired with the same ink pen and paper templatesover a pen tablet. Therefore, signature images are also availableon paper. Paper templates of 75 signers (and their associatedskilled forgeries) have been digitised with a scanner at 600 dpi.The resulting off-line subcorpus has 2250 images of signatures,with 15 genuine signatures and 15 forgeries per user. Thissignature corpus is publicly available at http://atvs.ii.uam.es.

6. Classification

Once the feature matrix is estimated, we need to solve a two-class classification (genuine or forgery) problem. A brief descrip-tion of the classification technique used in the verification stagefollows.

6.1. Least squares support vector machines

To model each signature, a least squares support vectorMachine (LS-SVM) has been used. SVMs have been introducedwithin the context of statistical learning theory and structural riskminimisation. Least squares support vector machines (LS-SVM)are reformulations to standard SVMs, which lead to solvingindefinite linear (KKT) systems. Robustness, sparseness, andweightings can be imposed on LS-SVMs where needed and aBayesian framework with three levels of inference has beendeveloped [40] for this purpose.

Only one linear equation has to be solved in the optimizationprocess, which not only simplifies the process, but also avoids theproblem of local minima in SVM. The LS-SVM model is defined inits primal weight space by

yðxÞ ¼xTjðxÞþb ð23Þ

where j(x) is a function that maps the input space into a higherdimensional feature space, x is the M-dimensional vector, and xand b the parameters of the model. Given N input–output learningpairs ðxi,yiÞARMxR,1r irN, least squares support vector ma-chines seek the x and b that minimize

minx,b,e

Jðo,eÞ ¼1

2xTxþg1

2

XN

i ¼ 1

e2i ð24Þ

subject to

yi ¼xTjðxiÞþbþei, 1r irN ð25Þ

In our case we use as j(x) mapping function a Gaussian RBFkernel. The meta parameters of the LS-SVM model are the width C

of the Gaussian and the g regularisation factor. The trainingmethod for the estimation of x and b can be found in [40]. In thiswork, the meta parameters (g, C) were established using a gridsearch. The LS-SVM trained for each signer uses the same (g, C)

http://atvs.ii.uam.es

Table 2

Results using LBPriu28,1 þLBPriu2

16,2. Tested with random forgeries.


meta parameters; further details about model construction aregiven in the next section.

Training Data set FAR (%) FRR (%) EER (%) FAR (s) FRR (s)

5 samples MCYT 0.75 26.40 3.81 0.74 9.22

GPDS-100 0.36 26.64 4.59 0.40 8.40

10 samples MCYT 1.52 15.23 2.38 0.82 9.32

GPDS-100 0.73 14.29 2.41 0.50 6.52

Table 3


16,2. Tested with skilled forgeries.


5 samples MCYT 5.00 24.56 12.82 3.79 9.70

GPDS-100 6.17 22.49 13.38 3.90 8.29

10 samples MCYT 9.84 13.20 10.68 3.70 8.65

GPDS-100 10.05 11.36 10.53 3.76 5.77

Table 4Results using GLCM based features. Tested with random forgeries.


5 samples MCYT 3.12 32.76 6.65 2.19 7.49

GPDS-100 0.46 37.39 6.40 0.45 6.12

10 samples MCYT 5.68 21.39 6.68 1.73 8.48

GPDS-100 1.19 26.34 4.31 0.74 7.11

Table 5Results using GLCM based features. Tested with skilled forgeries.


5 samples MCYT 6.49 30.93 16.27 4.16 8.78

GPDS-100 2.91 35.07 17.12 2.34 7.29

10 samples MCYT 9.72 21.47 12.65 3.45 8.27

GPDS-100 4.92 24.61 12.18 2.54 7.24

Table 6


16,2þGLCM. Tested with random forgeries.


5 samples MCYT 0.86 24.21 3.64 0.76 9.77

GPDS-100 0.27 21.87 3.75 0.34 9.62

10 samples MCYT 1.53 12.00 2.20 0.83 8.16

GPDS-100 0.55 10.35 1.76 0.43 5.83

7. Evaluation protocol

7.1. Experiments

Each signer is modelled by a LS-SVM, which is trained with 5and 10 genuine samples so as to compare the performance of themodel with the number of training samples. These samples werechosen randomly. Random forgeries (genuine samples from othersigners) were used as negative samples, in a similar way to thatoutlined by [41], in our case taking a genuine sample of each oneof the other users of the database (74 for the case of the MCYTCorpus and 99 for the GPDS Corpus). Keeping in mind the limitednumber of samples in the training, leave-one-out cross-validation(LOOCV) was used to determine the parameters of the SVMclassifier with RBF kernel (g, C).

For testing, random and skilled forgeries were taken intoaccount. For random forgeries, we select a genuine sample of eachone of the other users of the database (different to the one usedfor training). For skilled forgeries, all available forgeries wereused; this is 15 for the MCYT Corpus and 24 for the GPDS Corpus.

Training and testing procedure was repeated 10 times withdifferent training and testing subsets for the purpose of obtainingreliable results. Two classical types of error were considered: TypeI error or false rejection rate (FRR), which is when an authenticsignature is rejected, and Type II error or false acceptance rate(FAR), which is when a forgery is accepted. Finally the equal errorrate (EER) was calculated, keeping in mind that the classes areunbalanced.

To calculate FAR and FRR we need to define a threshold. As theLS-SVM has been trained as a target value +1 for genuinesignature and �1 for forgeries, we have chosen an a priori

constant threshold equal to 0 for all the signers, i.e. if the LS-SVMreturns a value greater or equal than 0, the signature is acceptedas genuine. If the LS-SVM returns a value lesser than 0, thesignature is considered a forgery and consequently rejected.

7.2. Results

Experiments were carried out using different values for LBPriu2P,R

parameters R and P. First, values were set to R¼1 and P¼8. Thenthey were set to R¼2 and P¼16. Finally, a combination at featurelevel of both pairs was used. Table 1 shows results obtained using5 genuine samples for training and evaluating with skilledforgeries. As can be seen the best results were obtained usingthe combination LBPriu2

8,1 þLBPriu216,2. This makes sense, because the

new feature vector of length 10+18¼28 includes information onthe first and second pixels rings around the central pixel. Tables 2and 3 show more detailed information about results obtainedwith LBPriu2

8,1 þLBPriu216,2. Tables 4 and 5 present results for GLCM

characterisation.

Table 1

Results using LBPriu2P,R . Trained with 5 samples and tested with skilled forgeries.

LBPriu2P,R parameters Data set FAR (%) FRR (%) EER (%)

R¼1, P¼8 MCYT 3.35 30.72 14.30

R¼2, P¼16 MCYT 3.17 28.37 13.25

{R¼1, P¼8}+{R¼2, P¼16} MCYT 5.00 24.56 12.82

R¼1, P¼8 GPDS-10 3.90 32.51 16.54

R¼2, P¼16 GPDS-10 4.24 30.07 15.66

{R¼1, P¼8}+{R¼2, P¼16} GPDS-10 6.17 22.49 13.38

In order to study the system performance when using acombination of LBPriu2

8,1 þLBPriu216,2and GLCM parameters, a feature

level fusion was carried out to obtain a feature vector ofdimension 10+18+8, equal to 36. Tables 6 and 7 present theresults obtained for random and skilled forgeries, respectively. Itis easy to see that the EER decreases when combining thedifferent grey level based features. So it seems that LBPriu2

P,R andGLCM texture measures are uncorrelated, which is logical, becauseeach texture measure is based on a different principle: LBPriu2

P,R isbased on thresholding and GLCM is based on joint statistics.

As stated above, the quality of the texture based parameters isnot solely due to the discriminative ability of the texture toidentify writers. The texture parameters, as defined, also includeshape information when including pixels in the stroke border. To

Table 7


16,2þGLCM. Tested with skilled forgeries.


5 samples MCYT 4.53 23.25 12.02 3.55 9.26

GPDS-100 5.13 20.82 12.06 3.43 8.44

10 samples MCYT 7.53 12.61 8.80 3.96 9.66

GPDS-100 8.64 9.66 9.02 3.52 6.52

Table 8


16,2þGLCM with BW signatures. Tested with random

forgeries.


5 samples MCYT 0.57 26.44 3.65 0.58 9.42

GPDS-100 0.34 23.44 4.06 0.34 8.96

10 samples MCYT 1.25 13.79 2.04 0.70 9.32

GPDS-100 0.68 11.29 1.99 0.46 6.21

Table 9


16,2þGLCM whith BW signatures. Tested with skilled

forgeries.


5 samples MCYT 3.93 26.20 12.84 3.35 8.91

GPDS-100 4.68 23.88 13.17 3.27 8.91

10 samples MCYT 7.86 13.92 9.37 2.87 8.65

GPDS-100 9.00 11.03 9.75 3.75 6.46

Table 10Comparison of proposed approach with other published methods.

EER (%) Value scale

[42] 25.10 Grey

[43] 22.40/20.00a B/W

[44] 15.00 B/W

[10] 11.00/9.28a B/W

[45] 10.18/6.44a B/W

Approach proposed (LBP+GCLM) 12.02/8.80a Grey

a 5/10 genuine samples used for training.

Table 11Using contour-hinge parameters proposed in [45].

Algorithm EER

(%)

Reported in [45] with MCYT Corpus 10.18

Implemented here with a posteriori score normalization proposed in

[45] with MCYT Corpus

10.32

Implemented here without score normalization with MCYT Corpus 14.81

Implemented here without score normalization using GPDS Corpus 15.17

Table 12


16,2þcontour-hinge. Tested with random forgeries.


5 samples MCYT 0.01 26.47 3.16 0.02 7.59

GPDS-100 0.01 22.99 3.71 0.01 6.17

10 samples MCYT 0.04 8.45 0.57 0.03 6.28

GPDS-100 0.02 7.76 0.98 0.03 4.17

Table 14


16,2þGLCMþcontour-hinge. Tested with random forgeries.


5 samples MCYT 0.03 20.17 2.43 0.03 6.73

GPDS-100 0.01 18.26 2.95 0.02 5.52

10 samples MCYT 0.15 5.07 0.47 0.15 4.93

GPDS-100 0.06 5.56 0.74 0.06 3.05

Table 13Results using GLCM+contour-hinge. Tested with random forgeries.


5 samples MCYT 0.02 27.75 3.32 0.03 7.58

GPDS-100 0.00 23.29 3.75 0.01 5.44

10 samples MCYT 0.05 9.12 0.62 0.06 6.81

GPDS-100 0.02 8.42 1.06 0.04 4.02


verify such an hypothesis, we have converted the signatures toblack and white and worked out the LBP and GLCM matrices. Theresults are given in Tables 8 and 9. It can be seen that the resultsare just a little bit worse than those in Tables 6 and 7. Thisconfirms that the texture features contain shape information andthat the grey level data provide some information about thewriter.

A comparison of the performance of different signature verifica-tion systems is a difficult task since each author constructs his ownsignature data sets. The lack of a standard international signaturedatabase continues to be a major problem for performancecomparison. For the sake of completeness, in Table 10 we presentsome results obtained by published studies that used the MCYTdatabase. Although it is not possible to carry out a direct comparisonof the results, since the methodologies of training and testing andthe classification strategies used by each author are different,Table 10 enables one to visualise results from the proposedmethodology alongside results published by other authors.

The next step in analysing grey scale based features is tocombine them with geometrical based features. It is supposedthat the two types of features will be uncorrelated and theircombination will improve the automatic handwritten signature

verification (AHSV) scheme. For geometrical based features wehave used the contour-hinge algorithm proposed in [46] and usedin [45] for AHSV with the MCYT Corpus. Table 11 shows theresults obtained by [45] using the contour-hinge algorithm andwith our implementation of it. To compare the results, we need totake into account that in our work we have not use a scorenormalization, i.e. the threshold is 0 for all the users. On the otherhand, [45] uses a user-dependent a posteriori score normalization,that is to say, their EER is an indication of the level of performancewith an ideal score alignment between users. The scorenormalization used by [45] is as follows: s0 ¼s�sl, where s isthe raw similarity score computed by the signature matcher, s0 isthe normalized similarity score, and sl is the user dependentdecision threshold at the ERR obtained from a set of genuine andimpostor scores for the user l. So, for a fair comparison we giveour results with the score normalization of [45] and without scorenormalization. As can be seen the counter-hinge parameters workslightly better with the MCYT than with the GPDS Corpus.

Tables 12–17 present results that confirm how features basedon grey level information can be combined with features based onbinary images to improve overall system performance. Thesetables offer information on the feature level combination ofLBPriu2

8,1 þLBPriu216,2þGLCMþcontour-hinge features. Again 5 and 10

genuine samples were used, respectively, in the training set forpositive samples, and random forgeries (genuine samples from

Table 15


16,2þcontour-hinge. Tested with skilled forgeries.


5 samples MCYT 2.21 26.43 11.90 1.66 8.27

GPDS-100 4.71 24.36 13.40 3.16 7.05

10 samples MCYT 6.54 8.69 7.08 2.28 6.38

GPDS-100 13.67 8.08 11.61 3.86 4.24

Table 16Results using GLCM+contour-hinge. Tested with skilled forgeries.


5 samples MCYT 1.64 33.31 14.31 1.29 7.68

GPDS-100 4.40 28.64 15.11 3.04 6.91

10 samples MCYT 5.51 13.31 7.46 2.30 8.25

GPDS-100 11.90 11.52 11.76 4.42 5.72

Table 17


16,2þGLCMþcontour-hinge. Tested with skilled forgeries.


5 samples MCYT 2.71 24.13 11.28 1.62 7.83

GPDS-100 4.79 23.09 12.88 2.74 6.68

10 samples MCYT 6.77 8.59 7.23 2.45 6.87

GPDS-100 13.13 7.46 11.04 3.86 3.91


others signers in the database) as negatives samples. We shouldnote that in this case the results with the GPDS Corpus are worsethan those for the MCYT Corpus because of the counter-hingeperformance.

8. Conclusions

A new off-line signature verification methodology based ongrey level information is described. The performance of thesystem is presented with reference to two experimental signaturedatabases containing samples from 75 and 100 individuals,including skilled forgeries. The experimental results for skilledforgeries (Tables 3 and 5) show that using grey level informationachieves reasonable system performance EER¼16.27% and12.82%, when LBPriu2

8,1 þLBPriu216,2 and GLCM features are used for

the MCYT Corpus. Overall system performance is improved whena feature-level fusion of LBPriu2

8,1 þLBPriu216,2 +GLCM features is im-

plemented. These latter results compare well with the currentstate-of-the-art (Table 10). A combination of the proposedapproaches LBPriu2

8,1 þLBPriu216,2þGLCM and the contour based ap-

proach proposed in [45] leads to further performance improve-ment, especially in the case of random forgeries. We suggest thatscore-level and decision-level fusions should be studied in thefuture.

Additionally, a simple and low computational cost segmenta-tion algorithm has been proposed based on posterisation.Although a procedure to reduce the effect of ink-type waspresented, more efforts need to be made in that particulardirection in order to improve this stage of our system. Never-theless, comparing the similar results obtained with MCYT andGPDS databases with the grey level based features, it seems thatthe proposed features display some invariance to pen typebecause the MCYT Corpus has been made with the same penand the GPDS Corpus with different pens.

Acknowledgments

This work has been funded by Spanish government MCINNTEC2009-14123-C04 research project; F. Vargas is supportedby the high level scholarships programme, Programme AlBan

No. E05D049748CO.

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Jesus F. Vargas was born in Colombia in 1978. He received his B.Sc. degree in Electronic Engineering in 2001 and M.Sc. degree in Industrial Automation in 2003, both fromUniversidad Nacional de Colombia. Since 2004, he is an Auxiliar Professor at Universidad de Antioquia, Colombia. He is currently a PhD student at Technological Centre forInnovation in Communications (CeTIC, Universidad de Las Palmas de Gran Canaria, Spain). His research deals with offline signature verification.

Carlos M. Travieso-Gonzalez received his M.Sc. degree in 1997 in Telecommunication Engineering at Polytechnic University of Catalonia (UPC), Spain. Besides, he receivedPh.D. degree in 2002 at ULPGC-Spain. He is an Associate Professor from 2001 in ULPGC, teaching subjects on signal processing. His research lines are biometrics,classification system, environmental intelligence, and data mining. He is a reviewer in international journals and conferences. Besides, he is an Image Processing TechnicalIASTED Committee member.

Jesus B. Alonso received his M.Sc. degree in 2001 in Telecommunication Engineering and Ph.D. degree in 2006, both from the Department of Computers and Systems atUniversidad de Las Palmas de Gran Canaria (ULPGC), Spain. He is an Associate Professor at Universidad de Las Palmas de Gran Canaria from 2002. His interests includesignal processing in biocomputing, nonlinear signal processing, recognition systems, and data mining.

Miguel A. Ferrer was born in Spain in 1965. He received his M.Sc. degree in Telecommunications in 1988 and Ph.D. in 1994, both from the Universidad Politecnica deMadrid, Spain. He is an Associate Professor at Universidad de Las Palmas de Gran Canaria, where he has taught since 1990 and heads the Digital Signal Processing Groupthere. His research interests lie in the fields of biometrics and audio-quality evaluation. He is a member of the IEEE Carnahan Conference on Security Technology AdvisoryCommittee.

doi:http://dx.doi.org/10.1109/ICETET.2008.134

http://herkules.oulu.fi/isbn9514270762/

http://www.ai.rug.nl/&sim;bulacu/

http://www.ai.rug.nl/&sim;bulacu/

off-line signature verification based on grey level information using texture features

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