BIOMETRIC SIGNATURE AUTHENTICATIONUSING RADON TRANSFORM-BASED WATERMARKING TECHNIQUES

Emanuele Maiorana, Patrizio Campisi, Alessandro Neri

Dipartimento di Elettronica Applicata,Universita degli Studi "Roma Tre",

Via della Vasca Navale 84, 00146 Roma, Italyphone: +39.06.55177064, fax: +39.06.55177026, e-mail: (maiorana, campisi, neri)@uniroma3.it

ABSTRACT commonly referred to as "fusion levels", can be implemented[5]. Fusion methods include, among the others, those aim-In this paper we propose a signature-based biometric authen-in at cobnn th difrn inomto leel emode

tication system, where watermarking techniques are used to iga obnn h ifrn nomto eesebdetication system,wher watermarkingtechniquesareus o in one single biometric signal. As far as signature verifica-embed some dynamic signature features in a static represen- tion is concered, the fusion of local and global characteristictation of the signature itself. User authentication can be per- [6], as well as the fusion of complementary verification mod-formed either by means of the only signature static image, or ules [7], has been proposed. Also watermarking can be usedby using it together with the dynamic features embedded in

to implement multi-modal biometric systems, as in [8] wherethe enrollment stage, by using a fusion approach. A multi-level authentication system, which is capable to provide two fingerp are watermark edwith9face teis Signadifferent levels of security, is then obtained. The proposed te w atmarkin aeen considredinh[9]. In this paperwatermarking techniques are based on the properties of the we pre amtl el signatureRadon transform which well fits to the signature images. A trobust embedding is obtained while keeping unaltered the onig- characteristics in an image of the signature itself, and where

score level fusion is used to combine different types of signa-ture properties. The proposed authentication system allows toobtain two levels of security, according to the specific appli-

1. INTRODUCTION cation.

Data security and integrity probably represent the main disad-vantages of biometric systems with respect to traditional per- 2. PROPOSED MULTI-LEVEL SIGNATURE BASEDsonal identification techniques: if biometric data are stolen, AUTHENTICATION SYSTEMit is not possible to replace them, unlikely than for an ID ora password. Therefore, when designing a biometric system, Signature-based authentication can be either static or dynamic.countermeasures to possible malicious attacks, like those de- In the static mode, also referred to as off-line, only the digitalscribed in [1], have to be taken into account. Encryption and image of the signature is available. In the dynamic mode, alsowatermarking are two widely known solutions for the secu- called on-line, signatures are acquired by means of a graphicrity needs. However, while encryption does not provide se- tablet or a pen-sensitive computer display, that provides thecurity after decryption, watermarking can be used to secure temporal samples of the pen position, in x(ta) and y(ta) co-and authenticate unencrypted data. Watermarking based ap- ordinates, and the pressure p(t,). Since on-line signatureproaches involve embedding biometric or authorization infor- authentication involves dynamic features, much more diffi-mation into the host data, which can be biometric data as well cult to forge than static ones, it is more suitable for personal[2]. Some approaches for the protection and authentication authentication in legal and commercial transactions requir-of biometric data using watermarking have been proposed in ing high-security. The enrollment procedure of the proposed[3] where robust watermarking techniques are used to em- multi-level signature based authentication system is sketchedbed codes or timestamps. When large scale biometrics are in Figure 1. After having acquired the signature through antaken into account the set of features used to identify a user electronic pad, some relevant dynamic features are extractedcan overlap with the features of other users. Therefore the and then embedded into the signature image by means ofneed to use information coming from different sources and watermarking techniques. Specifically, we use the pressureto properly combine them arises, thus leading to multi-modal values of the signature as the host signal where to embed thebiometrics approaches [4]. At this aim, different strategies, mark. Linear interpolation is implemented, both for the spa-

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-0-CILAlWavelet Coefficient Wrking W, igntur Image

e-Pad Original Image Marked Image>Dynamic Featur e s)d>Features l ,M

Extractirzatonn Watemnarking Key ( Z)

Fig. 1. Proposed enrollment scheme.

tial coordinate and for the pressure values, in order to ob- implement the continuous RT in the discrete domain, we re-tain the signature images from the acquired data. It is worth sort to the approach presented in [ 1], where an invertible andpointing out that by considering synthetic images whose in- non-redundant finite Radon Transform (FRAT) is proposed.tensity is proportional to the pressure applied by the writer, Specifically, given a real function f defined over a finite gridan higher discriminative capability, with respect to the simple Zp, being Zp {0, 1, , P - 1}, its FRAT is:binary signature images employed by conventional methods, 1is obtained. Referring to Figure 1, the proposed enrollment FRATf [k,1] =r[k, 1] E f[i,j], (2)scheme can be summarized in the following steps: first, the v (i,j)GLk,lacquired pressure image undergoes a two-level wavelet de-composition, then the four second level subbands are selected. where Lk,l defines the set of points that form a line onEach selected subband is decomposed into square blocks, and Lk,1 {(i, j) ki + I (mod P), i E Zp},some of them are then selected, depending on their energy (3)level. Two different embedding domains are then used, both LP,I {(l, j) j E Zp},derived from the Radon Transform (RT), as detailed in Sec- being k C Zp+1 the line direction and I its intercept.tion 3: the ridgelet and the Radon-DCT domain. The pickedblocks are projected in one of these two domains, and the 3.2. Embedding Domainsmost relevant projections' coefficients are selected. Dynamicfeatures extracted from the acquired signatures are finally em- The proposed watermark embedding domains are obtainedbedded in them by means of quantization index modulation from the Radon transform, aiming at focusing the energy of(QIM) watermarking [10]. The whole procedure is detailed each Radon projection in a limited number of coefficients.in Section 4. When wavelet decomposition is applied to the Radon projec-

When a low security level is needed the authentication can tions the so called ridgelet transform [1 1] is obtained. We alsobe performed using some selected static features extracted propose to perform the embedding in the domain obtained byfrom the signature images. Whereas, when a higher level applying the discrete cosine transform (DCT) to each Radonof security is required, authentication is accomplished on the projection, thus introducing here a combined Radon-DCT (R-base of the embedded dynamic features by themselves or to- DCT) domain.gether with the selected static features.

3.2.1. Ridgelet Domain3. RADON TRANSFORM AND EMBEDDING Given an integrable bivariate function f(x) = f(xi, x2), its

DOMAINS continuous ridgelet transform (CRT) defined in [11] can beevaluated by applying the wavelet transform in the Radon do-Signature images are sparse images characterized by line sin- manSpcfalythCRcnbeoaidbypliga

gularities in a 2-D domain. Therefore, the Radon transform 1-D waecetitansor toCRfT)ca follows:appears to be a good tool to analyze this kind of images.

CRTf(a,3,0) / j(T- )Rf(,T)dT. (4)3.1. Radon Transform C (O

The continuous Radon transform Rf (0, T) of an integrable From (4), it can be seen that an invertible finite ridgeletbivariate function f(x)= f(Xl, '2) is defined as: transform (FRIT) [11] can be derived from the application of

a 1-D discrete wavelet transform on each FRAT projection

Rf (, T) = A(Xl: X2)(Xl cos 0+x2fsin0-T)dxdX2, sequence (r [k, 0], r [k, 1], ,r[k, P-1]), for each directionRfO,) I] fxix26xioO+2sn-Tdid2 k (e Zp+i:

being (0}, T) E [0, 2X) x IR and d the Dirac distribution. (1) FRITf[k, q] =g[k,q], q EZp. (5)

value Rf (0, T) thus represent the integral of f(x) over a line Thanks to the wavelets' properties, the FRIT is able tooriented at an angle 0} and whose distance from the origin is T- concentrate the energy of each Radon projection sequence inTherefore the Radon transform maps each line in the spatial its first coefficients.domain ('1, 1C2) into a point in the (0, T) domain. Here, to

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3.2.2. Radon-DCTDomain are selected, and from the sequences associated to them, thefirst N values are extracted and used to built the matrix M(b):As an alternative to wavelet analysis, the DCT can be used fn

to obtain an energy compaction similar to the FRIT . A novel (embedding domain is thus defined, indicating with Radon- M(b) ( 4b)[ki,01 4(b)[ki,1] b)[ki,N -1]DCT (R-DCT) the transform derived from application of the K g( b)[k2,Ol g(b)[k2l1] .4b)[k2N11 J,DCT on each FRAT projection sequence (r[k, 0], r[k, 1],., (8)r[k,P- 1]), k C Zp+1: The procedure is iterated for all the Ba blocks selected

from the subband -y. The matrix Ma, having dimension 2Ba xR-DCTf [k, q] = c[k, q] w'[l] E l] P[1 (21 + 1)q] N is then built:

(6)M 2

with q E Zp, wo[O] = N, and wJ[l] = 2/N,I 0. M (9)Coefficients R-DCTf[k,0] = c[k, 0], k C Zp+1, representthe DC component of each projection k, and are therefore M(B)connected with the mean value of each Radon projection.

Doing this for each subband a' C F, four host vectors wa4. DYNAMIC SIGNATURE FEATURES EMBEDDING where to embed the mark are obtained by scanning the ma-

trixes Ma column-wise.As already outlined in Section 2, in our approach the hostpressure image data s[i, j] undergoes a two-level wavelet de- 4.1.2. Coefficients Selection in the Radon-DCTDomaincomposition. The second level subbands, namely S2LL [i, j],S2HL [i, j], S2LH [i, j], and S2HH [i, j], which represent the ap- The second proposed embedding method relies on the projec-proximation, the horizontal detail, the vertical detail, and the tion of the selected Ba blocks <b) [i, j], for each subband ,diagonal detail subband respectively, are selected for the em- in the R-DCT domain. As for the ridgelet domain embedding,bedding. Being signature images typically sparse images, the only the sequences associated to the two most energetic direc-subbands s,y [i, j], with FeF {2LL, 2HL, 2LH, 2HH}, tion k1 and k2 of each block are selected to be marked. Fromare then decomposed into blocks of PI x Pj pixels in order to them, the matrix M(b) is then built:perform a local analysis and to identify the proper areas where (b)C.Cthe watermark has to be embedded. This task is accomplished M(b) C"Y [ki, 1] J( [ki,2] t )[ki,N]by selecting only those blocks whose energy is greater than a K cb) [k2, 1] b) [k2, 2] c(b [k2, N] )fixed threshold TE. Indicating with sb) [i, j] the generic b- (10)th block extracted from the subband -y, it is then selected for By iterating the process for all the Ba selected blocks, thewatermark embedding if host vectors wy, a C F can be built as in Section 4.1.1. It

is worth pointing out that the DC coefficient c(b) [k, 0] of each

E(b) _ 1 P Pj 2 (7) projection k is not selected to be marked. This is done in orderE

pPJ> E to not modify the mean value of each Radon projection after

i=1 j=1 the watermarking. As can be derived from (2) and reportedthat is, if the block contains a meaningful fragment of the in [11], all the FRAT projections FRATf [k, 1], k C Zp+1 ofsignature. In our experiments we choose PI = Pi = P = 10 a function f defined over Zp should possess the same meanpixels. Once the blocks are selected, they are projected in value, related to the mean value of f. Leaving the DC coef-the ridgelet domain or in the R-DCT domain to choose the ficient unchanged after the watermarking means maintainingwatermark host coefficients as detailed in Section 4.1.1 and the original mean value of the Radon sequence, that remainsSection 4.1.2 respectively. equal to the mean values of all the other Radon projections

taken from the same block, in contrast to what happens with

4.1. Coefficients Selection the mark embedding in the ridgelet domain.

4.1.1. Coefficients Selection in the ridgelet Domain 4.2. Watermark Generation

The FRIT is applied to each block selected from subband 7, In the enrollment stage the watermark is generated by extract-whose total number is indicated as B~. Given the b-th block, ing from each user's signature the dynamic features detailedP + 1 FRIT sequences (4(b) [k, 01, (b) [k, 1],.., 4(b) [k, P - in Table 1. Specifically, for a given user, I signatures are ac-1]) related to each direction k C ZP+1 are then available. quired using an electronic digitizer tablet, and then the elevenOnly the two most energetic directions, namely k1 and k2, dynamic features [12, 13] given in Table 1 are evaluated and

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[Index J Description [Assigned Bits [Index Description1 Number of the Strokes 5 1 Sample Count2 Time Duration 7 2-4 Height, Width and Aspect Ratio3 Final X 10 5-7 Minimum, Mean and Maximum X Position4 Initial X 10 8-10 Minimum, Mean and Maximum Y Position5 Number ofX Maximums 6 11-12 X and Y Area6 Final Y 10 13-17 Statistical Moment M1,1,M1,2,M2,1,M0,3,M3,07 Initial Y 10 18-20 Minimum, Mean and Maximum Pressure Value8 Number ofY Maximums 6 21-32 Mean Pressure 12-segment9 Pen Up/Pen Down Ratio 8 33-44 Sample Count 12-segment10 Mean Instantaneous Velocity Direction 10 45-68 X and Y Area 12-segment11 Mean Instantaneous Acceleration Direction 10

Table 2. Static features extracted from each signature image.Table 1. Dynamic features extracted from each signature.

dimension 720 x 1440 pixels, in 12 equal-sized rectangularcollected in vectors d(i), with i = 1, , I. A vector d is segments [12]. As can be seen from Table 2, 15 features out ofthen calculated as the average of the dynamic feature vectors 68 are related to the signature pressure, typically consideredd(i), and its elements are binarized using the bit depths, given as an on-line characteristic.In order to select, among the Iin Table 1, we have experimentally set by evaluating the av- signatures acquired for the user u, a representative signature,erage variation range of the features under examination. The from vectors s(i) the mean Au and the variance o-2 featureso obtained binary vector, with length equal to 92 bits, is then vectors are calculated. A distance measure Du is introducedBCH coded to provide error resilience. We have chosen to and estimated for each of the I enrolled signatures of user uuse a (127,92) BCH code, which provides an error correction as follows:capability (ECC) equal to 5 bits. The coded binary vectorm, consisting of 127 bits, is then decomposed into 3 sepa- 68 (s)[h] - pu1[h)2rate marks m2LL, m2HL and m2LH with dimensions equal u Sh [h]to 32 bits, and a fourth mark m2HH with dimension equalto 31 bits. These marks are separately embedded, by means a l v . witof QIM [10] watermarking, in the corresponding hosts w-,

n h intr mg iin h oetvleDu,wtQI [10]inedwatermaing, in tectorrspndng. 1,... I, is then selected for each user. The selected signaturea C F, obtained as outlined in Section 4.1.fetrsaehecostoterepresents the one whose static features are the closest to theestimated mean, and becomes the host image where to embed

4.3. QIM Embedding the selected user's dynamic features.

In its simplest implementation, a QIM watermark system as-sociates each bit of a message m, namely mi, to a single host 6. AUTHENTICATION PROCEDUREelement wi, and let mi determine which quantizer has to beused to quantize wi. Typically, the two codebooks Uo and u, In the authentication stage the user is asked to provide hisassociated respectively to mi = 0 and mi 1 are defined as: signature by means of an electronic pad. His prototype sig-

nature with the embedded signature dynamic information can

2 ={zA+X .z e }b, {zA-+ ,z+ .E} (11) be stored either in a centralized database or in a card. When a2 low-security level is required the authentication is performed

where X is a secret key andA the quantization step. The com- on the base of the selected static features only. With refer-plete marked sequenceisindicatedas w Thence to Figure 2 the static features given in Table 2 are ex-plete marked sequence iS indicated as wm Thle watermarked g

signature image is then obtained by reversing the embedding tracted from the provided signature, collected in the vector

procedure. su, and compared with the static signature feature vector §u.If a higher security level is required, dynamic features areobtained from the acquired signature, collected in the vec-

5. ENROLLMENT PROCEDURE tor du, and compared with the dynamic signature features du,In the enrollment procedure we both extract the dynamic fea- extracted from the stored watermarked signature image. A

some tatic Malahanobis distance is used to compare the extracted fea-tures to be embedded in the signature image and some static tu cors das os:tures vectors as follows:features which will be used to perform the first level of userauthentication. For a given user , from each ofthe I acquired D(-, /(4 [h]-vT [h] )2signatures the 68 static features [12, 13] detailed in Table 2 are Dv,v r t[1 3extracted and collected in the vectors s($), with i =1, , I.h [h

We consider both global (the first 20) and local features where iKJ represents either the stored static or dynamic feature(the last 48), calculated by dividing each signature image, of vector, vtl the one obtained from the provided signature, and

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_ xtractioneatures Multi-level Authentication Low-levelSecurity- 0-: 00lx/ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Static lFeatures-based

l| _ + m Etrya Fetur Decision

. | \ / ~~~~~~~~~~~~~~High-levelSecurityII

> l~ ~~~~~~~~~Features-based -_FtaticFeatures2. e uth

Extraction methDs asaF ucinoeh PG ult ftemre

70 Disg~I~tanceEstdi~mat lynamic l

ynamic Feat r dd l_ Features-based

e-Pad Extraction LDe__c's__ =_ = ==o.n

Fig. 2. Proposed authentication scheme.

60% 50% methods, as a function of the JPEG quality of the marked-%0- Ridgelet Embedding 4 - 0e- Ridgelet Embedding---4% Rtadon-DCTEmbedding Rtadon-DCT Embedding _ image. The PSNR between the original and the JPEG com-

40% 40% pressed marked signature is around 50 for compressions withE35% ~35%

m30% 30% - JPEG quality equal to 90: marked signatures are thereforet20% w20% very similar to the original ones, and their differences are vi-co 15%0 Ab0.; tD 10% sually undetectable. Figure 3(b) shows the BER obtained

10% 0 10% when considering marked images with Gaussian noise added,5% -% ; as a function of the PSNR between the marked and the noisy

JPEG Q0ity Maked Noisy Signatue Image PSNR signature images. The simulations have been carried out by(a) (b) marking N = 6 values of each either ridgelet or R-DCT pro-

Fig. 3. Mark extraction performances. (a): BER vs. JPEG jection sequence, using A 100 for the QIM watermarkingquality level. (b): BER vs. marked and noisy image PSNR. algorithm. To summarize, overall better performances in term

of robustness are obtained when the mark embedding is per-a-2 the variance of vt, estimated during enrollment. If the formed in the novel R-DCT domain, with respect to the em-distance is less than a threshold TA, the user is authenticated. bedding performed in the ridgelet domain. Both methods leadditnei*esta hehl A th user is authenticate. to the same level of the watermark perceptual transparency.In Section 7 the performances achievable using only eitherthe static features or the dynamic features, and a combinationof both through score level fusion techniques, are presented. 7.2. Authentication System Performance

In order to test the authentication performances of our ap-7. EXPERIMENTAL RESULTS AND CONCLUSIONS proach, 50 signatures have been acquired from each of 30

users, taking for each of them 10 signatures in five differentIn this Section an extensive set of experimental results con- sessions during a week time span. In the enrollment stage,ceming the performances ofthe proposed signature-based au- 10 signatures (taken from the first session) were used to de-thentication system are presented. Specifically, we have char- termine the typical host signature image and to extract theacterized the system performances both in terms ofthe robust- dynamic features to be embedded, as described in Section 5.ness of the employed watermarking methods and in terms of The remaining 40 signatures for each subject were used tothe authentication capabilities of the proposed system. determine the false rejection rate (FRR) of the system. The

false acceptance rate (FAR) when random forgeries are con-

7.1. Mark Extraction sidered (FARRF) is tested taking for each user under exam-ination the fifty signatures of all the remaining twenty nine

The performances of the proposed embedding methods are users as random forgeries. The FAR when skilled forgeriesevaluated on the basis of 1500 signature images, taken from are considered (FARSF) is evaluated considering a test set of30 different users. The embedding, detailed in Section 4, is ten skilled forgeries, created using a training time of ten min-performed using binary marks of 127 bits which, in our case, utes for each signature whose original was made available torepresent the BCH encoded dynamic features extracted from the forger, for each subject. In Figure 4 the performances re-the acquired signature. lated to the use of both only static feature and only dynamic

Some attacks, like JPEG compression and additive ran- features are reported, with respect of the threshold TA. Alldom Gaussian noise, have been performed on the watermarked the images we have considered were compressed with a JPEGsignature images for testing the robustness of the proposed quality value equal to 90. AS it is shown, the equal error rateembedding methods. Figure 3(a) shows the obtained bit-error- (FER) achievable using only static features is approximatelyrate (BER) for the proposed ridgelet and R-DCT embedding 12% for both R-DCT and ridgelet embedding methods con-

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100% 100%' 40% 40,

-FRR -Fusion Fusion90% 90 FRR - - Dynamic - Dynamic~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Dnaic.....DnaiFAR (Skilled Forgeries) FA SildFrgre)Sai.0. FR(RndmFogeis). FAR (Random Forgeries) 30% Stai! 30%

70% 70%-60% .. ~~~~~~~~~~~~~~~~~60%U

40% 40 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1~~~~0%20-S30% 30...

20% 2~~~~ ~~ ~~~~~~0%-.... ......10% 10 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0%030% ........... ....... ... ...IS..20%.3 40%.0%.IS.....30%.40

0% FRR FRR~~~~.. .30

0 10 20 30 40 00 60 70 0 10 20 30 40 00 60 70 (a) (b)Threshold Threshold

(a) (b(100% 100%

90%..... ~~~~~ ...... ~~Fig. 5. Verification performances of individual and combined90% FRR ~~~~ ~~~~90%.-RFAR (Skilled Forgeries) ~ --FAR (Skilled Forgeries) is JA s

00%...FAR (Random Forgeries) 00%...FAR (Random Forgeries) syt RO sI 1S F R (a:Kcn-UId mi

- embedding; (b): Ridgelet domain embedding.30% ..30%.guarantee.a.low.security level, while.the.embedded.dynami

20% 2..... ..........1,.......... 0% features.cn be.extrcted.and.sed,.by.temselves.r.togethe4 0 % 1.. 0%

0EL 10

Fig.4. FRR~ FARRF,s andb FARactdSFnfor,(a)heseRadon toDCTedomain emedn,ttcfetrs (bwRdgitdoanemh1 N.eRtathacJ.Honnell,R.o MBoovie,a "AnheAnlysis ofMinutiaeMtch-

bedding, static features; (c): Radon-DCT domain embedding, Auth., pp. 223-228, 2001.dynamic features; (d): Ridgelet domain embedding, dynamic [2] A.K. Jamn, U. Uludag, "Hiding Biometric Data", IEEE Transactions onfeatures. PAMI, Vol. 25, No. II, pp: 1494-1498, 2003.

[3] N. K. Ratha, J. H. Connell, R. Bolle, "Secure Data Hiding in Wavelet

sidering random forgeries, and 15% considering skilled forg- Compressed Fingerprint Images", ACM Multimedia 2000 Workshops,eries. On the other hand, the use of dynamic features results pp: 127- 130, 2000.in better performances as far as R-DCT embedding is con- [4] A. A. Ross, K. Nandakumar, A.K. Jamn, "Handbook of Multibiomet-

cemed, with respect to the use of ridgelet embedding: in the rics", Springer 2006, USA.first case the achievable FER is approximately 5% for ran- [5] M. Faundez-Zanuy, "Data Fusion in Biometrics", IEEE Aerosp. anddom forgeries and 10% for skilled forgeries, while in the lat- Electr. Syst. Mag., Vol. 20, No.1, 2005.ter case the FER is approximately 17% for random forgeries [6] J. Fierrez-Aguilar, L. Nanni, J. Lopez-Pefialba, J. Ortega-Garcia, D.and 27% for skilled forgeries. The different behavior is due Maltoni, "An on-line Signature Verification System based on Fusion ofto the mark extraction capabilities of the two methods: as can Local and Global information", Int. Conf. on Audio and Video-basedbe seen from Figure 3, the R-DCT embedding approach of- Biometric Person Authentication, AVBPA, pp: 523-532, 2005fers better performances in terms of BER with respect to the [7] M. Fuentes, S. Garcia-Salicetti, B. Dorizzi, "on line Signature Veri-fi-

ridgelet embedding one. However, the application of a BCH cation: Fusion of a Hidden Markov Model and a Neural Network via a

code ith ECequl to to te binrizeddynamc feaures, Support Vector Machine", Int. Workshop on Frontiers in Handwritingcode wth FCCequalto 5 t the bnarizd dynaic feaures, Recognition, pp: 253-258, 2002.as described in Section 4.2, allows us to obtain adequate per- [8] A.K. Jamn, U. Uludag, R. L. Hsu, "Hiding a Face in a Fingerprint Im-formances even for the ridgelet embedding domain. Using age", Int. Conf. on Pattern Rec., 2002.images with worse quality, or applying FCC less than 5 inorder to embed more information in the signatures, the differ- [9] E. Maiorana, P. Campisi, A. Neri, "Multi-level Signature based Biomet-

ence btweentheathentcatio perfirmanes reated o the ric Authentication using Watermarking", SPIE Defense and Security,

use ofR-DCT and ridgelet embedding would be even greater.vo.67,Oln,207

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ably Good Methods for Digital Watermarking and Information embed-namic eatureperfrmance with hose elatedto ther fu-ding", IEEE Trans. on Inf. Theory, Vol. 47, pp: 1423-1443, 2001.

sion is shown in Figure 5 were the obtained ROCs are given. [11] M. N. Do, M. Vetterli, "The Finite Ridgelet Transform for Image Rep-Specifically, the fusion is implemented at the score level, us- resentation", IEEE Trans. on Im. Proc., Vol. 12, No. 1, pp: 16-28, 2003.ing the minmax normalization method, together with the sumrule1'fo th scr fuio [4].rAIA-Asevident, -_thefusonpprac [12]1 C. Vielhanuer, R. S,teinmet7 "Handwriting: Feature, Correlation Analy-