This study explores a method that learns about the image structure directly from the image ensemble in contrast to other methods where the relevant structure is determined in advance and extracted using hand-engineered techniques. In tasks involving the analysis of image ensembles, important information is often found in the higher-order relationships among the image pixels. Independent Component Analysis (ICA) is a method that learns high-order dependencies found in the input. ICA has been extensively used in several applications but its potential for the unsupervised extraction of features for handwritten signature verification has not been explored. This study investigates the suitability of features extracted from images of handwritten signatures using the unsupervised method of ICA to successfully discriminate between different classes of signatures.peer-reviewe

1st Workshop in Information and Communication Technology (WICT 2008)

Camilleri, Kenneth P.

Desira, Marco

OAR@UM

Handwritten Signature Verification by Independent Component AnalysisMarco DesiraDepartment of Computer ScienceSt Martins Institute of ITEmail: marco.desira@marcodesira.comKenneth P. CamilleriDepartment of Systems and Control EngineeringUniversity of MaltaAndDepartment of Computer ScienceSt Martins Institute of ITEmail: kpcami@eng.um.edu.mtAbstractAbstract This study explores a method that learnsabout the image structure directly from the image en-semble in contrast to other methods where the relevantstructure is determined in advance and extracted usinghand-engineered techniques. In tasks involving theanalysis of image ensembles, important information isoften found in the higher-order relationships among theimage pixels. Independent Component Analysis (ICA)is a method that learns high-order dependencies foundin the input. ICA has been extensively used in severalapplications but its potential for the unsupervisedextraction of features for handwritten signature ver-ification has not been explored. This study investigatesthe suitability of features extracted from images ofhandwritten signatures using the unsupervised methodof ICA to successfully discriminate between differentclasses of signatures.Index Termshandwritten signature verification, independentcomponent analysis, unsupervised learning1. IntroductionHandwritten Signature Verification is the processof verifying whether the features of a handwrittensignature can be classified as pertaining to the classof features of handwritten signatures of an individual.The analysis of handwritten signatures is dividedinto two main categories, based on: the method used tocapture the signatures; and subsequently the featureswhich can be extracted for analysis. The analysisof features extracted from scanned images of hand-written signatures is referred to as off-line or static,whereas the analysis of handwritten signatures whichare captured via digitizing tablets, tablet PCs or otherelectronic devices which can capture the trajectory ofhandwriting is referred to as on-line or dynamic [7].Off-line methods do not require the signer to bepresent during the verification process and rely onlyon features which can be extracted from the scannedsignature image, and thus require more complex pre-processing steps [13]. Off-line methods do not capturedynamics of the signature such as pressure and velocitythe lack of signer-sensitive characteristics which arecaptured in dynamic features makes off-line signatureverification a more difficult challenge [9].On-line signature verification methods have provedto be more accurate than off-line methods [11], [13]yet off-line signature verification systems are requiredwhen the signatory is not present at the verificationstage as may be required for verifying signatures onbank cheques.The process of signature verification should be ableto detect forgeries. Forgeries can be classified intotwo main categories: casual or random forgeries; andskilled and traced forgeries [11].Casual or random forgeries are created without priorknowledge about the appearance of the signature whichis being forged. In this case all that the forger knowsis the name of the person, whose signature is beingforged. Substitution forgeries where the forger provideshis own signature as a forgery are also classified ascasual forgeries [1], [11]. Although random forgeriesare less difficult to reject than skilled forgeries, randomforgeries amount to over 90In the case of skilled forgeries, the forger has accessto one or more copies of the signature which is beingforged. The forger has had time to practice the processof creating a forgery to best imitate the signature whichis being forged [11]. Skilled forgeries are more difficultto detect than random forgeries as the characteristicfeatures of a skilled and traced forgeries resembleclosely those of the imitated signature [10] thus makingskilled forgeries more difficult to discriminate fromauthentic signatures.In this study we propose the use of the unsupervisedlearning technique of independent component analysis(ICA) to extract structure directly from the signatureimage ensemble. Literature has shown that ICA cansuccessfully extract a representation of data from nat-ural mixtures such as those of sound sources andimages. The properties of the independent componentsextracted by ICA of signatures were investigated andthe outcome of the classification exercises which testfor the acceptance of genuine signatures and for therejection of random forgeries are discussed. Skilledforgeries are not used in this study.2. Independent Component AnalysisIndependent Component Analysis (ICA) is a methodwhich transforms multivariate (multidimensional) dataso as to make its essential structure more visible ormore accessible, thus facilitating the analysis of thedata. This representation is learnt from the data itself,thus the learning is unsupervised[12].2.1. ICA and high-order dependenciesIndependent Component Analysis learns both thehigh-order dependencies and the correlations found inthe input, and is thus considered to be a generalisationof Principal Component Analysis [4], [5]. IndependentComponent Analysis attempts to place the ICA basisvectors in the direction of maximum statistical depen-dencies and does not restrict them to be orthogonal ororthonormal [4].Higher-order methods such as ICA use informationabout the distribution of the input which is not foundin the covariance matrix, and thus the distribution ofthe input is not assumed to be Gaussian [12].One of the measures of nongaussianity is kurtosisor the fourth-order cumulant [12] (Equation 1). In thisimplementation we apply this measure to the inde-pendent components which are generated when ICAis applied to handwritten signature images. Gaussianrandom variables have a kurtosis of zero. We expectthe kurtosis of independent components to be nonzero.kurt(y) = E{y}4 − 3(E{y2})2 (1)Barlow [3] argues that it is important for our per-ceptual system to detect suspicious coincidences whichare new statistical regularities gathered as inputs fromthe environment. Barlow proceeds to argue that in thevisual input, edges constitute a suspicious coincidence.Barlow states that the detection of features by ourvisual cortex could be based on a redundancy reductionprocess which is essential to detect suspicious coinci-dences, such as edges which are localized and orientedfilters.Bell and Sejnowski [6] equate Barlows redundancyreduction problem to that of finding independent com-ponents by using a sigmoidal network of non-linearunits to maximize information transfer [5]. In theirexperiments Bell and Sejnowski [6] show that theindependent components resulting from ICA based oninformation maximization, are localized and orientedfilters which are in fact edges.In her study on Facial Image Analysis, Bartlett[4] explains that edges and elements of shape andcurvature are examples of high-order dependencies,where the relationship amongst three or more pixelsmust be addressed. Bartlett argues that in tasks such asface recognition, important information may be foundin the high-order relationships among the mage pixels.3. Architecture for the Processing of Sig-naturesBartlett [4] proposes two architectures for represent-ing face images for the purpose of face recognition.The representation is based on statistically independentcomponents which are derived from the image set. Inthis study of handwritten signatures we adopt one ofthe architectures, which is referred to as Architecture1 in [4].Figure 1. Image synthesis model adopted from [4].Architecture 1 is characterized by the image synthe-sis model depicted in Figure 1.We assume that each signature in X is a mixturecomprised of the independent components in S. Theobserved mixtures in X are a linear combination ofthe independent sources found in S and the weightsfound in A. By using the unmixing matrix WI , themixtures in X are transformed into approximations ofthe independent sources thus generating the rows ofU, where WIX = U.The independent components in the rows of U are aset of basis images that are statistically independent..By using A = W−1I as coefficients, the linear combi-nation of the basis images (independent components)regenerates the observed mixtures i.e. the signatureimages (Figure 2 below).Figure 2. The linear combination of the basis im-ages i.e. the linear combination of the independentcomponents as adopted from [4].Each row in A contains the set of coefficients bfor one image x. The coefficients in A constitute thefeature space which will be used for signature verifi-cation. The classification process adopted for signatureverification in this study varies slightly from that usedfor face recognition in [4].4. Preprocessing of the Signature ImagesThe different approaches to offline-signature verifi-cation have necessitated different preprocessing steps.These preprocessing steps prepare the signature imagesfor the different type of processing as may be requiredat the feature extraction phase.Some of the preprocessing steps encountered in theliterature [13] included: removal of blank edges of thesignature images (also referred to as data-area crop-ping); thresholding or binarization, noise reduction,removal of textured backgrounds, size normalizationof the signature images, thinning of the signaturestrokes to a width of one pixel also referred to asskeletonization, close contour tracing; blurring; androtation of the signature images.Most of these preprocessing steps are computation-ally expensive. The preprocessing proposed in thisstudy prior to executing the step of unsupervised learn-ing by ICA entails: converting the signature imagesto their grey-level equivalent by linearly rescaling theluminance of each image to the interval [0,255]; data-area cropping and scaling By bicubic interpolation.The signature images were scaled to 60 rows by 50columns. Such a small size was selected so as toreduce the size of the covariance matrix which hasto be created whilst computing PCA and during thewhitening phase.An original signature sample and a preprocessedsample are produced hereunder.Figure 3. Signature prior to preprocessing on theleft. Preprocessed image on the right.4.1. Reducing the feature spaceWe perform PCA on the preprocessed images forthe purpose of reducing the feature space. The pixel-grey values of the training image set are loaded intovectors x, by using row-by-row scanning of each ofthe 60-by-50 pixel window. The rows of the imageswere concatenated thus producing 13000 dimensionalvectors. The vector x, is centered by subtracting itsmean as defined in Equation 2 below.x←− x− E{x} (2)Reduction of the feature space is achieved by se-lecting m from n principal components, where m ≤n. The selection of the vectors is based on the amountof variance that is required to be represented in theapplication of use. PCA does not throw away high-order relationships, it simply does not separate them[4].4.2. WhiteningWhitening or sphering is a preprocessing step whichsimplifies the ICA problem. Prior to executing thelearning steps of ICA, the data in X is passed througha zero-phase whitening filter WZ which is defined astwice the inverse square root of the covariance matrixof the data (Equation 3) [4]. Whitening removes thefirst and second order statistics of the data [4].WZ = 2 ∗ 〈XXT 〉−1/2 (3)5. ICA through Information MaximizationDifferent ICA methods exist. Each ICA methodis comprised of an objective function which is im-plemented by an optimization algorithm [12]. Thealgorithms for implementing ICA include [12]: non-linear decorrelation algorithms; algorithms for max-imum likelihood; algorithms for information maxi-mization; non-linear PCA algorithms; the FASTICAalgorithm; and tensor-based algorithms. This studymakes use of information maximisation [5] as usedin [4] to implement the ICA Architecture 1.5.1. Training, Feature Extraction and TestingLet X be the matrix containing n training signatureimages in its rows. Let Pm be the matrix containingthe first m principal components of X which have beenselected as mixtures for input to ICA, where m ¡ n. ICAis performed on PmT so as to produce m independentsource images in the rows of the matrix U. The stepsto compute U follow:Let WX be the whitened version of PTm. WX isused as input to the nodes with sigmoidal activation.The matrix of learned weights W is produced. U isderived as Equation 4 and 5 [4].WI =W ∗Wz (4)U =WI ∗ PTm (5)The principal component representation of the set ofzero mean images in X based on Pm is Rm definedby Equation 6 [4].Rm = X ∗ Pm (6)The learning rate was initialized at 0.0005 andannealed down to 0.0001 as detailed in Table 1 below.Table 1. Learning rates and associated iterations.Learning Rate Number of Iterations0.0005 10000.0003 2000.0002 2000.0001 200The feature set of the training data are obtainedfrom the coefficients for the linear combination ofthe statistically independent sources U as defined inEquation 7 [4], hence, the coefficients held in Bconstitute the feature set of the training data.B = Rm ∗W−1I (7)The extraction of features from the test data setrequires that the test data be centered by deductingthe mean of the training data. A PCA representationof the test data is generated by using the principalcomponents Pm which were used during the trainingphase as defined in the equation below [4].RTest = XTest ∗ Pm (8)The coefficients required to represent the test datain the ICA feature space are computed by applyingEquation 9 [4].BTest = RTest ∗W−1I (9)5.2. A Similarity MeasureEvaluation of the performance of signature verifica-tion was carried out for the coefficient vectors b, bythe nearest neighbour algorithm based on the cosine ofthe angle (Equation 10) between the vectors.d =btest.btrain‖btest‖‖btrain‖ (10)Testing was carried out using the Leave-One-Outcross validation technique. Features of the test signa-tures were extracted as defined by Equation 9. Featureextraction from the test signatures was carried out byusing the principal component representation of thedata with which the testing was performed. Since theobjective is to verify the signature, the class with whichthe test signature is expected to match is known apriori.6. ImplementationICA was performed to extract features from threesets of data each containing a different number ofsignature classes as detailed in Table 2. The detailsof Test C which yielded the best results are discussedbelow. The signatures were randomly selected from adatabase of signatures collated by Azzopardi [2].Table 2. Training Signature Classes.Test Signers Signatures per Signature Class TotalA 5 5 25B 37 6 222C 26 24 6246.1. Feature ExtractionThe database of signatures contained 40 signaturesfor each signer. Twenty four signatures of 26 signerswere randomly selected for the training phase. PCA ofthe 624 signatures was carried out. PCA generated 624eigenvectors (principal components), of which the first300 principal components captured 90% of the totalvariation in the data (see Figures 4 and 5 below). ICAwas performed on the first 300 principal components.Figure 4. The 5 principal components with largesteigenvalues ordered by the magnitude of the cor-responding eigenvalues. Eigenvalue displayed un-der each principal component.Figure 5. The 5 principal components with low-est eigenvalues ordered by the magnitude of thecorresponding eigenvalues. Eigenvalue displayedunder each principal component.On comparing the independent components a sampleof which is displayed below to the independent com-ponents generated in tests A and B there seems to bea higher degree of separation or there is less apparentmixture in the images of the independent components.The vast majority of the ICs can be interpreted asbars or edges.7. Signature Verification and ResultsSignature Verification using the remaining 16 sig-natures of each of the 24 signers, totaling to 416signatures is carried out against the set of featuresextracted from the 624 signatures.Tests using a similarity measure based on the cosinebetween the coefficient vectors b were carried out. AFalse Rejection Rate (FRR) of 6.01Figure 6. ICs having the highest level of kurtosisIn a study of off-line signature verification systemsusing HMM, Yacoubi et al [9] reported an FRR of 1.178. ConclusionAs we increased the number of signatures at theinput a higher level of kurtosis was achieved. Fromthe images of the independent components it wasclear that a higher degree of separation was achievedwhere the kurtosis was further away from 0. Signatureverification against features extracted by using ICAwith the largest data set at the input yielded the bestresults. This study has shown that signature verificationcan be achieved by blindly obtaining the independentcomponents of a set of signatures and classifying theICA mixing coefficients without the need for detailedpre-defined extraction of features from the signatureimages, the latter being so far the classical approachtowards signature verification.References[1] R. Abbas, “Backpropagation networks prototype for off-line signature verification,” Minor thesis. Master ofApplied Science in Information Technology, 11–15, Jun.1999.[2] G. Azzopardi, “How effective are Radial Basis Func-tion Neural Networks for Offline Handwritten SignatureVerification?,” Thesis, B.Sc. Computing and InformationSystems, University of London,, 2006.[3] H.B. Barlow, “What is the computational goal of theneocortex?,” Large -Scale Neuronal Theories of theBrain, 1994.[4] M.S. Bartlett, “Face Image Analysis by UnsupervisedLearning ,” Kluwer Academic Publishers, Boston, 2001.[5] A.J. Bell,T.J. Sejnowski, “An information-maximizationapproach to blind separation and blind deconvolution,”Neural Computation, vol. 7, no. 6, pp. 1129–1159, 1995.[6] A.J. Bell,T.J. Sejnowski, “The ”Independent Compo-nents” of Natural Scenes are Edge Filters,” Vision Re-search, vol. 37, no. 23, pp. 3327–3338, 1997.[7] G. Dimauro, S. Impedovo, S. Modugno,et al.,“RecentAdvancements in Automatic Signature Verification,”Proceedings of the 9th Intl’ Workshop on Frontiers inHandwriting Recognition, 2004.[8] J. Drouhard,and R. Sabourin, “A Neural Network Ap-proach to Off-Line Signature Verification using Direc-tional PDF,” Pattern Recognition, vol. 29, no. -, pp. 415–424, 1996.[9] A. El-Yacoubi,A. Justino,and R. Sabourin, “An off-line signature verification system using hidden Markovmodel and cross-validation,” Proceedings XIII BrazilianSymposium on Computer Graphics and Image Process-ing, 2000.[10] B. Fang,Y.Y. Yang,C.H. Leung, “A smoothness in-dex based approach for off-line signature verification,”Proceedings of the Fifth International Conference onDocument Analysis and Recognition. ICDAR ’99, pp.785–787, 1999.[11] W. Hou,X. Ye,K. Wang, “A Survey of Off-line Signa-ture Verification,” Proceedings of the 2004 InternationalConference on Intelligent Mechatronics and Automation,pp. 536–541, 2004.[12] A. Hyvrinen,J. Hyvrinen,E. Oja, “Independent Compo-nent Analysis,” Wiley, New York., 2001.[13] F. Leclerc,R. Plamondon, “’Automatic Signature Ver-ification: The State of the Art -1989 - 1993,” Inter-national Journal of Pattern Recognition and ArtificialIntelligence, vol. 8, no. 3, pp. 643–660, Jun. 1994.[14] K. Ueda, “Investigation of off-line Japanese signatureverification using a pattern matching,” Proceedings. Sev-enth International Conference on Document Analysisand Recognition, vol. 2, no. 3, pp. 951–955, 2003.[15] A. Zimmer,L.L. Ling, “’A Hybrid on/Off Line Hand-written Signature Verification System,” ICDAR’03,vol. 1,pp. 424–428, Jun. 2003.

Handwritten signature verification by independent component analysis

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Handwritten signature verification by independent component analysis

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