05/12/03b. dorizzi on-line signature identity verification bernadette dorizzi, get/int, 9 rue...
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05/12/03 B. Dorizzi
On-line Signature Identity Verification
Bernadette Dorizzi,
GET/INT, 9 rue Charles Fourier, 91011 Evry
05/12/03 B. Dorizzi
Outline
• Generalities• Preprocessing• Feature extraction• Models :
• Cooperation local/global : Kashi 98• DTW (Jain : 2002)• HMM (Rigoll, Dolfing, Salicetti)
• Evaluation : Signature Competition at Conf SVC 2004
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On-line signatures
• Acquisition on an electronic tablet or with a special pen, able to record a sequence of points (speed and pression of the signature, not only the static image)
• Interest : behavioral more than physiological, difficult to imitate.
• Highly variable intra-class characteristics : enrollment will necessitate several samples of the signature
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Recognition
General scheme
Sequence of points
Sequence of features
A signature of a claimed client X
Learning
Use of the samples of the signature of X to create a model of X
The signature is presented at the input of the model of X and a similiraty measure is computed.Comparison to a threshold allows to accept or discard the signature
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Signature samples
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Performance evaluation
Two types of errors
FR=False Rejection FA=False Acceptation
FRR=Nb of FR
Nb of clients
FAR=Nb ofFA
Nb of imposteurs
TER= Nb of FR + Nb of FA
Total acces Nb
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Performance curves
FRR High security
ROC curve In order to make a decision a threshold has to be settled
EER: Equal Error rate
FAR
Low security
FRR
FAR
EER (equal error rate)
Threshold
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Data acquisition
• Depends on the capabilities of the hardware– High-end tablet : robust pressure sensibility, precise pen pressure
measure, measure of the pen orientation
– PDA : only coordinates and information on pen-up, pen-down•Coordinates : x(t),y(t)
•Pressure p(t)
•Orientation (t), (t)
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Preprocessings
• Resampling and smoothing of the trajectory
– Between 100 and 150 points per second (too many points, noise)
• Low-pass Filtering (the low frequencies carry the information)
• Apparent contradiction : point spacing on the trajectory . If irregular (dependant on the speed of the signing process) one capture the speed. But, in some parts of the trajectory there are very few points, thus little spatial information. (cf. Jain cf comprise between the 2).
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Local and contextual features
• Speed in x and y direction
• Acceleration in x et y direction
• Tangential Acceleration
• Cosine et sine of angle :
)(
)()(cos
tv
tvt x=
)(
)()(sin
tv
tvt y=
dynamical parameters
The signature is considered as a sequence of points. A vector of features is computed at each point of the trajectory
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)1()1()()( −−+== tttt δφ
• Cosine and sine of the angle which estimates the (t)
variation :
Contextual (shape) parameters
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Global Features(Kashi et al., IJDAR 98)
• Mixture of both shape and dynamical features– 2 time-related features : total signature time, ratio of pen-down
time to total time
– 6 other dynamic features depends on the writing velocity and acceleration
– 13 shape-related features
The signature is considered as a whole
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Dolfing approachPhilips Research Laboratory
• The signature is split into different portions (part of the trajectory between 2 values of de vy=0)
• To each portion is associated a vector of 32 features
The signature is considered as a sequence of points, these points are regrouped in several sub-parts . A feature vector is associated to each sub-part.
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Feature Description
– 13 spatial features– 13 dynamic features– 6 contextual features
• Spatial features:– sin and cos of the starting and ending angles : thetastart,
thetaend– 3 intermediate angles– Aspect ratio– La curvature– Existance of a pen-up
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Figure associated to the spatial features
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Dynamic features
• Number of samples nt• min, max, moy of speed v• acceleration a• pressure p• variation of pressure delta p• vmax-vmoy• pen-tilt with 2 angles
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Contextual features
• Sin et cos of angles psi1, psi2, psi3 which are the angles of the 3 lignes with x axe which start from the gravity center of the current portion towards the gravity center of the 3 preceeding segments.
seg1
seg2seg3
Seg courant
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Several Models of the signatures and associated similarity measures
• « A Hidden Markov Model approach to online handwritten signature verification », Kashi et al, IJDAR 1998. Computation of a global distance between 1 signature and a set of references signatures of writer i.
• « On-line signature verification », Jain et al. , Pattern Recognition, 2002 . DTW to compare two signatures considered as 2 sequences of features.
• Rigoll, Dolfing, Salicetti etc… : Modelization by a HMM of each writer (several signatures considered as sequences of features are considered) : computation of a likelihood measure for a signature to be produced by the HMM of writer i
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Global feature-based verificationKashi et al.
• A signature model for entrant i is a set of means and standard deviations , obtained during training from 6 instances of signatures
• Error measure Ei for a given signature claimed to be that of i:
• N is the total number of global features
• M i,k is the value of the K-th feature of the signature to verify
• i,k and i,k are the mean and standard deviation of feature k over the reference set of i.
Ei = Mik −μik( ) /σik( )2
k=1
N∑
⎛
⎝ ⎜
⎞
⎠ ⎟
1/2
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Dynamic Time Warping
• Local features are computed at each point of the trajectory
• A signature = a string (sequence of feature vectors)
• A signature model for a person is composed of 3 different samples of the signature
• String matching (DTW Dynamic Time Warping) allows the comparison of strings of different lengths.
• Finds an alignment between the points in the 2 strings such that the sum of the differences between each pair of aligned points is minimal
• To find the minimal difference, all possible alignments must be investigated.
• Dynamic programming is a method to implement that
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Mise en comparaison de 3 signatures d’une même personneS1, S2, S3
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Verification
• A test signature is compared to the model of signer i (represented by 3 signatures).
• 3 possible strategies : minimum of all the dissimilarity values, average of all the dissimilarity values, maximum of all the dissimilarity values
• Decision : comparison of this value to a threshold
• The threshold can be identical for all the writers or set individually for each writer.
• In this article, no forgeries data is used to calculate the thresholds.
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Writer Modelization by Hidden Markov model
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What is a HMM?
• Non deterministic automata with one or several states
• A double stochastic process
• A Markov chain representing the states of the HMM: S = {S1, S2, S3,……SN}
• A process which induces a sequence of observations
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What is a HMM?
state 1 state 2 state 3
O = (O1,..., Ot,...)
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Why a HMM?
• The different signatures of a same writer are variable. This variability will be well modelized by a HMM.
• This modelization will allow to consider a non stationary signal (the signature) as a piecewise-stationary signal.
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Components of a HMM• N: number of states in the model:
S = {S1, S2,……,SN}• A: Matrix of probability transitions
aij=P[qt+1=Sj|qt=Si], 1 i, j N • Initial distribution of the states:
i = P[q1 = Si], 1 i N• Emission law of the observations in each state
Bj(Ot)=P[Ot|qt=Sj], 1j N• Discrete HMM: Bj is a matrix• Continuous HMM: Bj is a mixture of gaussian probalility density
functions
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Markovian modelization of a signature
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Learning phase
• A process allowing the reestimation of the parameters of the HMM, in order to maximize the loglikelihood of the true signatures.
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Signature Verification
• Comparison of the loglikelihood of the signature, knowing the HMM model of the writer, with a threshold in order to take the decision
• «Distance» decision threshold– Accept if |Log(P(S|) - Lmean)|<, otherwise reject where
Lmean= mean loglikelihood on the learning database of the declared i client.
MMCof the writer
Signature Log-likelihood
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Systems Evaluation• Difficult because of the non availability of common databases : A lot of « home-
made » databases with no connection between them (between 9 and 100 individuals).
• In general the EER lies between 1% and 6%• Evaluation in presence of forgeries of more or less good qualities (skilled, over the
shoulder, random, rough etc…)• For instance, the Philips data base (very difficult due to the presence of high quality
imitations, including dynamics)• 1500 true signatures sur 51 persons, • 1470 imitations « over the shoulder »• 1530 imitations « home enhanced »• 240 professional imitations
• Non identical evaluation protocols : personal threshold versus global one• The threshold is generally determined in order that FAR=FRR (EER Equal Error
Rate) or in order to minimize TER (Equal Error Rate) on a development database (some signers that will not be considered in the test base) using forgeries.
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SVC 2004
• First International Signature Verification Competition – In conjunction with the First International Conference on Biometric
Authentication in Hong Kong (ICBA 2004)
• Two tasks:– Coordinate input only– Coordinate, pen orientation and pressure inputs
• Database for each task:100 writers– Training set:
• 5 among 20 genuine signatures per writer
– Evaluation set: • Unknown genuine signatures per writer • 20 skilled forgeries from 5 other contributors
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Conclusion
• Signature scan : a quite variable modality, resistant to forgeries, well accepted, but not suitable for each person
• Not so many applications :
• Natural with PDA, in banking contexts
• Some tools already available : smartpen, etc…
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References• J.G.A. Dolfing, "Handwriting recognition and verification, a Hidden Markov approach", Ph.D.
thesis, Philips Electronics N.V., 1998.
• M. Fuentes, S. Garcia-Salicetti, B. Dorizzi "On-line Signature Verification : Fusion of a Hidden Markov Model and a Neural Network via a Support Vector Machine", IWFHR8, Août 2002.
• J. Ortega-Garcia, J. Gonzalez-Rodriguez, D. Simon-Zorita, S. Cruz-Llanas, "From Biometrics Technology to Applications regarding face, voice, signature and fingerprint Recognition Systems", in Biometrics Solutions for Authentication in an E-World, (D. Zhang, ed.), pp. 289-337, Kluwer Academic Publishers, July 2002.
• A. Jain, F D. Griess, S.D. Connell « On-line signature verification », Pattern Recognition, , vol 35, pp.2963-2972, 2002
• J.G.A. Dolfing, "On-line signature verification with Hidden Markov Models", Proc. of ICDAR, pp. 1309-1312, 1998.
• R. Kashi, J. Hu, W.L. Nelson, W. Turin, "A Hidden Markov Model approach to online handwritten signature verification", Intl. J. on Document Analysis and Recognition, Vol. 1, pp. 102-109, 1998.
• G. Rigoll, A. Kosmala, "A systematic comparison of on-line and off-line methods for signature verification with Hidden Markov Models", Proc. of ICPR, pp. 1755-1757, 1998.