Online Signature Verification Based on the Hybrid HMM/ANN Model

IJCSNS International Journal of Computer Science and Network Security, VOL.7 No.3, March 2007

313

Online Signature Verification Based on the Hybrid HMM/ANN Model Zhong-Hua Quan1,2, Kun-Hong Liu1,2 1 Hefei Institute of Intelligent Machines, Chinese Academy of Science. Hefei, China 2 Department of Automation, University of Science and Technology of China. Hefei, China Generally speaking, signature verification can be Summary

divided into two groups: online and offline. In early

This paper presents a new approach based on

off-line cases, signatures are captured once the writing

HMM/ANN hybrid for online signature verification.

process is over, thus only static images are available.

The hybrid HMM/ANN model is constructed by using

Recently, more researches are carried on with the

a type of time delay Neural Networks as local

focus on the online signature verification, where

probability estimators for an HMM, where a posterior

signatures are acquired during the writing process with

probability of the model is worked out by the Viterbi

a special instrument, such as digital tablet. In fact,

algorithm, given an observation sequence. The

there is always dynamic information available in the

proposed HMM/ANN hybrid has a strong discriminant

case of online signature verification, such as velocity,

ability i.e, from a local sense, the ANN can be

acceleration and pressure which is more difficult to

regarded as an efficient classifier, and from a global

imitate than the static shape of signature. So, online

sense, the posterior probability is consistent with that

signature verification can usually achieve better

of a Bayes classifier. Finally, the experimental results

performance than the offline instance [1].

show that this approach is promising and competing.

For online signature verification, so far there have

Keywords

been many widely employed methods, for example,

Hidden Markov Model, Artificial Neural Networks, Online signature verification, Viterbi algorithm

Artificial Neural Networks (ANN)[2,3], dynamic time warping (DTW)[4,5], the hidden Markov models (HMM)[6,7], etc. Generally, the DTW is regarded as a popular method, but it usually suffers from the

1 Introduction

following two drawbacks: i) Heavy computational Signature verification is a biometrics method. Well

load and ii) Warping forgeries [8]. The first one can

known

and

make the DTW time-consuming while the second will

fingerprint identification, face recognition, retina scan,

make the verification more difficult. As an alternative,

signature verification, etc. They are being increasingly

the HMM is of capability to perform stochastic

adopted

and

matching for a model and a signature using a sequence

identification. Although attributes like iris, fingerprint,

of probability distributions of the features along the

and retina do not change overtime, they require special

signature. Practically, the HMM has been employed in

and relatively expensive instrument to acquire the

the filed of online signature verification for two

image. While the device for signature acquisition is

decades and has achieved some success. However, the

much cheaper. Furthermore, the most important

HMM also has its intrinsic limitations [9]. Among

advantage of signature verification is that it has been

these limitations, its poor discriminative power is fatal

accepted widely because of its long tradition in many

which

commercial fields, such as e-business, access control,

verification. Based on this consideration, in this paper

and so on.

we propose an HMM/ANN hybrid approach to online

biometrics

in

the

methods

personal

include

voice

authentication

limits

its application on the signature

signature verification. To the best of our knowledge, it


314

is the first time for this approach to be applied to the online signature verification. In the proposed model, the probability is estimated by an ANN so as to construct the HMM/ANN hybrid model, which leads to the following improvements: i) Higher model

Azimuth angle

γ (t )

of the pen with respect to the

tablet and v) altitude angle

ϕ (t )

of the pen with

respect to the tablet [18].

accuracy: ANN based estimate of probabilities does not require detailed assumptions about the form of the

2.2 Preprocessing

statistical distribution to be modeled, so as to

There are many methods for preprocessing, most of

guarantee the building of more accurate probability

which have been discussed in [12]. In this paper, each

models;

easily

signature is normalized on the position and scale

accommodate discriminate training [20]; and iii)

firstly, and then the extra time sequences such as curve

Context sensitive, etc.[10]. Further more, most of the

velocity, tangent angle are computed.

HMM

Usually, the normalization is accomplished by the

ii)

based

Discrimination:

approaches

for

ANN

can

online

signature

verification apply a type of left-right HMM directly, but scarcely consider the consistent between the handwriting process and the model. It is adapted in

following equations:

x1 (t ) = x(t ) − x , y1 (t ) = y (t ) − y

(1)

this paper by correspond each state with a class of strokes which go ahead with a determined direction,

where x (t ) represents the x-coordinate sequence

and consequently a type of ergodic model with explicit and

state duration is constructed for signatures.

x means the average of x(t ) .

This paper is organized as follows: Section 2 describes the signature data used in this paper and the preprocessing method, and the HMM/ANN hybrid

⎡ ⎤ x2 (t ) = K ⋅ x1 (t ) ⎢ ∑ x1 (t ) 2 + y1 (t ) 2 ⎥ ⎣ t ⎦

0.5

(2) 0.5

the verification method and Section 5 gives the

⎡ ⎤ y2 (t ) = K ⋅ y1 (t ) ⎢ ∑ x1 (t ) 2 + y1 (t )2 ⎥ ⎣ t ⎦

experimental results. At last, Section 6 concludes this

K is a constant that equals 16 in this paper. Addition

paper with some conclusive remarks.

to the basic time functions acquired by the digital

approach is presented in Section 3. Section 4 presents

tablet, there are two other types of derived time

2 Signature Data and Preprocessing

sequences which can be computed by the following equations.

2.1 Signature Data

vx (t ) = ( x2 (t ) − x2 (t − 1)) ⋅ 0.5 + ( x2 (t + 1) − x2 (t − 1)) ⋅ 0.25

The signature data used in this paper is from the

(3)

MCYT-100 database, which is licensed for research

v y (t ) = ( y2 (t ) − y2 (t − 1)) ⋅ 0.5

and includes 100 subjects. For each subject, there are

+ ( y2 (t + 1) − y2 (t − 1)) ⋅ 0.25 computes the velocity on x and y direction

25 genuine signatures and 25 skilled forgeries. Signatures are acquired using WACOM tablet (model INTUOS A6 USB) dynamically when the pen is

respectively. Then

moving on the tablet. This tablet provides the

θ (t ) = arctan(v y (t ) vx (t )) (4)

following

discrete-time

dynamic

sequences:

i) gives the tangent angle of the trajectory on time t

Position in x -axis, x (t ) ; ii) Position in y -axis,

and

y (t ) ; iii) Pressure p(t ) applied by the pen; iv)

x(t ) ≥ 0 ⎧θ (t ), θ (t ) = ⎨ ⎩θ (t ) + π , else

(5)


transforms

θ (t )

315

sometimes. To adapt to the all of the kinds of

into [− π2 , 32π ] .

applications, there are many types of HMMs proposed

The line speed sequence can be computed as:

and employed nowadays, such as continuous HMM

v(t ) = vx (t ) 2 + v y (t ) 2 (6)

[19, 21], autoregressive HMM [22], HMM with inclusion of explicit state duration density [15], and so

In this paper, the line speed v , pressure coordinates

x and

p(t ) ,

y are regarded as local

on. Now that there are so many types of HMMs, one must make several choices to design and apply a model for application.

dynamic features for comparison, they need no more

The first one is the choosing of model structure that

preprocessing other than the normalization since the

includes topology and number of states. To make such

original points retain the difference in writing speed

a choice, a preceding definition of the state is

and writing rhythm[16]. However, the tangent angle

necessary. But unfortunately, most of the related

sequence which is regarded as observed sequence for

works based on HMM just employed a left-right

HMM/ANN model is re-sampled to T equidistant

HMM for online signature verification and had no

point along the signature curve, where T equals the

explicit consideration about the meaning of the states.

point number before re-sampling.

There is only one can be used for reference that is proposed by Zou [13] where signatures are considered as composed of some stationary (or quasi- stationary)

3 The Hybrid HMM/ANN Model

segments and the states are corresponded with these

3.1 HMM Description

segments. However, there is a logical stigma for Zou’s

A standard HMM can be defined by the following parameters[19]:

work that there are some segments with the same features observed but the states underlying are different, since the HMM is left-right topology. In this

A set of N states S = {q1 , q2 ,L qN } ;

paper, a type of ergodic (or full connected) HMMs are employed,

A state transition matrix A = {aij } where aij is the

where

the

states

are

regarded

as

corresponding to a number of strokes which go ahead with a determinate direction. The rough direction of

transition probability from state qi to state q j :

each state is displayed in the following figure.

aij = Pr(q j at t + 1| qi at t ), 1 ≤ i, j ≤ N (7) q8

Set of M discrete symbols {v1 , v2 ,L vM } ; An observation probability matrix B = {b jk } , where

q7

q6

q1

q5

b jk is the probability of generating symbol vk from q2

state q j , and

q4 q3

The initial probability distribution for the states

π = {π j }, j = 1, 2,L N ; π j = Pr(q j at t = 1) . Figure 1. Bounds of direction for each state

Such

a

model

λ = {N , M , A, B, π }

can ,

be or

denoted

as

λ = [ A, B, π ]


316

As showed in Figure 1, there are 8 states defined in

assumed to be evenly distributed within the bound

advance for all signatures, but for a special instance,

otherwise a very small value is assigned. Further more,

e.g. signature displayed in Figure 2, there are not so

as displayed in figure 2, the direction of signature

many states. Moreover, the states should be hidden

trajectory changes gradually at the two ends of each

and not to be observed for HMM, so the exact states

state, so that, it is difficult to recognize the state

and number of states of a model would be determined

correctly at the ends of segments based on the

according to the signatures which are modeled. The

direction only. However, this puzzle can be readily

states defined in advance can be regarded as

solved if the state duration is considered. The last one of choice is about the global score for an

initialization for them.

observed sequence given a model. Usually the 1

maximum likelihood (ML) is computed as the global 08 06

0.5

0

03

0506

02

since a post probability is preferred according to the

03 05 03 05

Byes classification. So the discriminant HMM is

03

0303

employed in this paper which will be discussed in the

05

05

−0.5

06

06

06

score, but the ML is not appropriate to classification,

06

06 05

following subsection.

−1

3.2 The Discriminant HMM

02 −1.5 −2

−1.5

−1

−0.5

0

0.5

1

1.5

Discriminant HMM was firstly proposed by H. Bourlard[11]. For standard HMM, the goal is to find a model which maximizes the likelihood function

Figure 2. A sample recognized by the HMM/ANN hybrid model

P (O | λi ) for the observed sequence O. Whereas the

The second choice is about the state duration. As can be observed in Figure 2, there are some segments

goal of the Discriminant HMM is to find a model

where the state holds identical, and transitions

λi

P (λi | O) for

between different states only take place at the ends of

that maximizes a posterior probability

these segments. For such a configuration, the duration

a given sequence O. The Viterbi formulation of the

probability associated with state qi , with self

posterior probability can be written as P(λi | O) = max P( ql11 , L, ql1T , λi | O)

transition coefficient aii , is:

pi (d ) = (aii )

d −1

(9)

l1LlT

(1 − aii )

where qltt ∈ S with lt ∈ [1, N ] , t ∈ [1, T ] represents (8) states sequence. The right-hand side of Eq. (9) can be

However, for the relatively small number of states that correspond to segments of a signature, this distribution of state duration is inappropriate [7]. To model the handwriting process more accurately we prefer to use

factorized into: P(ql11 ,L , qlTT , λi | O) = P (ql11 , L, qlTT | O) P(λi | ql11 ,L, qlTT , O)

(10)

the models with explicit bounded state duration [15],

which suggests two separate steps for recognition. The

in which the self transition probabilities are set to zero,

first step is to find the best state sequence given the

[li , ui ] is assumed for

observation sequence O. The second step is to find the

and a bound of state duration

model each state. The duration probability for state

qi is

λi

from the state sequence without the

explicit dependence on O, so that


P(λi | ql11 , L, qlTT , O) = P(λi | ql11 , L, qlTT )

317

model is established. The scheme of the TDNN is

(11)

displayed in Fig.3.

For ASR, the first factor of Eq.(10) represents

As showed Fig.3, there are two layers of perceptrons

acoustic decoding, and the second one represents

(hidden and output layers) computing the post

phonological and lexical meanings, which is estimated

probability of the input field which is constituted by

from phonological knowledge of the vocabulary.

several units, each unit representing an observed value

However, for online signature verification, there is no

ot . Thus, if 2 p + 1 is the width of the contextual

distinct meaning for the two factors. Currently, most of the related works assume one model for each signer,

window, there are 2 p + 1 units in the input layer. Let

and the probability in Eq.(11) is usually simplified by

the number of output units equal that of the states, N ,

regarding it as a constant, e.g., 1. Such a strategy is

and each of the units correspond to a state. During

adopted in this paper also.

training, the output of the network is set according to

The other factor of Eq.(10) is immediately related to

the state associated with the center or “current” input

the local probability, which can be factorized into:

in a particular left and right context. Moreover, the

P(ql11 ,L , qlTT | O) = p(ql11 | O) p(ql22 | ql11 , O)

minimum squared error (MSE) criteria and the (12)

L p(qlTT | ql11 ,L , qlTT −−11 , O)

back-propagation algorithm is adopted for training the

Now each factor of Eq.(12) can be simplified by

interpreted as estimates of the local posteriori

relaxing the conditional constraint; especially, in the

probability of the states conditioned on a window of

TDNN. Thus the outputs of the TDNN can be

following the factors of Eq.(12) are assumed to only depend on the previous state and on a signal window

t+ p

observations p ( ql | Ot − p ) [11].

with width 2p+1. In fact, the local probability is

P ( q N | Ott−+ pp )

simplified as p(qltt | ql11 ,L, qltt−−11 , O) = p(qltt | qltt−−11 , Ott−+pp )

P ( q 2 | Ott−+ pp ) P ( q1 | Ott−+ pp )

(13) …

The following dynamic programming (DP) recurrence holds: P(ql | O1t ) = max[ P(qk | O1t −1 ) p(ql | ot , qk )]

(14)

…

k

where k runs over all possible states before states

ql ,

probability of reaching state

ql with emitting the

input

…

and P(ql | O1t −1 ) denotes the cumulated best path

vectors

x t + p −1

xt − p

xt + p

time delay

partial sequence O1t −1 .

3.3 TDNN as Probability Estimator

Figure 3. TDNN scheme for probability estimator

Many researchers have shown that the outputs of ANNs used in classification mode can be interpreted

It should be noticed that the previous state has not

as estimates of posteriori probabilities of the output

been take into account in computing the local

classes conditioned on the input [10, 11, 12]. In this

probability, since including the previous decision will

paper a time delay neural network (TDNN) is employ

result in a trouble of unbalanced training data for the

as the local poster probability estimator for the

networks. It is clear at a glance that the numbers of

discriminant HMM so a type of hybrid HMM/ANN


318

self transitions are much more than that of transitions

such a problem is to treat the state duration index d

from one state to another.

as the third independent variable, and to perform the

For simplification, it can be assumed that the posterior

dynamic

probability of states depend on the current state only, then the outputs of TDNN can be substituted into Eq.(14) directly.

P (ql | O1t ) = max[ P (qk | O1t −1 ) ⋅ p (qltt | ot )] k

programming

three-dimensional

searching

j

the

a

(t , i, d ) space [15]. Therefore, let

φt ( j, d ) = log( p(q j , d q = d | Ot )) represents

on

maximum

(16)

cumulated

posterior

probability in logarithm scale of progressing to state

(15) These equations hold valid when the context of observations are taken into account. Then the Viterbi algorithm to find the best state sequence can be efficiently implemented by a dynamic programming procedure.

qi

along the best state path and producing

observations

q j and producing the observations ot − d +1

state

3.4 Initialization and Training of the Hybrid Model In experiments, HMM and ANN are trained separately, and the training process of ANN is embedded in that

o1 through ot − d , and then entering

ot at this state, i.e.,

through

d −1

φt ( j, d ) = max{δ t − d (i ) + ∑ log( p(q j | ot − d ))} i

(

τ =0

of the HMM. The whole training procedure of the hybrid system is composed of iterations with the two

17)

steps:

all of the elements of

•

Recognition

(segmentation):

Each

training

signature is recognized by the hybrid HMM/ANN for the corresponding signer using the current parameters. •

where the output of the ANN is assumed to 1 for the correct state, and 0 otherwise. This iteration stops when the difference between the

lj

φl ( j, l j ) = ∑ log( p (q j | ot )) j

10−6 .

(18)

t =1

where

l j is the low boundary of duration for state

q j . And

δ t ( j ) = max{φt ( j, d )}

(19)

d

global posterior probability of the current iteration and that of the previous reaches a given threshold, e.g.,

are initialized to

−∞ , except that

Parameter reestimate: The HMM and ANN are trained according to the above segmentation,

φt ( j, d )

Finally, the global posterior probability score can be obtained according to the equation:

δT = max{max{φT ( j, d )}} j

d

Up to now, all of the discussion about HMM scheme

(20)

in the above sections have not taken the state duration

The best state sequence can be retrieved from the

into account. While the bounded state duration is

matrix which records the dynamic programming path:

included, it can be found that some identical

d −1

ϕ j (t ) = [arg max{δ t − d (i ) + ∑ log( p (q j | ot − d ))}, arg max{φt ( j , d )}] i

computations will have to be performed repeatedly if the conventional algorithm is adopted in implementing the Viterbi algorithm to recognize the states sequence (or to segment signatures). A strategy to circumvent

(21)

τ =0

d


319

where each element of the matrix records the best path

score of similarity between the signature and the

including the previous state and the duration of the

model can be defined as

previous state.

S map = (log P(λi | O) − μmap ) σ map (24)

The initialization of the hybrid HMM/ANN is accomplished by the following operations. At first, all of the reference signatures are segmented by the

If

Smap is less than a threshold, we can reject it

special points [13], then the signature which includes

directly. Otherwise, it should be verified further by the

the maximum number of segments is selected to

local comparison.

initialized the hybrid HMM/ANN model. The segments are labeled according to the direction of each

4.2 Local Comparison Based Verification

segment as displayed in Figure 1 and Figure 2. Then, the number of the states is set to equal the number of

Local time functions (such as

v(t ) , x(t ) , y (t )

labels, for example, the state number for the subject

p(t ) ) of a test signature and a template are

displayed in Figure 2 is set as 4. At last, the TDNN is

and

trained according to the labeled signature.

compared,

addition

to

the

HMM/ANN

based

verification. In this paper, all the referent signatures

4 Signature Verification Based on the Hybrid HMM /ANN and Local Comparison

are saved and one of which is selected as template. Further more, the local functions are compared between the aligned segments which worked by the HMM/ANN model.

4.1 HMM/ANN Based verification

While a signature is recognized by the HMM/ANN

Training of the hybrid HMM/ANN model is

model, not only a MAP is obtained, a segmentation of

accomplished by using the maximum a posterior

the signature which is characterized by the label

probability (MAP) criterion and applying the Viterbi algorithm. Based on the trained model λi , the global

sequence of states is worked out also. However, as

posterior probability

P (λi | O j )

variation of handwriting, it is impossible that the segments of different signatures are identical. And the

for the training

HMM employed are not left-right topology, segments

signatures can be worked out, and the mean and the

are not aligned instinctively. Thus a DP approach is

variance of which can be computed upon the referent

employed to match the segments and local comparison

signatures.

is performed consequently [14].

μ map = ∑ j P (λi | O j ) N

The distances of the local time functions are produced (22)

)2 N ⎞⎟ = ⎛ ∑ ( P (λ | O ) − μ σ map ⎜⎝ j i j map ⎠

by the local comparison procedure, e.g., for the velocity sequence, the distance can be computed by:

0.5

(23)

Dv = ∑ t vref (t ) − v 'test (t ) T

where O j represents the observed sequence of the where

(25)

vref represents the line speed of the template,

jth signature, and the N equals the total number of training signatures.

v 'test represents the speed of the test signature after

During verification, each signature claimed for

T equals the total length of the

belonging to a signer would be recognized by the

time warping and

corresponding model, thus the global MAP and the

vref . In this paper, the v(t ) , x(t ) , y (t ) and

segmentation of the signature can be worked out by the Viterbi algorithm. Assuming that the distribution of the genuine MAP is Gaussian distributions, the


320

p(t ) are used for local comparison, so the measure

0.35

0.3

of similarity of the comparison can be defined as

where the

∑

u∈[ v , x , y , p ]

μ

Du − μ Du σ Du (26)

and the

σ

0.25

0.2

are computed from the

FRR

Slocal = −

0.15

training data as in Section 4.1. 0.1

At last, the same strategy as that in Section 4.1 is adopted to reject the test signature as a forgery or accept it as a genuine one according to the similarity.

0.05

0

0

0.05

0.1

0.15

0.2

0.25

FAR

4.3 Decision Fusion The HMM/ANN based verification and the local

Figure 4: The trade-off curve for the FAR/ARR

comparison based verification are combined by sum From the Figure 4, it can be found that the EER

the similarity score of them.

Stotal = Smap + Slocal

(where FAR equals FRR) of the approach presented in (27)

this paper is about 0.12. Due to lacking of training samples, the statistical parameters for the similarity

Stotal is

scores are not accurate so that a unified threshold is

greater than a threshold, otherwise it is accepted as a

adopted for every subject. Nevertheless using a unified

genuine one.

threshold is not a good choice It can be validated by

And the signature is rejected as a forgery if

such a deed that the EER of the HMM/ANN based

5 Experimental Results

approach would decreased as low as 0.04 if a personalized threshold is adopted.

The MCYT-100 signature data used in this paper includes 100 signers, where there are 25 genuine

6 Conclusions

signatures and 25 forgeries for each signer. For each signer, 10 genuine signatures are randomly selected as

This paper proposed a heuristic approach for online

training samples and with the remained as test

signature verification based on HMM/ANN hybrid

samples.

model where an ANN is employed to recognize the

For online signature verification, two important

states underlying the observations. To the best of our

indicators are usually employed to evaluate the

knowledge, it is the first time for this model to be

performance of a verification system: false accept rate

applied to online signature verification. The most

(FAR) and false reject rate (FRR). The first represents

important advantage of employing the ANN as

the error rate of accepting forgeries as genuine

probability

signatures, and the later represents the error rate of

information is taken into account. Further more, a

rejecting genuine signatures.

distinct characteristic for the presented approach

The FAR and the FRR can be represented as a

compared with the others methods based on the HMM

function of the decision threshold. The trade-off-curve

is that an ergodic model with bounded states duration

of the FAR and the FRR for the proposed approach is

is adopted, so this model can describe the handwriting

shown in Figure 4.

process more accurately. At last, experimental results

estimators

is

that

the

contextual

validate the presented method is promising and competing.


The possible improvement on this work mainly lies in

321

[9] Edmondo Trentin, Marco Gori. A Survey of Hybrid

two aspects: 1) The combination of this approach with

HMM/ANN

other methods such as comparison of the global

Recognition.

Models

for

Automatic

Speech

features; 2) Fusion of the decision. There are several

[10] Herve Bourlard, Nelson Morgan. Hybrid HMM/ANN

verifiers combined in this paper, and the decision

Systems for Speech Recognition: Overview and New

making based on the combined verification is

Research Directions. Adaptive Processing, LNAI 1387,

straightforward which need more investigation for

389-417, 1998.

improvement. And these will be our future works.

[11] Richard, M.D. and Lippmann, R.P. Neural Network Classifiers Estimate Bayesian a Posteriori Probabilities. Neural Computation, (3): 461-483, 1991. [12] Heme Bourlard, and Christian J. Wellekens, Links

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Zhong-Hua Quan received the Bachelor and Master degree of military

in

HeFei

Artillery

Academy of the PLA, in 1994 and 2003, respectively. From Sept. 2003 on, in pursuit for Doctor degree in Pattern Recognition & Intelligent System in USTC.

Kun-Hong Liu received the B.S. and M.S. degree in the School

of

Physics

OptoElectronics Technology of Fujian Normal University in June 1999 and June 2004, respectively. From Sept. 2005 on, in pursuit for Doctor’s degree in Pattern Recognition & Intelligent System in University of Science & Technology of China, Hefei