Li S.Z., Jain A.K. (eds.) Encyclopedia of Biometrics

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Off-line signature features

Off-line signature veriﬁcation systems usually rely

on image processing and shape recognition techni-

ques to extract features. As a consequence, additional

preprocessing steps such as image segme ntation and

binarization must be carried out. Features are

extracted from gray-scale images, binarized images,

or skeletonized images, among other possibilities.

The proposed feature sets in the literature are nota-

bly heterogeneous, specially when compared with the

case of on-line veriﬁcation systems. These include,

among others, the usage of image transforms (e.g.,

Hadamard), morphological operators, structural

representations,

▶ graphometr ic features [14], direc-

tional histograms, and geometric features. Readers are

referred to [15] for an exhaustive listing of off-line

signature features.

Related Entries

▶ Feature Extraction

▶ Off-line Signature Veriﬁcation

▶ On-line Signature Veriﬁcation

▶ Signature Matching

▶ Signature Recognition

References

1. Plamondon, R., Lorette, G.: Automatic signature veriﬁcation

and writer identiﬁcation: the state of the art. Pattern Recogn.

22(2), 107–131 (1989)

2. Lei, H., Govindaraju, V.: A comparative study on the consistency

of features in on-line signature veriﬁcation. Pattern Recogn. Lett.

26(15), 2483–2489 (2005)

Signature Features. Table 2 Extended set of local features. The upper dot notation (e.g., x

) indicates time derivative

# Feature Description

1 x-coordinate x

2 y-coordinate y

3 Pen-pressure z

4 Path-tangent angle y

¼arctan(y

∕ x

)

5 Path velocity magnitude

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

6 Log curvature radius r

¼log(1 ∕ k

)¼log(υ

∕

), where k

is the curvature of the

position trajectory

7 Total acceleration magnitude

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ c

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ u

, where t

and c

are respectively the

tangential and centripetal acceleration components of the pen

motion

8 Pen azimuth g

9 Pen altitude f

10–18 First-order derivative of features 1–9 x

19–27 Second-order derivative of features 1–9

€

28 Ratio of the minimum over the maximum

speed over a window of 5 samples

¼min {υ

n4

,...,υ

} ∕max {υ

n4

,...,υ

}

29–30 Angle of consecutive samples and first

order difference

¼arctan(y

y

n1

∕x

x

n1

)

31 Sine s

¼sin(a

)

32 Cosine c

¼cos(a

)

33 Stroke length to width ratio over a window

of 5 samples

k¼n

k¼n4

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ðx

x

k1

þðy

y

k1

max x

n4

;:::;x

fgmin x

n4

;:::;x

34 Stroke length to width ratio over a window

of 7 samples

k¼n

k¼n6

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ðx

x

k1

þðy

y

k1

max x

n6

;:::;x

fgmin x

n6

;:::;x

1190

Signature Features

3. Richiardi, J., Ketabdar, H., Drygajlo, A.: Local and global feature

selection for on-line signature veriﬁcation. In: Proceedings of

IAPR eighth International Conference on Document Analysis

and Recognition, ICDAR, Seoul, Korea (2005)

4. Kholmatov, A., Yanikoglu, B.: Identity authentication using im-

proved online signature veriﬁcation method. Pattern Recogn.

Lett. 26(15), 2400–2408 (2005)

5. Fi errez, J., Ramos-Castro, D., Ortega-Garcia, J., Gonzalez-

Rodriguez, J.: HMM-based on-line signature veriﬁcation: feature

extraction and signature modeling. Pattern Recogn. Lett. 28(16),

2325–2334 (2007)

6. Fierrez-Aguilar, J., Nanni, L., Lopez-Penalba, J., Ortega-Garcia, J.,

Maltoni, D.: An on-line signature veriﬁcation system based on

fusion of local and global information. In: Proceedings of IAPR

Signature Features. Figure 3 Examples of functions from the 27-feature set presented in Table 2 for a genuine signature

(left) and a forgery (right) of a particular subject.

Signature Features

1191

International Conference on Audio- and Video-Based Biometric

P erson Authentication, AVBPA, Springer LNCS-3546, pp. 523–532

(2005)

7. Jain, A.K., Zongker, D.: Feature selection: evaluation, applica-

tion, and small sample performance. IEEE Trans. Pattern Anal.

Mach. Intell. 19(2), 153–158 (1997)

8. Nelson, W., Turin, W., Hastie, T.: Statistical methods for on-line

signature veriﬁcation. Int. J. Pattern Recogn. Artif. Intell. 8(3),

749–770 (1994)

9. Lee, L.L., Berger, T., Aviczer, E.: Reliable on-line human signa-

ture veriﬁcation systems. IEEE Trans. Pattern Anal. Mach. Intell.

18(6), 643–647 (1996)

10. Dolﬁng, J.G.A., Aarts, E.H.L., van Oosterhout, J.J.G.M.: On-line

signature veriﬁcation with Hidden Markov Models. In: Proceed-

ings of the International Conference on Pattern Recognition,

IEEE Press, pp. 1309–1312 (1998)

11. Van, B.L., Garcia-Salicetti, S., Dorizzi, B.: On using the Viterbi

path along with HMM likelihood information for online signa-

ture veriﬁcation. IEEE Trans. Syst. Man Cybern. B 37(5),

1237–1247 (2007)

12. Muramatsu, D., Matsumoto, T.: Effectiveness of pen pressure,

azimuth, and altitude features for online signature veriﬁcation.

In: Proceedings of IAPR International Conference on

Biometrics, ICB, Springer LNCS 4642 (2007)

13. Martinez-Diaz,M.,Fierrez,J.,Galbally,J.,Ortega-Garcia,J.:Towards

mobile authentication using dynamic signature veriﬁcation: use-

ful features and performance evaluation. In: Proceedings Interna-

tional Conference on Pattern Recognition, ICPR, pp. 1–6 (2008)

14. Sabourin, R.: In: Off-line signature veriﬁcation: recent advances

and perspectives. Lect. Notes Comput. Sci. 1339 84–98 (1997)

15. Impedovo, D., Pirlo, G.: Automatic signature veriﬁcation: The

state of the art. IEEE Trans. Syst. Man Cybern. C Appl. Rev.

38(5), 609–635 (2008)

Signature Matching

MARCOS MARTINEZ-DIAZ

,JULIAN FIERREZ

EIICHIRO HANGAI

Biometric Recognition Group - ATVS, Escuela

Politecnica Superior, Universidad Autonoma de

Madrid, Madrid, Spain

Department of Electrical Engine ering Tokyo

University of Science, Japan

Synonyms

Signature similarit y computation

Definition

The objective of signature matching techniques is to

compute the similarity between a given signature and a

signature model or reference signature set. Several pat-

tern recognition techniques have been proposed as

matching algorithms for signature recognition. In on-

line signature veriﬁcation systems, signature matching

algorithms have followed two main approaches. Fea-

ture-based algorithms usually compute the similarity

among multidimensional feature vectors extracted

from the signature data w ith statistical classiﬁcation

techniques. On the other hand, function-based algo-

rithms perform matching by computing the distance

among time-sequences extracted from the signa-

ture data with technique such as Hidden Markov Mod-

els and Dynamic Time Warping. Off-line signature

matching has followed many different approaches,

most of which are related to image processing and

shape recognition.

This essay focuses on on-l ine signature matching,

although off-line signature matching algorithms are

brieﬂy outlined.

Introduction

As in other biometric modalities, signature matching

techniques vary depending on the nature of the features

that are extracted from the signature data. In feature-

based systems (also known as global), each signature

is represented as a multidimensional feature vector,

while in function-based systems (also known as local)

signatures are represented by multidimensional time

sequences. Signature matching algorithms also depend

on the enrollment phase. Model-based systems estimate

a statistical model for each user from the training

signature set. On the other hand, in reference-based

systems the features extracted from the set of training

signatures are stored as a set of template signatures.

Consequently, given an input signature, in model-

based systems the matching is performed against a

statistical model, while in reference-based systems the

input signature is compared with all the signatures

available in the

▶ reference set.

Feature-Based Systems

Feature-based systems usually employ classical pattern

classiﬁcation techniques. In refere nce-based systems, the

▶ matching score is commonly obtained by using a dis-

tance measure between the feature vectors of input and

template signatures [1, 2], or a trained classiﬁer. Distance

1192

Signature Matching

measures used for signature matching include Eucli

dean, weighted Euclidean, and Mahalanobis distance. In

model-based systems, trained classiﬁers are emplo yed,

including approaches such as Neural Networks, Gaussian

Mixtur e Models [3] or Parzen Windows [4].

Function-Based Systems

In these systems, multidimensional time sequences

extracted from the signature dynamics are used as fea-

tures. Given the similarity of this task to others related to

speaker rec ognition, the most popular approaches

in local signature veriﬁcation are related to algorithms

proposed in the speech recognition community.

Among these, signature veriﬁcation systems using

▶ Dynamic Time Warping (DTW) [5, 6, 7] or Hidden

Markov Models (HMM) [8, 9, 10 , 11] are the most

popular approaches in signature veriﬁcation. In such

systems, the captured time functions (e.g., pen coordi-

nates, pressure, etc.) are used to model each user sig-

nature. In the following, Dynamic Time Warping and

Hidden Markov Models are outlined. An brief over-

view of other techniques is also given.

Dynamic Time Warping

▶ Dynamic Time Warping (DTW) is an application of

the Dynamic Programming principles to the problem

of matching discrete time sequences. DTW was origi-

nally proposed for speech recognition applications

[12]. The goal of DTW is to ﬁnd an elastic match

among samples of a pair of sequences X and Y that

minimizes a predeﬁned distance measure. The algo-

rithm is described as follows. Let’s deﬁne two

sequences

X ¼ x

; x

; :::; x

Y ¼ y

; y

; :::; y

ð1Þ

and a distance measure as

dði; jÞ¼ x

 y



ð2Þ

between sequence samples. A warping path can be

deﬁned as

C ¼ c

; c

; :::; c

ð3Þ

where each c

represents a correspondence (i, j) be-

tween samples of X and Y . The initi al condition of the

algorithm is set to

¼ gð1; 1Þ¼dð1; 1Þwð1Þð4Þ

where g

represents the accumulated distance after

k steps and w(k) is a weighting factor that must be

deﬁned. For each iteration, g

is computed as

¼ g ði; jÞ¼min

k1

þ dð c

ÞwðkÞ



ð5Þ

until the Ith and Jth sample of both sequences respec-

tively is reached. The resulting normalized distance is

DðX; Y Þ¼

k¼1

wðkÞ

ð6Þ

where ∑ w(k) compensates the effect of the length of

the sequences.

The weighting factors w(k) are deﬁned in order to

restrict which correspondences among samples of both

sequences are allowed. In Fig. 1a, a common deﬁnition

of w(k) is depicted, and an example of a warping path

between two sequences is given. In this case, only three

transitions are allowed in the computation of g

. Con-

sequen tly, Eq. (5 ) becomes

¼ gði; jÞ¼min

gði; j  1Þþdði; jÞ

gði  1; j  1Þþ2dði; jÞ

gði  1; jÞþdði; jÞ

ð7Þ

which is one of the most common implementations

found in the literature. In Fig. 1b, an example of point

correspondences between two signatures is depicted to

visually show the results of the elastic alignment.

The algorithm has been further reﬁned for signa-

ture veriﬁcation by many authors [5, 7], reaching a

notable veriﬁcation performance. For example, the

distance measure d(i, j) can be alternatively deﬁned,

or other normalization techniques may be applied

to the accumulated distance g

among sequences.

DTW can be also applied independently for each

stroke, which may be specially well suited for oriental

signatures, since they are generally composed of seve-

ral strokes. Although the DTW algorithm has been

replaced in speech-related applications by more pow-

erful approaches such as HMMs, it remains as a highly

effective tool for signature veriﬁcation as it is best

suited for small amounts of training data, which is

the common case in signature veriﬁcation.

Hidden Markov Models

Hidden Markov Models (HMM) have been widely

used for speech recognition applications [13] as well

Signature Matching

1193

as in many handwriting recognition applications.

Several approaches using HMMs for dynamic signa-

ture veriﬁcation have been proposed in the last years

[8, 9, 10, 11]. An HMM represents a double stochas-

tic process, governed by an underlying Markov

chain, with a ﬁnite number of states and a random

function set that generate symbols or observations

each of which is associated with one state [11].

Observations in each state are modeled with GMMs

in most speech and handwriting recognition applica-

tions. In fact, GMMs can be considered a single-state

HMM and have also been successfully used for signa-

ture veriﬁcation [14]. Given a seque nce of multi-

dimensional vectors of observations O deﬁned as

O ¼ o

; o

; ...; o

;

corresponding to a given signature, the goal of HMM-

based signature matching is to ﬁnd the probability that

this sequence has been produced by a Hidden Markov

Model M

PðOjMÞ;

where M is the signature model computed during

enrollment.

The basic structure of an HMM using GMMs to

model observations is deﬁned by the following elements:



Number of hidden states N.



Number of Gaussian mixtures per state M.



Probability transition matrix A ¼ {a

}, which con-

tains the probabilities of jumping from one state to

another or staying on the same state.

In Fig. 2, an example of a possible HMM con-

ﬁguration is shown. Hidden Markov Models are

usually trained in two steps using the enrollment

signatures. First, state transition probabilities and

observation statistical models are estimated using

a Maximum Likelihood algorithm. After this, a re-

estimation step is carried out using the Baum-Welch

algorithm. The likelihood between a trained HMM

and an input sequence (i.e., the matching score) is

computed by using the Viterbi algorithm. In [10],

the Viterbi path (that is, the most probable state tran-

sition sequence) is also used as a similarity measure.

A detailed description of Hidden Markov Models is

given in [13].

Within HMM-based dynamic signature veriﬁca-

tion, the existing approaches can be divided in regional

and local. In regional approaches, the extracted time

Signature Matching. Figure 1 (a) Optimal warping path between two sequences obtained with DTW. Point-to-point

distances are represented with different shades of gray, lighter shades representing shorter distances and darker

shades representing longer distances. (b) Example of point-to-point correspondences between two genuine

signatures obtained using DTW.

1194

Signature Matching

sequences are further segmented and converted into

a sequence of feature vectors or observations, each

one representing regional properties of the signature

signal [9, 11]. Some examples of segmentation bound-

aries are null vertical velocity points [9] or changes in

the quantized trajectory direction [11]. On the other

hand, local approaches directly use the time functions

as obse rvation sequences for the signature modeling

[8, 10, 14].

Finding a reliable and robust model struc ture for

dynamic signature veriﬁcation is not a trivial task.

While too simple HMMs may not allow to model

properly the user signatures, too complex models

may not be able to model future realizations due to

overﬁtting. On the other hand, as simple models have

less parameters to be estimated, their estimation may

be more robust than for complex models. Two main

parameters are commonly considered while selecting

an optimal mode l structure: the number of states and

the number of Gaussian mixtures per state [8]. Some

approaches consider a user-speciﬁc number of states

[10], proportional to the average signature duration or

a user-speciﬁc number of mixtures [14]. Most of the

proposed systems consider a left-ro-right conﬁgura-

tion without skips between states, also known as

Bakis topolog y (see Fig. 2).

Other Techniques

More examples of signature matching techniques in-

clude Neural Networks, in particular Bayesian,

multilayer, time-delay Neural Networks and radial-

basis functions among others have been applied for

signature matching. Other examples include Structural

approaches, which model signatures as a sequence, tree

or graph of symbols. Support Vector Machines have

also been applied for signature matc hing. The reader is

referred to [15] for an exhaustive list of references

related to these approaches.

Fusion of the feature- and function-based

approaches has been reported to provide better perfor-

mance than the individual systems [4].

Off-line Signature Matching

The proposed approaches for off-li ne signature match-

ing are notably heterogeneous compared to on-line

signature veriﬁcation. These are mostly related to

image and shape recognition techniques and classical

statistical pattern recognition algorithms. They include

Neural Networks, Hidden Markov Models, Support

Vector Machines and distance-based classiﬁers among

others. A summary of off-line signature matching tech-

niques can be found in [15].

Related Entries

▶ Off-line Signature Veriﬁcation

▶ On-line Signature Veriﬁcation

▶ Signature Features

▶ Signature Recognition

Signature Matching. Figure 2 Graphical representation of a left-to-right N-state HMM, with M-component GMMs

representing observations and no skips between states.

Signature Matching

1195

References

1. Nelson, W., Turin, W., Hastie, T.: Statistical methods for on-line

signature veriﬁcation. Int. J. Pattern Recogn. Artif. Intell. 8(3),

749–770 (1994)

2. Lee, L.L., Berger, T., Aviczer, E.: Reliable on-line human signa-

ture veriﬁcation systems. IEEE Trans. Pattern Anal. Mach. Intell.

18(6), 643–647 (1996)

3. Martinez-Diaz, M., Fierrez, J., Ortega-Garcia, J.: Universal Back-

ground Models for dynamic signature veriﬁcation. In: Proceed-

ings IEEE Conference on Biometrics: Theory, Applications and

Systems, BTAS, pp. 1–6 (2007)

4. Fierrez-Aguilar, J., Nanni, L., Lopez-Penalba, J., Ortega-Garcia, J.,

Maltoni, D.: An on-line signature veriﬁcation system based

on fusion of local and global information. In: Proceedings

of IAPR International Conference on Audio- and Video-Based

Biometric Person Authentication, AVBPA, Springer LNCS-3546,

pp. 523–532 (2005)

5. Sato, Y., Kogure, K.: Online signature veriﬁcation based on

shape, motion and writing pressure. In: Proceedings of sixth

International Conference on Pattern Recognition, pp. 823–826

(1982)

6. Martens, R., Claesen, L.: Dynamic programming optimisation

for on-line signature veriﬁcation. In: Proceedings fourth Inter-

national Conference on Document Analysis and Recognition,

ICDAR, vol. 2, pp. 653–656 (1997)

7. Kholmatov, A., Yanikoglu, B.: Identity authentication using im-

proved online signature veriﬁcation method. Pattern Recogn.

Lett. 26(15), 2400–2408 (2005)

8. Fierrez, J., Ramos-Castro, D., Ortega-Garcia, J., Gonzalez-

Rodriguez, J.: HMM-based on-line signature veriﬁcation:

feature extraction and signature modeling. Pattern Recogn.

Lett. 28(16), 2325–2334 (2007)

9. Dolﬁng, J.G.A., Aarts, E.H.L., van Oosterhout, J.J.G.M.: On-line

signature veriﬁcation with Hidden Markov Models. In: Proceed-

ings of the International Conference on Pattern Recognition,

ICPR, pp. 1309–1312. IEEE CS Press (1998)

10. Van, B.L., Garcia-Salicetti, S., Dorizzi, B.: On using the Viterbi

path along with HMM likelihood information for online signa-

ture veriﬁcation. IEEE Trans. Syst. Man Cybern. B 37(5),

1237–1247 (2007)

11. Yang, L., Widjaja, B.K., Prasad, R.: Application of Hidden

Markov Models for signature veriﬁcation. Pattern Recogn.

28(2), 161–170 (1995)

12. Sakoe, H., Chiba, S.: Dynamic programming algorithm optimi-

zation for spoken word recognition. IEEE Trans. Acoust. 26,

43–49 (1978)

13. Rabiner, L.R.: A tutorial on Hidden Markov Models and selected

applications in speech recognition. Proceedings of the IEEE

77(2), 257–286 (1989)

14. Richiardi, J., Drygajlo, A.: Gaussian Mixture Models for

on-line signature veriﬁcation. In: Proceedings of ACM SIGMM

Workshop on Biometric Methods and Applications, WBMA.

pp. 115–122 (2003)

15. Impedovo, D., Pirlo, G.: Automatic signature veriﬁcation: The

state of the art. IEEE Trans. Syst. Man. Cybern. C Appl. Rev.

38(5), 609–635 (2008)

Signature Recognition

OLAF HENNIGER

,DAIGO MURAMATSU

AKASHI MATSUMOTO

,ISAO YOSHIMURA

ITSU YOSHIMURA

Fraunhofer Institute for Secure Information

Technology, Darmstadt, Germany

Seikei University, Musashino-shi, Tokyo, Japan

Waseda University, Shinjuku-ku, Tokyo, Japan

Tokyo University of Science, Shinjuku-ku, Tokyo,

Japan

Ritsumeikan University, Sakyo-ku, Kyoto, Japan

Synonyms

Handwritten signature recognition; signature/sign

recognition

Definition

A si gnature is a handwritten representation of name of

a person. Writing a signature is the established method

for authentication and for expressing deliberate deci-

sions of the signer in many areas of life, such as banking

or the conclusion of legal contracts. A related concept is

a handwritten personal sign depicting something else

than a person’s name. As compared to text-independent

writer recognition methods, signature/sign recognition

goes with shorter handwriting probes, but requires to

write the same name or personal sign every time. Hand-

written signatures and personal signs belong to the

behavioral biometric characteristics as the person must

become active for signing.

Regarding the automated recognition by means of

handwritten signatures, there is a distinction between

on-line and off-line signature recognition. On-line sig-

nature data are captured using digitizing pen tablets,

pen displays, touch screens, or speci al pens and include

information about the pen movement over time (at

least the coordinates of the pen tip and possibly also the

pen-tip pressure or pen orientation angles over time).

In this way, on-line signature data represent the way a

signature is written, which is also referred to as signa-

ture dynamics. By contrast, off-line (or static) signa-

tures are captured as grey-scale images using devices

such as image scanners and lack temporal information.

1196

Signature Recognition

Overview

Off-line and On-line Signatures

A number of features that are suitable for automated

comparison can be extracted from handwritten signa-

tures. The features depend on the ty pe of data captured

and the chosen comparison method. Handwriting data

can be classiﬁed into



on-line data captured during the writing process

using devices such as digitizing tablets, Tablet PC’s,

or special pens



off-line data captured from paper after the writing

process using devices such as image scanners or

cameras

Dynamic information, like

▶ stroke order, writing

▶ speed, and ▶ pen pressure, is available in on-line

data, whereas only static information, like the shapes

of handwritten characters, is available in off-line data.

There is a multitude of methods for comparing hand-

written signatures, see under on-line signatures and

off-line signatures below.

Applications

Handwritten signatures are generally used for veriﬁca-

tion (conﬁrming a claimed identity through one-to-

one comparisons of biometric features), but rarely for

identiﬁcation (ﬁnding identiﬁers attributable to a per-

son through one-to-many search among biometric

features in a large database) [1]. Handwritten signa-

tures have been used for a long time for authentication

purposes in many applications, such as credit cards,

banking transactions, agreements, and legal documents.

Off-line signature serve as a unique means to verify the

authenticity of a person through past records, such as

signatures on traveler’s cheques.

Strengths and Weaknesses

In order that handwritten signatures are useable for

recognizing persons, genuine signatures (i.e. signatures

written by the persons themselves whose names they

represent) need to be sufﬁciently repeatable over time

with respect to the comparison criteria, and forgeries

(i.e. signatures not written by the persons themselves

whose names they represent) need to be distinguish-

able from the genuine signatures by means of the

comparison criteria [2]. As for some persons the hand-

written signatures may vary considerably from signa-

ture to signature, the permanence of handwritten

signatures is considered lower than that of many phys-

iological biometric characteristics. As forgers can learn

with some effort how to imitate the signatures of their

victims, also the distinctiveness of handwritten signa-

tures is lower than that of many physiological biomet-

ric characteristics. However, forging the signature

dynamics is considerably harder than just forging the

signature shape [3, 4] because information about the

signature dynamics is less easily accessible to potential

forgers than information about the signature shape.

The strengths of handw ritten signatures compared

to other biometric characteristics lie in a high level and

wide spread of user acceptance and in the fact that

handwritten signatures are regarded as an evidence of

a deliberate decision on the part of the signer. Further-

more, people can modify their signatures in case of

successful forgeries. By contrast, physiological biomet-

ric characteristics such as ﬁngerprints or irises cannot

be modiﬁed.

Performance Testing of Signature

Verification Systems

Types of Testing

Users may obtain feedback (accepted or rejected) from

the signature veriﬁcation system, which then inﬂuences

their subsequent input signatures. Genuine users will

become accustomed to the system, and forgers w ill use

this feedback to improve their signatures. Thus, in

order to determine the performance in practice, sce-

nario tests and operational tests (where users input

signatures to a prototype or operational veriﬁcation

system) are preferable. Such tests, however, are expen-

sive and time consuming, and it is extremely difﬁcult to

conduct tests on a large population. Moreover, since

the decision threshold of the system must be ﬁxed, we

cannot evaluate the overall performance of the system.

Tests on databases can be easily conducted and a

large population can be tested. Moreover, such tests

can be conducted under the same conditions whenever

needed, and we can compare the different sy stems and

evaluate the overall performance of a system by assum-

ing different decision thresholds. Thus, technology

Signature Recognition

1197

tests using pre-existing or specially collected databases

of genuine signatures and forgeries are useful to develop

practical systems.

Neither scenario nor technology tests, by itself, are

sufﬁcient to evaluate the actual performance. There-

fore, both tests should be conducted to estimate the

performance of the system in practice.

Evaluation Protocol

The performance of a signature recognition system

depends on the writing conditions and instruments,

skill of writers, required level of similarity for accep-

tance or rejection, and precision and reliability of tem-

plates. The performance of a system is also highly

dependent on the quality of the sample images to be

veriﬁed. Thus, the design and conﬁguration of the test

should be carefully considered when performing eval-

uation experiments:



The number of training signatures input during

enrollment: 3–20 training signatures, or more,

have generally been used in previous studies. For

instance, in [5], ﬁve signatures were used for

training.



Selection method of training signatures from a da-

tabase: Some researchers select training signatures

randomly from genuine signatures, and some

researchers select them from the ﬁrst several signa-

tures of the ﬁrst session. Considering the actual

situation, it is reasonable to select the ﬁrst several

signatures for training. In [ 5], genuine signatures

were collected from two sessions, and training sig-

natures were randomly selected from the ﬁrst ses-

sion. This process was repeated ten times.



Types of forgeries available for training: In general,

skilled forgeries are not available, and thus, genuine

signatures of other peop le are used as random for-

geries. In [5], skilled forgeries were not supplied for

training.



Parameters of decision threshold: Some researchers

determine the parameters for the decision thresh-

old using all of the data, including test data, and

other researchers determine them using only train-

ing data. In the former case, the evaluated result is

termed ‘‘ideal’’ [6].

Forgery Data

The measured false match rate, which is useful for

predicting the forgery resistance of a signature

recognition system, depends on the degree of effort

with which signatures of other persons are tried to be

imitated. Different types of signature forgeries requir-

ing different skill levels can be distinguished, such as:



Random forgery (also accidental forgery or zero-

effort impostor attempt) where an impostor with-

out knowledge of the genuine signature presents

any handwriting



Simple forgery where an impostor with knowledge

of the genuine signature mimics it from memory

without practice



Simulated forger y where an impostor traces a genu-

ine signature without prior practice



Skilled forgery where an impostor mimics the gen-

uine signature after practicing

The quality of skilled forgeries depends on the capa-

bility of the forgers, what kind of information they

know, how they practice, and how motivated they are.

False match rates measured based on zero-effort

impostor attempts, where impostors submit their

own biometric characteristics while claiming to be

someone else, are meaningful for biometric systems

based on physiological characteristics, but are of less

relevance for predicting the forgery resistance of signa-

ture recognition systems where impostors can easily

take action to inﬂuence the outcome of recognition

attempts in their favor. A skilled forgery is the most

difﬁcult to distinguish from a gen uine signature.

Therefore, for a reliable prediction of the forgery resis-

tance of signature recognition systems, the measure-

ment of false match rates should be based on skilled

forgeries. In [5], random forgeries and skilled forgeries

were separately used for evaluation.

Signature Databases

For many years, there were no publicly available data-

bases. Therefore, each researcher needed to generate

his or her own private databases and evaluate algo-

rithms using them. These databases were not shared

with other researchers, and thus, it was difﬁcult to

compare the performance of algorithms under the

same conditions. This is due to the difﬁculty in

providing forgeries that possess a sufﬁcient level of

quality. Forgers, imposters, and seasoned document

examiners refuse to or are reluctant to furnish evidence

of skillful forgery because such evidence is considered

valuable private property.

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Signature Recognition

In the meantime, several on-line signature data-

bases have been developed and made available by sev-

eral research groups. For example, databases collected

by Munich and Perona [7], MCYT [8], BIOMET [9],

SVC2004 [5], and MYIDEA [10] are available. These

databases contain genuine signatures and skilled for-

geries of varying quality. Forgeries in some databases

were written by forgers who knew dynamic informa-

tion about genuine signatures, whereas forgeries in

other databases were written by forgers who knew

only shape information about genuine signatures.

Practical experience with respect to forgeries on bank

cheques may be accumulated in places such as Brazil, or

in criminal science studies in police institutions [11].

Databases are useful to compare different signature

recognition algorithms. However, each database is col-

lected based on a different policy, and they inevitably

differ in nature. Thus, evaluation using only a database

is not sufﬁcient to determine the overall perf ormance.

Off-line Signatures

Introduction

Off-line signature recognition is the recognition of

handwritten signatures based on a two-dimensional

gray image obtained by an item of equipment such as

a scanner, an optical reader, or a digitizer. Figure 1

depicts an example of an off-line signature.

Since the invention of writing in human society,

the signature on a document (or picture, including

monochrome brush painting) has been the most com-

mon means of authenticating the writer (or painter)

of the document (or picture). Not only leaders but

also persons accorded with responsibility in various

capacities have had to put their signatures on paper

and recognize those of the others. Thus, signature

recognition has naturally been done off-line. It is only

with the recent development of an on-line technology

for biometric recognition that the relevance of off-line

recognition has been reduced. The relative character-

istics of on-line and off-line methods of signature

recognition will be di scussed later.

The written name of the writer was originally used

as signature. In the course of the traditional use of

signatures, people started including symbols and dis-

torting them in order to increase their uniqueness and

beauty. In general, this made it impossible to recover

the writers’ names from such signatures. Further, some

signatures, like names, are merely personal signs that

help establish authenticity. In this sense, off-line signa-

ture recognition merely entails pattern recognition of

questionable images on a two-dimensional space by

referring to registered reference images, which may be

reduced to a template [3, 12, 2].

The following sections describe the basic modules

of the recognition procedure (i.e. data capture, prepro-

cessing, quality assessment, feature extraction, format-

ting, comparison, decision) for off-line signatures [13].

Basic Operation

Cutting off

In this module, a rectangular space containing the

entire image is identiﬁed, and the gray image of this

area is acquired using an appropriate item of equip-

ment such as a scanner.

Preprocessing

The size of questionable images is not always the sam e

as that of the reference images. Normalizing the size of

a questionable image is necessary in order to compare

it with templates and thereby facilitate recognition.

The background color of the sheet is not always

white. In fact, all cheques contain colored patterns for

preventing counterfeits, as shown in Fig. 2 [14]. As a

result, eliminating the effect of the background pattern

and the adjustment of gray levels is inevitable in pre-

processing. In general, the binarizing of gray levels up

to a certain threshold is preferred to obtain a steady

performance of the system .

Normalizing the angle to the baseline (if it exists)

proves to be effective in adjusting the signature

Signature Recognition. Figure 1 Off-line signature image.

Signature Recognition

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