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forgeries. There is not a ﬁxed number of forgeries avail-

able for each user. Over-the-shoulder forgeries were

produced by letting the forger observe the signing pro-

cess. Home-improved forgeries were produced by giving

to the forgers samples of the signature static image and

letting them to practice at home. Professional forgeries

were performed by forensic document examiners.

MCYT Bimodal Database

The MCYT bimodal database is comprised of signatures

and ﬁngerprints from 330 individuals [2]. Signa-

tures were acquired using a Wacom Intuos A6 tablet

with a sampling frequency of 100 Hz. The users signed

repeatedly on a paper with a printed grid placed over the

pen tablet. The following time sequences are captured:

position coordinates, pressure, azimuth, and altitude.

There are 25 genuin e signatures and 25 forgeries

per user, leading to 16,500 signatures in the database.

For each user, signatures were captured in groups of 5.

First, 5 genuine signatures, then 5 forgeries from an-

other user, repeating this sequence until 25 signatures

from each type, were performed. Each user provided 5

forgeries for the 5 previous users in the database. As

the user is forced to concentrate on different tasks

between each group of genuine signatures, the varia-

bility between groups is expected to be higher than the

one within the same group.

Genuine signatures and forgeries corresponding

to 75 users from the MCYT database were scanned

and are also available as an off-line signature database.

This signature corpus is one of the most popular for the

evaluation of signature veriﬁcation algorithms that are

being used by more than 50 research groups worldwide.

BIOMET Multimodal Database

The BIOMET multimodal database [6] is comprised of

ﬁve modalities: audio (voice), face, hand, ﬁngerprint,

and signature. The signatures were captured using

a Wacom Intuos2 A6 pen tablet and an ink pen with

a sampling rate of 100 Hz. The pen coordinates,

pen-pressure, azimuth, and altitude signals were cap-

tured. The database contains data from 84 users , with

15 genuine signatures and up to 12 forgeries per user.

Signatures were captured in two sessions separate d by

3–5 months. In the ﬁrst session, 5 genuine signatures

and 6 forgeries were acquired. The remaining 10

genuine signatures and 6 forgeries were captured in

the second session. Forgeries are performed by 4 dif-

ferent users (3 forgeries each). This database contains

2,201 signatures, since not all users have complete data:

8 genuine signatu res and 54 forgeries are missing.

SVC2004 Database

Two signature databases were released prior to the

Signature Veriﬁcation Competition (SVC) 2004 [7]

for algorithm development and tuning . They were

captured using a Wacom Intuos digitizing tablet and

a Grip Pen. Due to privacy issues, users were advised to

use invented signatures as genuine ones. Nevertheless,

users were asked to thoroughly practice their invented

signatures to reach a reasonable level of spatial and

temporal consistency.

The two databases differ in the available data, and

correspond to the two tasks deﬁned in the competi-

tion. One contains only pen position information,

while the other provides pressure and pen orientation

(azimuth and altitude) signals also. Each database con-

tains 40 users, with 20 genuine signatures and 20 for-

geries per user acquired in two sessions, leading to

1,600 signatures per database. Forgeries for each user

were produced by at least four other users, aided by a

visual too l, which represented the signature dynamics

on a display. Both occidental and asian signatures are

present in the databases.

SUSIG Database

The SUSIG database consists of two sets: one cap-

tured using a pen tablet w ithout v isual feedback

(Blind subcorpus) and the othe r using a pen tablet

with an LCD display (Visual subcorpus) [8]. There are

100 users per database, but these do not coincide,

as the Visual subcorpus was captured 4 years after

the Blind one. For the Blind subcorpus, a WACOM

Graphire2 pen tablet was used. The Visual subcorpus

was acquired using an Interlink Electronics ePad-ink

tablet, with a pressure-sensitive LCD. In both subcor-

pora, the pen coordinates and the pen pressure si gnals

were captured using a sampling frequency of 100 Hz.

While performing forgeries, users had prior visual

input of the signing process on a separate screen or

on the LCD display for the Blind and Visual subcorpus

respectively.

1180

Signature Databases and Evaluation

For the Blind subcorpus, 8 or 10 genuine signatures

were captured in a single session. The users also

provided 10 forgeries from another randomly selected

user. Two sessions were performed in the Visual sub-

corpus. During each one, users provided 10 genuine

signatures and 5 forgeries.

MyIDea Multimodal Database

This signature set is a subset of the MyIDea Multimod-

al Biometric Database [9]. AWacom Intuos2 A4 graph-

ic tablet was used at a sampling rate of 100 Hz. Pen

position, pressure, azimuth, and altitude signals were

captured. This data set has the particularity that the

user must read loud what he is writing, allowing what

the aut hors call CHASM (Combined Handwriting and

Speech Modalities). This corpus consists of ca. 70 users.

Signatures were captured in 3 sessions. During each

session, each user performed 6 genuine signatures

and 6 forgeries, with visual access to the images of the

target signatures.

BiosecurID Multimodal Database

This database was collected by 6 different Spanish

research institutions [3]. It includes the following bio-

metric traits: speech, iris, face, signature, handwriting,

ﬁngerprints, hand, and keystroke. The data were cap-

tured in 4 sessions distributed in a 4 month time span.

The user population was speciﬁcally selected to contain

a uniform distribution of users from different ages

and genders. Nonbiometric data were also stored,

such as age, gender, handedness, vision aids, and man-

ual worker (if the user has eroded ﬁngerprints). This

allows studying speciﬁc demographic groups.

The signature pen-position, pressure, azimuth, and

altitude signals were acquired using a Wacom Intuos3

A4 digitizer at 100 Hz. During each session, two sig-

natures were captured at the beginning and two at the

end, leading to 16 genuine signatures per user. Each

user performed one forgery per session of signatures

from other three users in the database. The skill level

of the forgeries is increased by showing to the forger

more information of the target signature incremen-

tally. In the ﬁrst session, forgers have only visual access

to one genuine signature; more data (i.e., signature

dynamics) are shown in further sessions and forgers

are let more time to train. Off-line signature data are

also available, since signatures were captured using an

inking pen.

BioSecure Multimodal Database

The BioSecure Multimodal Database was collected by

11 European institutions under the BioSecure Network

of Excellence [10]. It has three data sets captured in

different scenarios: DS1 was captured remotely over

the internet, DS2 was acquired in a desktop environ-

ment, and DS3 under mobile conditions. The database

covers face, ﬁngerprint, hand, iris, signature, and

speech modalities and includes two signature subcor-

pora corresponding to the DS2 and DS3 data sets.

These two data sets were produced by the same group

of 667 users. The DS2 data set was captured using a

Wacom Intuos3 A6 digitizer at 100 Hz and an ink pen

while the user was sitting. On the other hand, the DS3

data set was captured with a PDA. Users were asked to

sign while standing and holding the PDA in one hand,

emulating realistic operating conditions. An HP iPAQ

hx2790 with a sampling frequency of 100 Hz was used

as capture device. The pen position, pressure, azimuth,

and altitude signals are available in DS2, while only the

pen position is available on DS3 due to the nature of

the PDA touch-screen.

Signatures were captured in two sessions and in

blocks of 5. An average of two months was left be-

tween eac h session. During each session, users were

asked to perform 3 sets of 5 genuine signatures and

5 forgeries between each set. Following this protocol,

each user performed 5 forgeries for the previous 4

users in the database. Thus, 30 genuine signatures and

20 forgeries are available for each user. Forgeries are

collected in a ‘‘worst case’’ scenario. For DS2, the

users had visual access to the dynamics of the signing

process of the signatures they had to forge on a com-

puter screen. In DS3, each forge r had access to the

dynamics of the genuine signature on the PDA screen

and a tracker tool allowing to see the original strokes.

Some users were even allowed to sign following the

strokes produced by the tracker tool, reproducing

thus the geometr y and dynamics of the forged signa-

ture with high accu racy.

The DS3 data set is the ﬁrst multisession database

captured on a PDA and represents a very challenging

database [11]. Apart from the high accuracy of the

Signature Databases and Evaluation

1181

forgeries, signatures from DS3 present sampling errors

and irregular sampling rates. Moreover, pen posi-

tion signals during pen-ups are not available, since

the acquisition device captures the pen dynamics only

when the PDA stylus is in contact with the touch-

screen surface.

The capture process for both DS2 and DS3 is shown

in Fig. 1. Examples of signatures from the BioSecure

Signature subcorpora corresponding to DS2 and DS3

are presented in Fig. 2. Unconnected samples represent

that at least one sample is missing between them due to

sampling errors.

In Table 1, the main features of the described sig-

nature databases are presented.

Signature Verification Evaluation

Campaigns

Despite the usage of a common database, one of the

main difﬁculties when comparing the performance of

different biometric systems is the different experimen-

tal conditions, under which each system is evaluated by

its designers. To overcome these difﬁculties, evalua-

tions and competitions provide a common reference

for system comparison on the same database and pro-

tocol. Public evaluations in the ﬁeld of automatic sig-

nature veriﬁcation are less common than for other

biometric modalities such as ﬁngerprint or speech.

In particular, only evaluations for the on-line signature

veriﬁcation modalit y have been proposed. These in-

clude the Signature Veriﬁcation Competition (SVC),

which took place in 2004 [7], the signature modality of

the BioSecure Multomodal Evaluation Campaign held

in 2007 [12], and the BioSecure Signature Evaluation

Campaign in 2009 [13].

Signature Verification Compe tition

(SVC 2004)

The Signature Veriﬁcation Competition (SVC 2004)

represents the ﬁrst public evaluation campaign in the

ﬁeld of signature veriﬁcation [7]. The competition was

divided into two tasks, depending on the available

signature signals. In Task 1, only the pen position

signals (x,y) and the sample timestamps were available.

In Task 2, the pen pressure p and azimuth and altitude

angles (y,g) were also available. Participants had prior

access to a signature dataset for each task. These data

sets were later released for public access, and are

referred to as the SVC2004 database. Signatures from

40 users are present in each data set. This evaluation

has the particularity that users were advised to use

invented signatures because of privacy issues. More-

over, they did not have visual feedback from the sign-

ing process, since signatures were captu red with a

digitizing tablet and a special pen.

The evaluation results were ﬁrst released to par-

ticipants, which then had the choice to remain anony-

mous. The best Equal Error Rate (EER) in Task 1

was of 2.84% against

▶ skilled forgeries and 1.85%

for

▶ random forgeries. In Task 2 (which included

pressure and pen-inclination signals), the lowest

EERs were 2.89% against skilled forgeries and 1.70%

against random forgeries.

Signature Databases and Evaluation. Figure 1 PDA signature capture process in the BioSecure DS3 - Mobile Scenario

dataset (left) and pen-tablet capture process in the BioSecure DS2 - Access Control Scenario dataset (right). The

acquisition setup and paper template used in DS2 is similar to the ones used in MCYT, BIOMET, MyIDea and BiosecurID.

1182

Signature Databases and Evaluation

BioSecure Multimodal Evaluation

Campaign (BMEC 2007)

The BioSecure Multimodal Evaluation Campaign

(BMEC) was held in 2007 with the aim of compar-

ing the performance of veriﬁcation systems from

different research groups on individual biometric

modalities and fusion scenarios [14]. Two scenarios

were considered: access control and mobile condi-

tions. In particular, the Mobile Scenario consisted of

four modalities and fusion, using a subset of the

BioSecure Multimodal Database DS3 captured on

mobile conditions (i.e., using portable devices such

as a PDA).

Signature Databases and Evaluation. Figure 2 Examples of signatures and associated signals from the BioSecure

Multimodal Database DS2 and DS3 signature subcorpora captured using a pen tablet (top) and a PDA (bottom),

respectively. As can be seen, there are missing samples for the signature captured with PDA, and no signals are available

during pen-ups, contrary to the pen-tablet case.

Signature Databases and Evaluation

1183

In this evaluation, a signature subset from the Bio-

Secure Multimodal DS3 database was used. A set of

signatures from 50 users was previously released to

participants for algorithm development and tuning.

For each user, 20 genuine signatures (15 from the ﬁrst

session and 5 from the second) as well as 20 forgeries

were available.

Eleven signature veriﬁcation systems from seven

independent European research institution s were pre-

sented to the evaluation. The results of the evaluation

and a description of each system that participated can

be found in [12]. Another evaluation study in similar

conditions, including a comparative analysis with

respect to the BMEC participants, can be found in

[11]. The best Equal Error Rate (E ER) in the evalua-

tion was of 4.03% for random forgeries and of 13.43%

for skilled forgeries. The relatively high EER for skilled

forgeries reveals the high quality of the forgerie s

acquired in this database.

BioSecure Signature Evaluation Campaign

(BSEC 2009)

The BioSecure Signature Evaluation Campaign is

aimed at measuring the impac t of mobile acquisition

conditions, time variability, and the information con-

tent of signatures in the performance of veriﬁcation

algorithms [13]. Signature subsets from the BioSecure

Multimodal Databases DS2 (pen tablet) and DS3 (PDA

touch-screen) corresponding to 50 users have been

released to participants prior to the evaluation. At the

time of publication, the results of the evaluation cam-

paign are still not available.

Related Entries

▶ Biometric Sample Acquisition

▶ Off-line signature veriﬁcation

▶ Performance Evaluation, Overview

▶ Signature Recognition

References

1. Munich, M.E., Perona, P.: Visual identiﬁcation by signature

tracking. IEEE Trans. Pattern Anal. Mach. Intell. 25(2),

200–217 (2003)

2. Ortega-Garcia, J., Fierrez-Aguilar, et al.: MCYT baseline corpus:

a bimodal biometric database. IEE Proc. Vis. Image Signal Pro-

cess. 150(6), 391–401 (2003)

3. Fierrez, J., Galbally, J., Ortega-Garcia, J., Freire, M.R., Alonso-

Fernandez, F., Ramos, D., Toledano, D.T., Gonzalez-Rodriguez,

J., Siguenza, J.A., Garrido-Salas, J., Anguiano-Rey, E., de Rivera,

G.G., Ribalda, R., Faundez-Zanuy, M., Ortega, J.A., Cardenoso-

Payo, V., Viloria, A., Vivaracho, C.E., Moro, Q.I., Igarza, J.J.,

Sanchez, J., Hernaez, I., Orrite-Urunuela, C., Martinez-Contreras,

F., Gracia-Roche, J.J.: Biosecurid: A multimodal biometric data-

base. Pattern Analysis & Applications (to appear) (2009)

Signature Databases and Evaluation. Table 1 Summary of the most popular on-line signature databases. The symbols

x,y,p,y,g denote pen position horizontal coordinate, vertical coordinate, pen pressure, azimuth and altitude respectively

Name Device Users Sessions

Signatures per user

Signals Interval between sessionsGenuine Forgeries

PHILIPS Pen tablet 51 3–5 30 up to 70 x,y,p,y,g 1 week approx.

BIOMET Pen tablet 84 3 15 up to 12 x,y,p,y,g 3–5 months

MCYT Pen tablet 330 1 25 25 x,y,p,y,g -

SVC2004 Task 1 Pen tablet 40 2 20 20 x,y min. 1 week

SVC2004 Task 2 Pen tablet 40 2 20 20 x,y,p,y,g min. 1 week

SUSIG Blind Subcorpus Pen tablet 100 1 8 or 10 10 x,y,p -

SUSIG Visual Subcorpus Pen tablet 100 2 20 10 x,y,p 1 week approx.

MyIDea Pen tablet ca. 100 3 18 18 x,y,p,y,g days to months

BioSecurID Pen tablet 400 4 16 16 x,y,p,y,g

1 month approx.

BioSecure DS2 Pen tablet ca. 650 2 30 20 x,y,p,y,g 1 month approx.

BioSecure DS3 PDA ca. 650 2 30 20 x,y,p,y,g 1 month approx.

1184

Signature Databases and Evaluation

4. Vargas, J., Ferrer, M., Travieso, C., Alonso, J.: Off-line hand-

written signature GPDS-960 corpus. In: Proceedings of ninth

International Conference on Document Analysis and Recogni-

tion, ICDAR, vol. 2, pp. 764–768. Curituba, Brazil (2007)

5. Dolﬁng, J.G.A., Aarts, E.H.L., van Oosterhout, J.J.G.M.:

On-line signature veriﬁcation with Hidden Markov Models.

In: Proceedings of the International Conference on Pattern

Recognition, ICPR, pp. 1309–1312. IEEE CS Press. Brisbane,

Australia (1998)

6. Garcia-Salicetti, S., Beumier, C., Chollet, G., Dorizzi, B., Jardins,

J.L.L., Lanter, J., Ni, Y., Petrovska-Delacretaz, D.: BIOMET: A

multimodal person authentication database including face,

voice, ﬁngerprint, hand and signature modalities. In: Proceed-

ings of IAPR International Conference on Audio- and Video-

based Person Authentication, AVBPA, pp. 845–853. Springer

LNCS-2688. Brisbane, Australia (2003)

7. Yeung, D.Y., Chang, H., Xiong, Y., George, S., Kashi, R.,

Matsumoto, T., Rigoll, G.: SVC2004: First international signa-

ture veriﬁcation competition. In: Proceedings of International

Conference on Biometric Authentication, ICBA, pp. 16–22.

Springer LNCS-3072 (2004)

8. Kholmatov, A., Yanikoglu, B.: Newblock Susig: an on-line signa-

ture database, associated protocols and benchmark results. Pat-

tern Analysis & Applications (2008)

9. Dumas, B., Pugin, C., Hennebert, J., Petrovska-Delacretaz, D.,

Humm, A., Evequoz, F., Ingold, R., Rotz, D.V.: MyIDea -

multimodal biometrics database, description of acquisition pro-

tocols. In: Proceedings of third COST 275 Workshop (COST

275), pp. 59–62. Hatﬁeld, UK (2005)

10. Association BioSecure: BioSecure multimodal database. (http://

www.biosecure.info) (2007). Last Accessed 03 March, 2009

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

Towards mobile authentication using dynamic signature veriﬁ-

cation: useful features and performance evaluation. In: Proc.

Intl. Conf. on Pattern Recognition, ICPR pp. 1–6 (2008)

12. TELECOM & Management SudParis: BioSecure Multimodal Eval-

uation Campaign 2007 Mobile Scenario - experimental results.

Tech. rep. (2007). (http://biometrics.it-sudparis.eu/BMEC2007/

ﬁles/Results_mobile.pdf). Last Accessed 03 March, 2009

13. TELECOM & Management SudParis: Biosecure Signature

Evaluation Campaign, BSEC 2009. http://biometrics.it-sudparis.

eu/BSEC2009. URL http://biometrics.it-sudparis.eu/BSEC2009

14. Alonso-Fernandez, F., Fierrez, J., Ramos, D ., Ortega-Garcia, J .:

Dealing with sensor interope rabil ity in multi-bi ometr ics: the

UPM experience at the BioSecure Multimodal E valuation 2007.

In: Defense and Security Symposium, Biometric Technologies

forHumanIdentiﬁcation,BTHI,Proc.SPIE,vol.6944.Orlando,

USA (2008)

Signature Dataset

▶ Signature Databases and Evaluation

Signature Features

MARCOS MARTINEZ-DIAZ

,JULIAN FIERREZ

EIICHIRO HANGAI

Biometric Recognition Group - ATVS, Escuela

Politecnica Superior, Universidad Autonoma de Madrid,

Campus de Cantoblanco, Madrid, Spain

Department of Electrical Engine ering, Tokyo

University of Science, Japan

Synonyms

Signature characteristics

Definition

Signature features represent magnitudes that are extrac-

ted from digitized signature samples, with the aim of

describing each signature as a vector of values. The

extraction and selection of optimum signature features

is a crucial step when designing a veriﬁcation system.

Features must allow each signature to be described in a

way that the discriminative power between signatures

produced by different users is maximized while allowing

variability among signatures from the same user.

On-line signature features can be divided into two

main types. Global features model the signature as

a holistic multidimensional vector and represent mag-

nitudes such as average speed, total duration, and

aspect ratio. On the other hand, local features are

time-functions derived from the signals, such as the

pen-position coordinate sequence or pressure signals,

captured with digitizer tablets or touch-screens.

In off-line signature veriﬁcation systems, features

are extracted from a static signature image. They can

also be classiﬁed as global, if they consider the imag e as

a whole (e.g., image histogram, signature aspect ratio);

or local, if they are obtained from smaller image

regions (e.g., local orientation histogram s).

This entry is focused on on-line signature features,

although a brief outline of off-line signature features

is also given.

Introduction

Several approaches to extract discriminative informa-

tion from on-line signature data have been proposed

Signature Features

1185

intheliterature[1]. The existing systems can be broadly

divided into two main types: Global systems, in which a

holistic vector representation consisting of a set of

global features (e.g., signature duration, direction

after ﬁrst pen-up) is derived from the signa ture trajec-

tories [2, 3], and function-based systems, in which time

sequences describing local properties of the signature

are used for recognition [4, 5], (e.g., position, acceler-

ation). Although recent works show that global

approaches are competitive with respect to local meth-

ods in some circumstances [6], the latter approach has

traditionally yielded better results. Despite this advan-

tage, systems based on local features usually employ

matching algorithms, which are computationally more

expensive than global-feature ones.

Due to the usually low amount of training data

in signature veriﬁcation,

▶ feature selection techniques

must be applied in order to reduce the feature vector

dimensionality. These techniques allow of ﬁnding the

optimal feature set for each system or scenario [7].

Feature extraction and preprocessing

Signature features are, in general, extracted from

the time functions captured from the pen dynamics

while an individual signs. In most cases, the capture

of time functions from the handwritten signature

is carried out with acquisition devices such as digitiz-

ing tablets or touch-screens. These devices provide

pen position information (i.e. horizontal x and verti-

cal y coordinates), and in some cases, pen pressure

z and pen inclination (

▶ azimuth and ▶ altitude).

A diagram showing the nature of the captured signals

and an example of the signals from a real signature

are shown in Fig. 1. Other less common examples of

on-line signature acquisition devices are special pens

with dedicated hardware inside that captures signa-

ture data such as coordinate, force, or velocity

information.

The sampling rate of these devices is, in general, bet-

ween 100 and 200 Hz. Since the maximum frequencies

of the pen movements during handwriting are 20-30 Hz

[1], these sampling rates satisfy the Nyquist criterion.

Preprocessing steps before feature extraction may

be performed, such as position, size and rotation nor-

malization, noise ﬁltering, or resampling. In some

works, resampling is avoided as it degrades the velocity

related features [4].

Global features

Global feature-based systems describe each signature

as a multidimensional vector where each element

consists on a feature extrac ted from the whole pen

trajectory. Many feature sets have been proposed in

the literature [2, 3, 8, 9], with variable sizes and a

maximum size of 100 features [6]. Due to the train-

ing data scarcity and adverse effects of the curse of

dimensionality, feature selection techniques must be

applied to reduce the feature vector size. In Table 1,

the 100 features described in [6] are presented.

This global feature set includes most of the features

described in previous works from other authors.

Features are arrange d in the order of descending

individual discriminative power. In Fig. 2, examples

of the distribution of global features presented in

Table 1 are shown.

Local features

Local features represent time sequences extracted

from the signature raw captured data. A set of local

features leads to a multidimensional discrete se-

quence that describes a signature. Depending on the

matching algorithm, feature sets of vary ing sizes have

been proposed in the literature. As a rule of thumb,

Dynamic Time Warping-based algorithms employ

few loc al features, while systems b ased on Hidden

Markov Models or Gaussian Mixture Models employ

larger feature sets. In Table 2, the most popular local

features found in the literature are presented [2, 3, 4, 5,

10, 11, 12].

As in the case of global features, feature selection

algorithms must be applied to discriminate the best

performing feature set. Usually, small feature sets are

selected for Dynamic Time Warping-based matching

algorithms. In these systems, speed-related features

extracted from the ﬁrst derivative of the pen-coordi-

nate time sequences (features 10-11 in Table 2) have

shown to be very effective [4]. On the other hand,

larger feature sets are used when Hidden Markov or

Gaussian Mixture Models are employed [5, 11] for

signature matching. Features related to second-order

derivatives (features 19-27 in Table 2) have not proved

to signiﬁcantly improve the system veriﬁcation perfor-

mance [3]. Examples of the local features presented in

Table 2 are depicted in Fig. 3.

1186

Signature Features

The usage of features related to pen orientation

(azimuth and altitude) is a subject of controversy.

Although some authors report that these features in-

crease the veriﬁcation performance [12], others have

reported a low discriminative power fo r these features

[2]. Moreover, these features are not always available,

since many touch-screen acquisition devices such as

Tablet-PCs or PDAs are unable to capture pen orienta-

tion information.

The fusion of the global and local feature-based

systems has been reported to provide better perfor-

mance than the individual systems [6].

Signature Features. Figure 1 (a) Representation of the position, azimuth and altitude of the pen with respect to the

capture device. (b) Example of raw captured data from a signature.

Signature Features

1187

Signature Features. Table 1 Set of global features sorted by individual discriminative power (T denotes time interval,

t denotes time instant, N denotes number of events, y denotes angle. Note that some symbols are deﬁned in different

features of the table (e.g., D in feature 7 is deﬁned in feature 15)

Ranking Feature Description Ranking Feature Description

1 signature total duration T

2 N(pen-ups)

3 N(sign changes of dx∕dt and dy∕dt) 4 average jerk



5 standard deviation of a

6 standard deviation of v

7 (standard deviation of y)/D

8 N(local maxima in x)

9 standard deviation of a

10 standard deviation of v

11 j

rms

12 N(local maxima in y)

13 t(2nd pen-down)∕T

14 (average velocity



v)/v

x,max

min

¼ðy

max

y

min

Þðx

max

x

min

ðD

pendowns

i¼1

ðx

max ji

x

min ji

ÞÞD

16 (x

last pen-up

x

max

)∕D

17 (x

1st pen-down

x

min

)∕D

18 (y

last pen-up

y

min

)∕D

19 (y

1st pen-down

y

min

)∕D

20 (T

v)∕(y

max

y

min

)

21 (T



v)∕(x

max

x

min

) 22 (pen-down duration T

)/T



v ∕v

y,max

24 (y

last pen-up

y

max

)∕D

Tððdy=dtÞ=ðdx=dtÞ>0Þ

Tððdy=dtÞ=ðdx=dtÞ<0Þ



v ∕v

max

27 (y

1st pen-down

y

max

)∕D

28 (x

last pen-up

x

min

)∕D

29 (velocity rms v)/v

max

ðx

max

x

min

ÞD

ðy

max

y

min

ÞD

31 (velocity correlation v

x,y

)/v

max

32 T(v

>0jpen-up)∕T

33 N( v

¼0) 34 direction histogram s

35 (y

2nd local max

y

1st pen-down

)∕D

36 (x

max

x

min

)/x

acquisition range

37 (x

1st pen-down

x

max

)∕D

38 T(curvature>Threshold

curv

)∕T

39 (integrated abs. centr. acc. a

)/a

max

40 T(v

>0)∕T

41 T(v

<0jpen-up)∕T

42 T(v

>0jpen-up)∕T

43 (x

3rd local max

x

1st pen-down

)∕D

44 N(v

¼0)

45 (acceleration rms a)/a

max

46 (standard deviation of x)/D

Tððdx=dtÞðdy=dtÞ>0Þ

Tððdx=dtÞðdy=dtÞ<0Þ

48 (tangential acceleration rms a

)/a

max

49 (x

2nd local max

x

1st pen-down

)∕D

50 T(v

<0jpen-up)∕T

51 direction histogram s

52 t(3rd pen-down)∕T

53 (max distance between points)∕A

min

54 (y

3rd local max

y

1st pen-down

)∕D

55 (



x x

min

)∕



x 56 direction histogram s

57 direction histogram s

58 T(v

<0)∕T

59 T(v

>0)∕T

60 T(v

<0)∕T

61 direction histogram s

62 (1st t(v

x,min

))/T

63 direction histogram s

64 T(1st pen-up)∕T

65 spatial histogram t

66 direction histogram s

67 (y

max

y

min

)/y

acquisition range

68 (1st t(v

x,max

))/T

69 (centripetal acceleration rms a

)/a

max

70 spatial histogram t

71 y(1st to 2nd pen-down) 72 y(1st pen-down to 2nd pen-up)

73 direction histogram s

74 t(j

x,max

)∕T

75 spatial histogram t

76 j

x,max

77 y(1st pen-down to last pen-up) 78 y(1st pen-down to 1st pen-up)

79 (1st t(x

max

))/T



81 T(2nd pen-up)∕T

82 (1st t(v

max

))/T

1188

Signature Features

Signature Features. Table 1 (Continued)

Ranking Feature Description Ranking Feature Description

83 j

y,max

84 y(2nd pen-down to 2nd pen-up)

85 j

max

86 spatial histogram t

87 (1st t(v

y,min

))/T

88 (2nd t(x

max

))/T

89 (3rd t(x

max

))/T

90 (1st t(v

y,max

))/T

91 t(j

max

)∕T

92 t(j

y,max

)∕T

93 direction change histogram c

94 (3rd t(y

max

))/T

95 direction change histogram c



97 direction change histogram c

98 y(initial direction)

99 y(before last pen-up) 100 (2nd t(y

max

))/T

Signature Features. Figure 2 Examples of genuine signatures and forgeries (left) and scatter plots of 4 different

global features from the 100-feature set presented in Table 1 (right). The signatures belong to the BioSecure database

and the Figure has been adapted from [13].

Signature Features

1189