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05/12/03

B. Dorizzi



On
-
line Signature Identity
Verification

Bernadette

Dorizzi,


GET/INT,

9

rue

Charles

Fourier,

91011

Evry

Bernadette.Dorizzi@int
-
evry.fr

05/12/03

B. Dorizzi

Outline


Generalities


Preprocessing


Feature extraction


Models :



Cooperation local/global : Kashi 98


DTW (Jain : 2002)


HMM (Rigoll, Dolfing, Salicetti)


Evaluation : Signature Competition at Conf SVC
2004


05/12/03

B. Dorizzi

On
-
line signatures


Acquisition on an electronic tablet or with a
special pen, able to record a sequence of points
(speed and pression of the signature, not only the
static image)


Interest : behavioral more than physiological,
difficult to imitate.


Highly variable intra
-
class characteristics :
enrollment will necessitate several samples of the
signature

05/12/03

B. Dorizzi

Recognition

General scheme

Sequence of points

Sequence of features

A signature of

a claimed client X

Learning

Use of the samples of the

signature of X to create

a model of X

The signature is presented at the
input of the model of X and a
similiraty measure is computed.

Comparison to a threshold allows
to accept or discard the signature

05/12/03

B. Dorizzi

Signature samples

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B. Dorizzi

Performance evaluation

Two types of errors

FR=False Rejection FA=False Acceptation


FRR=

Nb of FR

Nb of clients

FAR=

Nb ofFA

Nb of imposteurs

TER=

Nb of FR

+

Nb of FA

Total acces Nb

05/12/03

B. Dorizzi

Performance curves

FRR

High
security

ROC curve

In order to make a decision a

threshold has to be settled

EER: Equal Error rate

FAR

Low security

FRR

FAR

EER (equal error rate)

Threshold

05/12/03

B. Dorizzi

Data acquisition


Depends on the capabilities of the hardware


High
-
end tablet : robust pressure sensibility, precise pen pressure
measure, measure of the pen orientation


PDA : only coordinates and information on pen
-
up, pen
-
down


Coordinates : x(t),y(t)


Pressure p(t)


Orientation
q
(t),
y
(t)

05/12/03

B. Dorizzi

Preprocessings


Resampling and smoothing of the trajectory


Between 100 and 150 points per second (too many
points, noise)


Low
-
pass Filtering (the low frequencies carry the
information)


Apparent contradiction : point spacing on the trajectory . If
irregular (dependant on the speed of the signing process)
one capture the speed. But, in some parts of the trajectory
there are very few points, thus little spatial information.
(cf. Jain cf comprise between the 2).

05/12/03

B. Dorizzi

Local and contextual features


Speed in
x

and
y
direction


Acceleration in
x

et
y
direction


Tangential Acceleration


Cosine et sine of angle


:

)
(
)
(
)
(
cos
t
v
t
v
t
x


)
(
)
(
)
(
sin
t
v
t
v
t
y


dynamical parameters

The signature is considered as a sequence of points. A vector of features


is computed at
each point of the trajectory

05/12/03

B. Dorizzi

)
1
(
)
1
(
)
(
)
(





t
t
t
t





Cosine and sine of the angle which estimates the

(t)

variation :


Contextual (shape) parameters

05/12/03

B. Dorizzi

Global Features

(Kashi et al., IJDAR 98)


Mixture of both shape and dynamical features


2 time
-
related features : total signature time, ratio of pen
-
down
time to total time


6 other dynamic features depends on the writing velocity and
acceleration


13 shape
-
related features


The signature is considered as a whole

05/12/03

B. Dorizzi

05/12/03

B. Dorizzi

Dolfing approach

Philips Research Laboratory


The signature is split into different portions (part of the trajectory
between 2 values of de v
y
=0)






To each portion is associated a vector of 32 features

The signature is considered as a sequence of points, these points are

regrouped in several sub
-
parts . A feature vector is associated

to each sub
-
part.

05/12/03

B. Dorizzi

Feature Description


13 spatial features


13 dynamic features


6 contextual features


Spatial features
:


sin and cos of the starting and ending angles : thetastart,
thetaend


3 intermediate angles


Aspect ratio


La curvature


Existance of a pen
-
up


05/12/03

B. Dorizzi

Figure associated to the spatial
features

05/12/03

B. Dorizzi

Dynamic features


Number of samples nt


min, max, moy of speed v


acceleration a


pressure p


variation of pressure delta p


vmax
-
vmoy


pen
-
tilt with 2 angles


05/12/03

B. Dorizzi

Contextual features


Sin et cos of angles psi1, psi2, psi3 which are the angles of the 3 lignes
with x axe which start from the gravity center of the current portion
towards the gravity center of the 3 preceeding segments.

seg1

seg2

seg3

Seg courant

05/12/03

B. Dorizzi

Several Models of the signatures and
associated similarity measures


«

A Hidden Markov Model approach to online handwritten
signature verification

», Kashi et al, IJDAR 1998.
Computation of a global distance between 1 signature and a
set of references signatures of writer i.


«

On
-
line signature verification

», Jain et al. , Pattern
Recognition, 2002 . DTW to compare two signatures
considered as 2 sequences of features.


Rigoll, Dolfing, Salicetti etc… : Modelization by a HMM of
each writer (several signatures considered as sequences of
features are considered) : computation of a likelihood
measure for a signature to be produced by the HMM of
writer i


05/12/03

B. Dorizzi

Global feature
-
based verification

Kashi et al.


A signature model for entrant i is a set of means
m

and standard
deviations
s
, obtained during training from 6 instances of signatures


Error measure E
i

for a given signature claimed to be that of i:





N is the total number of global features


M
i,k

is the value of the K
-
th feature of the signature to verify



m

i,k

and
sm

i,k

are the mean and standard deviation of feature k over
the reference set of i.

05/12/03

B. Dorizzi

Dynamic Time Warping


Local features are computed at each point of the trajectory


A signature = a string (sequence of feature vectors)


A signature model for a person is composed of 3 different samples of the
signature


String matching (DTW Dynamic Time Warping) allows the comparison of
strings of different lengths.


Finds an alignment between the points in the 2 strings such that the sum of the
differences between each pair of aligned points is minimal


To find the minimal difference, all possible alignments must be investigated.


Dynamic programming is a method to implement that


05/12/03

B. Dorizzi

Mise en comparaison de 3 signatures d’une même personne

S
1
, S
2
, S
3

05/12/03

B. Dorizzi

Verification


A test signature is compared to the model of signer i (represented by 3
signatures).


3 possible strategies : minimum of all the dissimilarity values, average of all
the dissimilarity values, maximum of all the dissimilarity values


Decision : comparison of this value to a threshold


The threshold can be identical for all the writers or set individually for each
writer.


In this article, no forgeries data is used to calculate the thresholds.


05/12/03

B. Dorizzi

Writer Modelization by Hidden
Markov model

05/12/03

B. Dorizzi

What is a HMM?



Non deterministic automata with one or
several states


A double stochastic process



A Markov chain representing the states of the
HMM:
S = {S
1
, S
2
, S
3
,……S
N
}




A process which induces a sequence of observations

05/12/03

B. Dorizzi

What is a HMM?

state 1

state 2

state 3

O = (O
1
,..., O
t
,...)

05/12/03

B. Dorizzi

Why a HMM?


The different signatures of a same writer are
variable. This variability will be well
modelized by a HMM.


This modelization will allow to consider a
non stationary signal (the signature) as a
piecewise
-
stationary signal.

05/12/03

B. Dorizzi

Components of a HMM


N
: number of states in the model:

S = {S
1
, S
2
,……,S
N
}


A
: Matrix of probability transitions

a
ij
=P[q
t+1
=S
j
|q
t
=S
i
], 1


i, j


N



Initial distribution of the states
:


i

= P[q
1

= S
i
], 1


i


N


Emission law of the observations in each state
B
j
(O
t
)=P[O
t
|q
t
=S
j
], 1

j


N


Discrete HMM: B
j

is a matrix


Continuous HMM: B
j

is a mixture of gaussian probalility
density functions

05/12/03

B. Dorizzi

Markovian modelization of a signature

05/12/03

B. Dorizzi

Learning phase


A process allowing the reestimation of the
parameters of the HMM, in order to
maximize the loglikelihood of the true
signatures.

05/12/03

B. Dorizzi

Signature Verification


Comparison of the loglikelihood of the signature,
knowing the HMM model


of the writer, with a
threshold in order to take the decision


«Distance»

decision threshold


Accept if
|Log(P(S|

)
-

L
mean
)|<

, otherwise reject
where

L
mean
= mean loglikelihood on the learning
database of the declared i client.

MMC

of the writer

Signature

Log
-
likelihood

05/12/03

B. Dorizzi

Systems Evaluation


Difficult because of the non availability of common databases : A lot of
«

home
-
made

» databases with no connection between them (between 9 and
100 individuals).


In general the EER lies between 1% and 6%


Evaluation in presence of forgeries of more or less good qualities (skilled, over
the shoulder, random, rough etc…)


For instance, the Philips data base (very difficult due to the presence of high
quality imitations, including dynamics)


1500 true signatures sur 51 persons,


1470 imitations «

over the shoulder

»


1530 imitations «

home enhanced

»


240 professional imitations


Non identical evaluation protocols : personal threshold versus global one


The threshold is generally determined in order that FAR=FRR (EER Equal
Error Rate) or in order to minimize TER (Equal Error Rate) on a development
database (some signers that will not be considered in the test base) using
forgeries
.


05/12/03

B. Dorizzi

SVC 2004


First International Signature Verification Competition


In conjunction with the First International Conference on Biometric
Authentication in Hong Kong (ICBA 2004)


Two tasks:


Coordinate input only


Coordinate, pen orientation and pressure inputs


Database for each task:100 writers


Training set:


5 among 20 genuine signatures per writer


Evaluation set:


Unknown

genuine signatures per writer


20 skilled forgeries from 5 other contributors

05/12/03

B. Dorizzi

Conclusion


Signature scan : a quite variable modality,
resistant to forgeries, well accepted, but not
suitable for each person


Not so many applications :


Natural with PDA, in banking contexts


Some tools already available : smartpen,
etc…

05/12/03

B. Dorizzi

References


J.G.A. Dolfing, "Handwriting recognition and verification, a Hidden Markov approach",
Ph.D. thesis, Philips Electronics N.V., 1998.


M
.

Fuentes,

S
.

Garcia
-
Salicetti,

B
.

Dorizzi

"On
-
line

Signature

Verification

:

Fusion

of

a

Hidden

Markov

Model

and

a

Neural

Network

via

a

Support

Vector

Machine",

IWFHR
8
,

Août

2002
.


J
.

Ortega
-
Garcia,

J
.

Gonzalez
-
Rodriguez,

D
.

Simon
-
Zorita,

S
.

Cruz
-
Llanas,

"From

Biometrics

Technology

to

Applications

regarding

face,

voice,

signature

and

fingerprint

Recognition

Systems",

in

Biometrics

Solutions

for

Authentication

in

an

E
-
World,

(D
.

Zhang,

ed
.
),

pp
.

289
-
337
,

Kluwer

Academic

Publishers,

July

2002
.



A
.

Jain,

F

D
.

Griess,

S
.
D
.

Connell

«

On
-
line

signature

verification

»,

Pattern

Recognition,

,

vol

35
,

pp
.
2963
-
2972
,

2002


J
.
G
.
A
.

Dolfing,

"On
-
line

signature

verification

with

Hidden

Markov

Models",

Proc
.

of

ICDAR,

pp
.

1309
-
1312
,

1998
.



R
.

Kashi,

J
.

Hu,

W
.
L
.

Nelson,

W
.

Turin,

"A

Hidden

Markov

Model

approach

to

online

handwritten

signature

verification",

Intl
.

J
.

on

Document

Analysis

and

Recognition,

Vol
.

1
,

pp
.

102
-
109
,

1998
.



G
.

Rigoll,

A
.

Kosmala,

"A

systematic

comparison

of

on
-
line

and

off
-
line

methods

for

signature

verification

with

Hidden

Markov

Models",

Proc
.

of

ICPR,

pp
.

1755
-
1757
,

1998
.