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
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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
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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
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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
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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)
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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).
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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
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B. Dorizzi
)
1
(
)
1
(
)
(
)
(
t
t
t
t
•
Cosine and sine of the angle which estimates the
(t)
variation :
Contextual (shape) parameters
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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
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B. Dorizzi
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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.
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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
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B. Dorizzi
Figure associated to the spatial
features
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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
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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
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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
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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.
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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
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B. Dorizzi
Mise en comparaison de 3 signatures d’une même personne
S
1
, S
2
, S
3
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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.
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B. Dorizzi
Writer Modelization by Hidden
Markov model
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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
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B. Dorizzi
What is a HMM?
state 1
state 2
state 3
O = (O
1
,..., O
t
,...)
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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.
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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
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B. Dorizzi
Markovian modelization of a signature
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Learning phase
•
A process allowing the reestimation of the
parameters of the HMM, in order to
maximize the loglikelihood of the true
signatures.
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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
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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
.
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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
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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
.
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