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In this paper we propose a new method for generating synthetic handwritten signature images for biometric applications. The procedures we introduce imitate the mechanism of motor equivalence which divides human handwriting into two steps: the working out of an effector independent action plan and its execution via the corresponding neuromuscular path. The action plan is represented as a trajectory on a spatial grid. This contains both the signature text and its flourish, if there is one. The neuromuscular path is simulated by applying a kinematic Kaiser filter to the trajectory plan. The length of the filter depends on the pen speed which is generated using a scalar version of the sigma lognormal model. An ink deposition model, applied pixel by pixel to the pen trajectory, provides realistic static signature images. The lexical and morphological properties of the synthesized signatures as well as the range of the synthesis parameters have been estimated from real databases of real signatures such as the MCYT Off-line and the GPDS960GraySignature corpuses. The performance experiments show that by tuning only four parameters it is possible to generate synthetic identities with different stability and forgers with different skills. Therefore it is possible to create datasets of synthetic signatures with a performance similar to databases of real signatures. Moreover, we can customize the created dataset to produce skilled forgeries or simple forgeries which are easier to detect, depending on what the researcher needs. Perceptual evaluation gives an average confusion of 44.06% between real and synthetic signatures which shows the realism of the synthetic ones. The utility of the synthesized signatures is demonstrated by studying the influence of the pen type and number of users on an automatic signature verifier.
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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, MANUSCRIPT ID 1
Static Signature Synthesis: A Neuromotor
Inspired Approach for Biometrics
Miguel A. Ferrer, Moises Diaz-Cabrera and Aythami Morales
Abstract—In this paper we propose a new method for generating synthetic handwritten signature images for biometric
applications. The procedures we introduce imitate the mechanism of motor equivalence which divides human handwriting into
two steps: the working out of an effector independent action plan and its execution via the corresponding neuromuscular path.
The action plan is represented as a trajectory on a spatial grid. This contains both the signature text and its flourish, if there is
one. The neuromuscular path is simulated by applying a kinematic Kaiser filter to the trajectory plan. The length of the filter
depends on the pen speed which is generated using a scalar version of the sigma lognormal model. An ink deposition model,
applied pixel by pixel to the pen trajectory, provides realistic static signature images. The lexical and morphological properties of
the synthesized signatures as well as the range of the synthesis parameters have been estimated from real databases of real
signatures such as the MCYT Off-line and the GPDS960GraySignature corpuses. The performance experiments show that by
tuning only four parameters it is possible to generate synthetic identities with different stability and forgers with different skills.
Therefore it is possible to create datasets of synthetic signatures with a performance similar to databases of real signatures.
Moreover, we can customize the created dataset to produce skilled forgeries or simple forgeries which are easier to detect,
depending on what the researcher needs. Perceptual evaluation gives an average confusion of 44.06% between real and
synthetic signatures which shows the realism of the synthetic ones. The utility of the synthesized signatures is demonstrated by
studying the influence of the pen type and number of users on an automatic signature verifier.
Index Terms—Biometric recognition, off-line signature verification, synthetic generation, motor equivalence theory, kinematic
theory of human movements, ink deposition model.
—————————— ——————————
1 INTRODUCTION
HE use of biometric traits has become well-established
in commerce and forensics [1]. The most commonly
used traits for identification or verification are the face [2],
the fingerprint [3] and the iris [4]. Among the most chal-
lenging biometrics are those related to human behavior
because of their unpredictable variability. It is well-
established that during the early stages of development
the human neuromotor system learns a way of writing,
walking, key stroking, etc. that contains a sort of ‘water
mark for the person’s identity. This water mark is diffi-
cult to imitate or disguise by a forger because of the dif-
ferences between individuals neuromuscular systems.
This therefore gives a theoretical advantage to these be-
havioral biometrics. It is, however, enormously difficult
to detect and characterize this water mark. This is because
of both the relatively few samples generally available and
the inherent variability of human behavior. This can
change not only for psychological reasons but also be-
cause of the adaptation of different postures, the wearing
of different dress, the use of different writing tools and
for other unaccountable factors.
In a behavioral biometric such as the handwritten sig-
nature, research nowadays tends to focus on improving
recognition accuracy, although topics such as interopera-
bility, standards, scalability and template protection are
also gaining attention. Obtaining statistically reliable
performance evaluation is not only time consuming and
expensive but also requires the availability of large data-
bases and common benchmarks. Well-established exper-
imental protocols and benchmarks alleviate some of the
drawbacks in performance evaluation. Several standards
[5], procedures [6], databases (e.g. [7][8][9][10]) and com-
petitions (e.g. [11]) have been developed for this purpose.
Additionally, legal issues regarding data protection ham-
per the sharing and distribution of biometric data [1][12].
The use of synthetic biometric data in large datasets
has recently emerged as an aid to more accurate perfor-
mance evaluation. Such data has been applied to finger-
prints [11], faces [13], the iris [14], speech [15], handwrit-
ing [16] and even signatures [17][18][19][20]. These da-
tasets can improve the assessment of vulnerability and
algorithm robustness. Legal considerations are, of course,
paramount.
The proposals in the literature for synthetic handwrit-
ten signatures are as follows [19]:
Generation of duplicated samples. The synthesis algorithm
generates new samples from those of an existing user.
The generator produces new duplicates through several
transformations. An example of dynamic signature du-
plication can be found in [21] for improving enrollment in
dynamic signature verification. In [18] new static signa-
tures are generated from two dynamic samples produced
by the same user. The GAVAB static handwritten signa-
ture database comprises signatures duplicated by affine
transformation of the original signatures [8].
xxxx-xxxx/0x/$xx.00 © 200x IEEE Published by the IEEE Computer Society
————————————————
All Authors are with the Instituto Universitario para el Desarrollo Tecno-
lógico y la Innovación en Comunicaciones, Universidad de Las Palmas de
Gran Canaria, Las Palmas, 35017, Spain. E-mail: {mferrer, mdiaz, amora-
les}@idetic.eu.
T
2 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, MANUSCRIPT ID
Generation of new synthetic identities. Here, the new
signers and their signatures are created from statistical
descriptors. Although there are several handwriting syn-
thesizers in the literature, few synthesize samples for a
new identity. Popel in [17] describes an approach for
signature generation using a model based on visual char-
acteristics extracted from the time domain. After a visual
validation, no clear quantitative results are given. A novel
methodology is proposed by Galbally et al. in [19][20] for
the generation of synthetic on-line signatures on the basis
of flourish and isolated characters. Their method com-
bines the advantages of both spectral analysis and the
kinematic theory of rapid human movements to generate
the master signature of a new identity. Similarly, a pro-
posal to use heuristic procedures to generate genuine and
forged signatures is proposed at [21].
Recognizing that signing is a human task which in-
volves complex cognitive functions and fine motor con-
trol, this paper proposes a novel method of generating
both genuine and forged signatures of new synthetic
identities. This is performed by attempting to emulate the
mechanism of motor equivalence which is defined as the
personal ability to perform the same movement pattern
by different muscles.
The motor equivalence theory, also known as the De-
grees of Freedom (DoF) problem, it was formulated by K.
Lashley [22] and it was N. Bernstein who articulated it in
its current form [23]. Their studies are based on the activi-
ty of the Central Nervous System (CNS) which controls
posture and movement and focus on the kinematical
properties, seen from a musculo-skeletal viewpoint.
The motor equivalence theory suggests that the brain
stores in two steps the movements aimed at performing a
single task. The first is called effector-independent which
stores the movement in an abstract form as a spatial se-
quence of points representing the action plan. The parie-
tal cortex in general, and the posterior parietal cortex and
the occipitotemporal junction in particular, are suggested
in [24] as the most important brain region for representa-
tion of the action plan. The second step is called effector
dependent and consist of a sequence of motor commands
directed at obtaining particular muscular contractions
and articulatory movements in order to execute the action
plan [25] .
Applying the equivalence model to handwriting, the
action plan may be represented in terms of strokes which
are encoded in terms of relative positions and spatial
directions. Once the movement has been planned, the
motor control delivers the commands to specific muscles
to produce the handwriting.
In [26] it is suggested that fast and coordinated move-
ments cannot be executed solely under feedback control
since biological feedback is slow. Thus [26] proposes that
the brain needs to acquire an inverse model of the object
to be controlled by motor learning. Focusing on the inter-
nal inverse model of the limbs created by the cerebellum,
[26] calculates the motor commands which compensate
for the arm’s dynamics. Therefore, in the human devel-
opment stage, early handwriting actions are highly de-
manding of attention, slow to execute, clumsy and not
particularly accurate. After long-term practice, the
movements become quick, smooth, automatic, and can be
performed effortlessly, using minimal cognitive re-
sources. This all suggests that the internal model could be
replicated by a kinematic filter.
The kinematic filter is designed based on the kinematic
theory which describes a stroke velocity profile as the
output of a system made of two neuromuscular systems:
one, an agonist, acting in the direction of the movement,
and the other, an antagonist, acting in the opposite direc-
tion, compensating for the arm dynamics or inertia. The
composition of the agonist, antagonist and arm inertia
produce the well-known stroke overlapping which con-
veys handwritten quadratic trajectories [27][28][29][30].
Using motor equivalence, the inverse model and kine-
matic theory, we propose an off-line handwritten signa-
ture synthesizer. Obviously, we do not pretend to model
the mechanism of motor equivalence. Our idea is to con-
struct a synthetic signature generator, inspired by motor
Fig. 1. Motor equivalence approach to synthetic off-line signature generation.
MIGUEL A. FERRER ET AL.: STATIC SIGNATURE IMAGE SYNTHESIS: A NEUROMOTOR INSPIRED APPROACH FOR BIOMETRICS PAGE 3
equivalence hypotheses, which is built as follows (see Fig.
1): Firstly, we define the signature trajectory plan, which
imitates the action plan; Secondly, we use an approach to
the inverse internal models based on kinematic filters.
Thirdly, given a synthetic identity, we propose a model of
within and between individuals for constructing different
signature samples and a method for generating forgeries
at different skill levels. To the best of our knowledge, this
is the first work which deals with the generation of realis-
tic synthetic genuine and synthetic forged signatures each
of which may contain text and a flourish, if there is one. A
particular merit of our proposal is the possibility of con-
trolling the synthesized identity’s stability and the syn-
thesized forger’s skill by tuning no more than four pa-
rameters. All the constants and parameters of the pro-
posed model are worked out from the statistical distribu-
tion of global and local properties from the signatures in
well-known public databases, such as the MCYT Off-line
and GPDS960GRAYsignature. An ink deposition model is
used for creating realistic static signature images.
The aims of our experiments are: firstly, to determine
the ability, in terms of the equal error rate, of the synthe-
sizer to generate identities with different stability and
forgers with different skills; and secondly to be able to
assess the realism of the generated images by a perceptual
survey. Furthermore, a synthetic database of 4000 syn-
thetic signers with 24 genuine samples and 30 forgeries
with different inks is generated and made publicly avail-
able at http://www.gpds.ulpgc.es/download. This data-
base is obviously free of any legal concerns on privacy.
The paper is presented as follows: sections 2 and 3 re-
spectively describe the trajectory plan and the inverse
motor approaches. Section 4 is devoted to the ink model.
Section 5 is dedicated to the signature synthesizer param-
eters. Section 6 is focused on the performance and percep-
tual experiments while section 7 shows a case study of the
usefulness of the signature synthesizer. The eighth section
closes the paper with conclusions and suggested future
research.
2 SYNTHETIC SIGNATURE TRAJECTORY PLAN
This section proposes a trajectory plan which imitates the
cognitive action plan for a handwritten signature. During
the early development stage, human beings learn in visu-
al coordinates the spatial sequence associated with the
motor task [24] of generating a signature. Firstly, the se-
quence of points needed to generate the inked trace is
learned. Then, the sequence of motor commands is ac-
quired and executed as a single action.
We assume the Western style of signing, which is either
one of or a combination of a text and a flourish. The pro-
posed trajectory plan is described in two steps: text trajec-
tory and flourish trajectory. If both exist, once defined,
they are scaled and connected. The method allows the
generation of several types of signatures with different
complexity levels.
2.1 Text Trajectory Plan
Learning to write is a complex procedure which starts
with lines and scribbles. After reaching the age of about 3
years, most children understand that writing is made by
combining lines, curves, and repeated patterns. About a
year later, children begin to use letters in their own
style. Usually they start by experimenting with the letters
in their own names, as these are the letters most familiar
to them. Thus, children begin to learn the shape and se-
quence of the letters in their name although their motor
control is not yet accurate.
In some countries, children start their handwriting
practice using printed worksheets. These help them to
guide the height, width and length of each alphabetical
letter they write or trace, whether in upper or lower case,
and to construct the numerals. The tracing of lines or the
joining up of dots, within the lines on a worksheet, helps
them to learn each letter shape and the writing sequence.
The lines help the formation of spatial relationships be-
tween objects thus creating the spatial memory or cogni-
tive map. Once this is acquired, a child is able to select an
ordered sequence of target points to perform fluent writ-
ing.
The cognitive map of the writing sequence is imitated
in this paper by a letter trajectory plan which consists of:
i) a grid of possible trajectory points, distributed in the
signing area, which simulates the cognitive map; and ii) a
set of letter trajectory plans which describe the sequence
of trajectory points necessary to write each letter. The text
trajectory plan is built by concatenating horizontally the
letter trajectory plan of each letter with the necessary
horizontal spaces between them.
The grid of trajectory points for each letter is shown in
Fig. 2. Each point is labeled with a number. The distance
Fig. 2. (a) Grid of trajectory points with their labels of the letter trajectory plan for letter ‘P’; (b) Text trajectory plan for ‘Peterobtained by
concatenating the letter trajectory plans. The text trajectory plan is depicted in dark magenta and the link plan between letters in yellow.
.
4 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, MANUSCRIPT ID
between columns and rows of the grid define the letter
shape and writing style which is generally different for
different writers but constant for each writer.
For each letter, the trajectory plan is defined as a se-
quence of trajectory points. For instance, the trajectory
plan for the letter ‘Pis defined as the following sequence
of trajectory points: {5, 1, 8, 15, 22, 23, 24, 17, 10, 3}. For the
letter ‘eit is {11, 18, 25, 24, 17, 10, 11, 12, 19, 26} and so on.
The result can be seen in Fig. 2 . The trajectory points in
which the pen should stop because the writer has lifted
the pen from the paper (for instance to write the upper
horizontal line in the letter ‘t’ or because of a discontinui-
ty or a pen direction change) are marked as the initial
point of a new stroke. Note that these trajectory points are
not necessarily related with the so called target point in
the cortex action plan. This procedure to synthesize off-
line signatures is loosely based on the motor equivalence
model theory but it does not pretend to model or simulate
it.
Finally, the trajectory plan of a given text is defined by
concatenating the trajectory plan of different letters, as in
Fig. 2. The distance between letters is related to the grid
size and defined later, although it appears constant in Fig.
2.
2.2 Flourish Trajectory Plan
The flourish trajectory points are defined as a sequence of
points randomly generated inside a synthetic signature
envelope. This envelope attempts to imitate the signing
area that often limits the flourish area in the user brain.
The signature envelope is modeled by means of an
Active Shape Model (ASM) which consist of a mean
signature shape , a matrix of eigenvectors which
describe the main modes of variation of the envelope and
a vector  of weights [31][32]. The ASM is trained
according the methodology proposed in [31] with the
MCYT off-line database.
A new synthetic signature envelope is obtained as
 . This is calculated by selecting the vector
weights randomly from within a uniform distribution of
mean zero and deviation equal to , where
are the eigenvalues of the matrix eigenvectors.
The flourish trajectory points are located randomly in-
side the signature contour. The number of target points is
constant for a given user. As the signature envelope con-
tains the signature, the flourish trajectory points are ran-
domly located as separately as possible, taking into ac-
count that the line joining the consecutive trajectory
points does not cross the envelope. An example is shown
in Fig. 3.
If there are both a text and a flourish, their trajectory
plans are combined in three steps. The first displaces the
geometrical center of the text trajectory plan to the mass
center of the signature envelope. The second resizes the
text trajectory plan to adjust the scale between both
trajectory plans. The scale is the ratio between the text
length and the horizontal contour width. The value for
the scale is an identity constant. In the third step, the
signature trajectory plan is obtained by concatenating the
text and flourish trajectory plan adding, if the text and
flourish are connected, a link between the end of the text
trajectory plan and the beginning of the flourish trajectory
plan. An example where both trajectory plans are
connected can be seen in Fig. 3.
3 MOTOR CONTROL APPROACH
Once the signature trajectory plan is defined, an inverse
model for motor control is applied to obtain a realistic
human signature trajectory. Theories on how the arm
reaches planned trajectories are a central issue in motor
control. The strokes are considered as primitives from
which complex movements are assumed to be planned
and executed. The strokes reflect some of the fundamen-
tal properties of a writer’s neuromuscular system, as well
as some of the basic features of the motor control strate-
gies employed to produce these simple movements.
Among these basic features, the most remarkable is the
invariance of the velocity profile of the end-effector for a
subject performing a rapid stroke over a wide range of
movement size and speed [33]. Many of the different
computational models can be classified into two main
types: kinematic and dynamic. The kinematic model has
been found to be successful in reproducing the various
invariants observed in rapid strokes.
The kinematic theory describes a stroke velocity pro-
file as the output of a system made of two neuromuscular
systems: one, an agonist, acting in the direction of the
movement, and other, an antagonist, acting in the oppo-
site direction, compensating for the arm dynamics or
inertia. The composition of the agonist, antagonist and
arm inertia produce the well-known stroke overlapping
which convey handwritten quadratic trajectories. The
kinematic theory models the velocity of both movements
by a Delta-lognormal. Each lognormal is characterized by
its amplitude , time of occurrence , the log time delays
and the log-response time . The velocity profile of a
stroke is then:


(1)
where



for , and 0 elsewhere.
Introducing the kinematic model within the trajectory
plan will convert the sequence of straight lines into a
trajectory similar to that produced by the human control
motor. Two approaches to producing handwriting trajec-
Fig. 3. Signature envelope, text and flourish trajectory plan of “james
smith”.
Signature envelope
Flourish trajectory points
Text-Flourish connection
MIGUEL A. FERRER ET AL.: STATIC SIGNATURE IMAGE SYNTHESIS: A NEUROMOTOR INSPIRED APPROACH FOR BIOMETRICS PAGE 5
tories have been identified: 1) the space oriented models
which approach the trajectory formation on the basis of
the capability of expressing and controlling the trajectory
of the hand in space; and 2) the muscle oriented models
which attempt to relate the trajectory formation to the
muscle geometry and muscle properties [34]. The existing
space oriented models of handwriting comply with the
hypothesis that handwritten trajectories are divided into
simple strokes which can be composed by concatenating
them and smoothing the transition between consecutive
segments. To preserve the handwritten aspect, the com-
posite planar trajectory should be bicubic and the linking
between strokes must guarantee continuity up to the
second time derivative [34].
Several methods provide rules for satisfying the two
conditions simultaneously, such as composite Bezier
curves and regular spline functions. A previous paper
[31], proposes forming the signature trajectory by linking
the trajectory points with straight lines and polynomial
smoothing using a Savitsky-Golay filter [35].
In this paper, we use a simpler and equally efficient
smoothing of the trajectory plan using a Kaiser filter
whose finite impulse response is defined as:
 
 
 

(2)
where is a zeroth order Modified Bessel function of the
first kind. corresponds to the length of the filter
and β is the shape factor. In this work β is fixed to zero
and its variation is left for future work. We guess β could
be useful for simulating some effects of ageing or hand-
writing disorders. As the length of the filter is related to
the apparent speed of the stroke, higher speed conveys
greater inertia and therefore longer filters, it is called
kinematic filter.
The above procedures are useful for signatures with
just flourishes and produces trajectories similar to a hu-
man being, but several issues arise when generating sig-
natures with both a text and a flourish. Writing the text
requires a finer finger control motor than writing the
flourish for which the major movement is made by the
forearm. The wrist usually moves during the whole sign-
ing process. Thus, according to the equivalence motor
theory, for generating text and flourish we need more
degrees of freedom than in the case of generating just the
flourish because of the greater number of muscles in-
volved.
Thus, we use a multi-level motor scheme based on sev-
eral kinematic filters of variable length that simulate the
inertia of the different muscles used for handwriting.
Note that this is an operational approach not necessarily
related to real muscles or movements. In short, our pro-
posal relies on three kinematic filters which are heuristi-
cally related to the finger, forearm and wrist applied as
follows:
1. For the signature text, the trajectory points are
linked by straight lines and divided into strokes. These
are defined for each letter plan. Fig. 5.a shows an example
of stroke division.
2. The finger speed profile is then estimated. The pro-
file of each stroke j at the pixel is obtained as


following the
Delta-lognormal model. The parameters 


are fixed for each identity since they rep-
resent the identity’s motor system. The parameter values
are obtained randomly in the range given by [33]. Finally,
the finger speed profile
of the signature text is obtained
by adding the stroke speed profiles as

 where
 is the number of strokes. The
is normalized to a
maximum value equal to 1. It is actually a scalar version
of the sigma lognormal model [35]. An example can be
seen at Fig. 5.b.
3. The finger speed profile is used to select the length
of the kinematic filter that programs the finger control
motor. The kinematic filter length at pixel is calculated
as 
where  is a user constant which
depends on the image resolution and the mean speed of
the finger. The result of applying the inertia filter can be
seen at Fig. 5.c. where we suppose that  is equal to
the maximum distance between columns or rows of the
trajectory grid.
4. For the flourish, straight lines link the flourish trajec-
tory points. Each corner is marked as a new stroke. The
Delta lognormal parameters of each stroke are randomly
worked out and the flourish speed profile
is obtained
by adding the speed of each stroke. In this case, the filter
length is obtained as

. We use  in-
stead of  because the motor system for the flourish is
different from the motor system for the signature text. As
the flourish is written quicker than the text, so 
.
The result of applying the text and flourish kinematic
filters can be seen at Fig. 6.b and Fig. 6.c respectively.
5. The wrist moves continuously when writing both the
signature text and flourish. Thus we apply a third kine-
matic filter to the signature. In this case, the strokes are
considered as the groups of connected letters (a word
with all the letters connected, several connected letters, an
isolated letter, etc.). The Delta lognormal parameters are
obtained for each stroke randomly and the wrist speed
profile
is calculated. The kinematic filter length is ob-
Fig. 4. a) Trajectory plan of letters “james with stroke division
marked with a circle and each consecutive stroke with change in
color; b) Velocity profile
based on scalar Sigma lognormal normal-
ized to maximum amplitude equal to one; and c) The resulting hand-
writing word after applying the finger control motor approach.
Fig. 5. a) Trajectory plan of letters “james with stroke division
marked with a circle and each consecutive stroke with change in
color; b) Velocity profile
based on scalar Sigma lognormal normal-
ized to maximum amplitude equal to one; and c) The resulting hand-
writing word after applying the finger control motor approach.
(a)
(b)
(c)
6 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, MANUSCRIPT ID
tained at each pixel as

. Fig. 6.d show an
example of applying the wrist kinematic filter when
 is two times the maximum distance between col-
umns or rows of the trajectory grid.
4 INK MODEL FOR REALISTIC IMAGES
The tool used most for handwriting is the ballpoint pen.
So we have used the ink deposition model of a ballpoint
to produce realistic images, as at [31][37].
The ballpoint pen is a writing instrument which dis-
penses ink from an internal reservoir through the rolling
action of a metal ball at its tip. Mainly due to ink viscosity
and gravity or reservoir pressure, the ink flows from the
reservoir to coat the ball. Handwriting is produced by
rolling the ball on a sheet which deposits the ink on the
paper. Our model supposes that the ballpoint pen gener-
ates a sequence of inked spots when rolling.
The spot shape is modelled as an ellipse the vertical
and horizontal axes of which are given by 
and 
where is the pen tip diameter
and the pen inclination angle. The major axis of the
ellipse is perpendicular to the pen azimuth . Both are
calculated by supposing that a pen pivot is located 
from the lower right hand corner of the paper and at
 above the paper. This assumes an average hand
size.
Although the pen speed and pressure are not always
correlated [38], this paper assumes that the spot gray level
amplitude is inversely proportional to the speed. Let the
pen speed at dot be equal to



. The normalized pressure is pre-
sumed to be 

. The spot gray level
amplitude is defined as  where  and
 are random numbers in the range  and
 respectively. To take into account the pen tip
irregularities or deposition failures, the spot is multiplied
by a random normal noisy spot defined as 
The signature images is obtained by overlapping the con-
secutive spots so as to correspond to the rolling action of
the ballpoint pen. The maximum dark value is taken into
account by cropping the signature level intensity to .
The last step in improving the realism of the off-line
signature images is to approximate the calculated stroke
gray level histogram to a real ink histogram distribution.
The histogram of the generated strokes is equalized to
match one of the ink histograms of the three more usual
ink types: fluid, viscose and solid [39].
These inks plus the usual commercial ball pen diame-
ters   mean that 18
pen types are available. Additionally, the variables ,
 are randomly generated for each signature. An ex-
ample of the result can be seen in Fig. 7. The effect is real-
istic although there is room for improvements, e.g. to
create striated ink deposition.
5 SYNTHETIC SIGNATURE PARAMETERS FOR
DATABASE GENERATION
A signature database contains several genuine samples of
the same signer plus several forgeries of each signer made
by different forgers. Each genuine signature is different
from the others and the difference among them is called
the within class variability. The differences between the
different signers is called the between class variability.
For synthetic signature generation, the between variabil-
ity is obtained by changing the parameters that generate
the signatures.
These parameters are divided into three groups. The
first group contains the parameters needed to generate
the morphology and lexicon of the signature. We under-
stand these terms to mean respectively the form and for-
mation, i.e., the number of words, letters per word,
whether the signature has a flourish, the relationship
between the text and flourish length and so on. The sec-
ond and third groups include the parameters required to
generate the trajectory plan and the motor control param-
eters respectively.
To obtain realistic synthetic signatures, most of the
parameters range has been obtained by the analysis of
real signatures databases as detailed in the next section.
Fig. 6. a) Trajectory plan of the signature, b) result of applying the finger kinematic filter, c) result of filtering by the forearm kinematic filter
and, d) signature after applying the wrist kinematic filter.
MIGUEL A. FERRER ET AL.: STATIC SIGNATURE IMAGE SYNTHESIS: A NEUROMOTOR INSPIRED APPROACH FOR BIOMETRICS PAGE 7
5.1 Real Database Analysis for Defining the
Parameters Range of Synthetic signatures
The database analysis of real signatures has been per-
formed by manual counting of the parameters needed for
producing synthetic signatures and their frequency mod-
eled by a probability density function (pdf) estimated by
the histogram method.
Two public Western off-line corpuses have been used
for the counting: the MCYT and GPDS databases.
The MCYT off line database [7] includes 75 signers, 15
genuine signatures and 15 deliberate or skilled forgeries
for each signer. All signature data was acquired with the
same pen and the same paper templates.
The GPDS960GraySignature corpus [41] contains 24
genuine signatures and 30 deliberate forgeries from 881
individuals. The genuine signatures were written with the
same ink and the forgeries with 10 different inks. Both
databases were scanned at 600dpi with 256 gray levels.
The peculiarities we examined which allow the gener-
ation of a more realistic synthetic database imitating the
proportions of a real database are listed below:
1. The measured probability of signatures containing
flourish and text is 86.6%. The probability of signatures
with only either a flourish or a text is 8.3% and 5.1% re-
spectively.
2. Fig. 8.a shows the distribution of words in the signa-
ture, up to the third word. Those with one word: 50%,
with two words: 36.3% and with three words: 13.7%.
3. Fig. 8.b shows the distribution of the number of let-
ters per signature. This is modeled by a normal distribu-
tion of mean 5.5 and sigma 2.2.
4. The number of flourish corners is related to the flour-
ish complexity which is a relevant signature parameter.
Fig. 8.c shows the distribution of the number of flourish
corners which is approximate by a lognormal distribution
of  and  which corresponds to a mean
equal 5.38 and variance equal to 5.5. As real signatures
can include two flourishes, the second one is approximat-
ed by using the same probability distribution with
 and .
5. Some signatures have wider texts in relation to the
flourish widths than others. To model this fact, the distri-
bution of the ratio between the text and flourish widths is
worked out and represented in Fig. 8.d. This distribution
can be fitted by a lognormal distribution of  and
 which corresponds to a mean equal to 0.85 and
variance equal to 0.11.
6. Real signatures present an inclination or skew. This is
measured by enveloping the signature by an ellipse and
working out the angle of the major axis. Fig. 8.e shows the
distribution of the measured skew which is approximated
by a generalized extreme value probability density func-
tion with shape parameter , scale parameter
 and a location parameter .
7. Similarly, the slant effect is another personal feature
needed to imitate the generation of synthetic signatures.
The estimated distribution of the signature slant is de-
picted at Fig. 8.f. It suggests again a generalized extreme
value probability density function but with a shape  
, scale , and a location .
8. The distribution of the letter size, in terms of their
width in millimeters, in the above mentioned databases is
shown at Fig. 8.g. It can be approximated by a normal
distribution of  and σ  .
9. The distribution of the space in millimeters between
letters is shown at Fig. 8.h. It can be approximated by a
normal distribution of  and σ  .
10. Fig. 8.i estimates the distribution of the space be-
tween words in millimeters as a normal distribution of
 and .
Other interesting data we use to help generate the syn-
thetic database are as follows:
The probability of connecting the last letter of the text
with the beginning of the flourish is fixed at 58%.
Of the signatures with a flourish, 81% have just one
flourish and 19% of them have a second non-
connected flourish.
The probability of all the letters being connected is
59%.
5.2 Parameters to Generate a Synthetic Signature
The parameters we use to generate automatically the
signature of a new synthetic identity are given in three
groups below.
Parameters to define the signature lexical morphology
1.  Probability that the
signature includes only text, only flourish or text plus
flourish. Their values are obtained from the real database
counting given at section 5.1.
2. : Probability of the text and the flourish
being connected. This is worked out with the probability
given at section 5.1.
3. : Number of words in the signature text, ob-
tained with the pdf of Fig. 8.a.
4. : Number of letters in each word, as in pdf
from Fig. 8.b.
5. : Signature text, for instance “James Smith”. The
Fig. 7. Real signature stroke detail from GPDS database (left); detail of synthetic (right).
8 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, MANUSCRIPT ID
text is randomly obtained taking into account the occur-
rence probability of each letter in the English language.
So, we do not automatically generate real texts but ficti-
tious texts as corresponds to synthetic signatures.
6. : Probability of all the letters of the text being
joined, as modeled at section 5.1
7.  Number of flourishes, as modeled at section 5.1.
8. The number of corners per flourish obtained from
the distribution in Fig. 8.c. The positions of the corners

 are located as defined at section 2.2.
Parameters to generate the trajectory plan
9. 
 : Positions of the flourish corners
obtained as defined at section 2.2.
10. 
The distance between columns of the grid
trajectory points (see Fig 9) that define the letter shape
and size. Taking into account the distribution at Fig. 8.g
and a 600dpi image, this is obtained randomly in the
range [530] pixels for each identity.
11. 
Distance between rows of the grid trajectory
points defined in the same way as .
12.  This defines the ratio 
 which is obtained randomly from the
distribution of Fig. 8.d. The ratio is fitted to the synthetic
signature by estimating:




(5)
and scaling the letter size as follows: 
 and.
13. : Variability of the letter. A letter is never written in
exactly the same way by a writer, so we introduce a vari-
able to control the letter shape variability. This can be
described as inner word variability. Each time a letter is
generated, the grid trajectory points are moved inside a
circle of radius is equal to as shown at Fig 9. Each writ-
er has his own variability. The radius depends on the
letter size and it is heuristically fixed for each identity in
the range  where  


.
14. : Variability of the baseline. This is different from
the variability of the other trajectory points because of the
expected ability of a healthy writer to write on or close to
a straight line. Therefore, the variability or circle radius of
the trajectory points 5, 12, 19, 26 and 33 is smaller than 
(see Fig 9). This variable is randomly set up in the
range pixels for each identi-
ty.
15.  Space between consecutive letters for an identi-
ty. See distribution Fig. 8.h.
16.  Space between consecutive words for an identi-
ty, as modeled by Fig. 8.i.
17.  Variability of the space between letters. This is
not constant even within the same word. So it changes
among the letters and can be seen as an example of inner
word variability. Therefore, each time a letter is added,
the space to the prior letter is obtained as 
which is calculated as random value in the range
 pixels. This range has been
heuristically adjusted.
18.  Variability of the space between words. As in
the case of , each time a word is added, the space to
the prior word is obtained as  which is calcu-
lated as a random variable in the heuristic range 
 pixels.
19.  The signature skew is modeled as Fig. 8.e and
is accomplished by rotating the signature trajectory plan.
20. : The slant of the handwriting. Following the
distribution of Fig. 8.f, this is achieved by applying an
affine transformation to the text trajectory plan.
Parameters to generate the motor control approach
The values of the following four parameters are inspired
by [33]. The last four have been set heuristically:
21. : Location parameter of the agonist log
normal distribution. This is used to obtain the velocity
profile. Randomly defined in the range [-0.70].
22. : scale parameter of the agonist log nor-
mal distribution. This is used to obtain the velocity pro-
file. Randomly assigned to the identity in the range
[0.20.6].
23. : Location parameter of the antagonist
lognormal distribution. This is used to obtain the velocity
profile. Randomly worked out in the range [-0.50.7].
24. : Scale parameter of the antagonist
lognormal distribution. This is used to obtain the velocity
profile. In the range [0.20.6].
25. : Length of the smoothing filter for the finger
motor model. This variable depends on the letter size, so
its range is defined between .
26. : Length of the smoothing filter for the forearm
Fig. 8. Distribution of modeled features from real off-line signatures
from MCYT and GPDS database and their approximated pdfs.
Fig 9. Definition of the distance between columns and rows  of
the grid trajectory points and the radius  and  for within word
letter class variability.
MIGUEL A. FERRER ET AL.: STATIC SIGNATURE IMAGE SYNTHESIS: A NEUROMOTOR INSPIRED APPROACH FOR BIOMETRICS PAGE 9
motor model. This variable depends on the flourish size.
This is  times the maximum of the distances between
the flourish corners. The range of this variable is 
 .
27. : Length of the smoothing filter for the wrist
motor model. From experiments we conducted, the range
of this variable is set between .
By varying these parameters randomly, according to
their probability density function, 98% of the cases found
in the real databases can be generated by the synthesizer.
One example of a signature that the synthesizer cannot
generate one with two lines of text.
It is possible to generate signatures with just a text line
(   and   ) or only a flourish (
and  ). For signature with text and a flour-
ish both parameters are equal to .
The complexity of the text line is set up by parameters
 and  which correspond to the number of
words and letters in the signature text. The signature
complexity increases with the number of words and let-
ters.
On the other hand, the complexity of the flourish is ad-
justed by the parameter  and  which corresponds to
the number of flourishes and number of corners in the
flourish. If the number of flourishes or corners increases,
the signature is more complex.
The readability of the signature is related to the length
the kinetic filters whose parameters are called ,
 and . If the value of these parameters increas-
es, this implies an increase in the handwriting speed,
resulting in the text line becoming less and less legible.
Fig. 10 show the change in text line readability as the
kinematic filter length is increased.
5.3 Parameters to Generate Multiple Samples of a
Synthetic Identity
The above variables allow us to generate the master sig-
nature of a new synthetic identity. In this section we de-
scribe the procedure required to define the synthetic sign-
er stability or the within variability, i.e. the differences
between multiple genuine samples.
In this paper, the within variability is controlled by
two parameters. The first refers to the flourish and the
second to the text and neuromuscular kinematic filters.
These parameters are:
1.  Radius of flourish corner ball. We introduce
the variability in the flourish by changing the position of
the corners of the flourish. The new corners lie inside a
ball of radius  around the user corners

 .
2.  Within text variability. Each time a signer pro-
duces a new signature, it keeps the same cognitive map
and action plan but the neuromuscular path slightly
changes its conditions due to different posture, equilibri-
um condition, etc. therefore introducing slight differences
in the handwritten text. In the synthetized signature this
is modeled by changing the value of the following text
parameters: , , , , , , , ,
,  and . With the variable  we define
the percentage that each variable changes, i.e., for the new
synthetic signature sample the new  value will be a
random number between   
 and so on. Obviously, we check that the newly
obtained values are within the given parameter range.
Otherwise, the maximum or minimum value is assigned,
depending on which values exceed the range.
The within variability of the identity will be propor-
tional to  and .
5.4 Parameters to Generate Forgery Samples
In the case of forgery generation, as the forger imitates the
genuine signature, he or she will try to extract the action
plan from the original signature, so the forger follows a
similar trajectory to the genuine signature but with a
higher variability than the within class variability because
of mistakes in the reconstruction of the action plan and
the different neuromuscular systems between the forger
and genuine signer.
The above principles are summarized in two parame-
ters, the first related to the flourish and the second to the
text. These variables are:
1.  Radius of the forgery flourish ring. As in the
case of genuine identity, the flourishes made by a synthet-
ic forger are generated by moving the flourish corners. To
simulate the greater variability of the forgers and their
difficulties in capturing the exact corner position, we use
a ring instead of a ball. Therefore  is a vector com-
prising the inner and an outer ring radius. The bigger the
intersection area between the genuine ball and the forgery
ring, the more skilled the forger.
2.  Forger text variability. This parameter is intend-
ed to simulate the forger variability for writing the text.
As in the case of , it expresses the percentage variabil-
ity in respect the parameter value but in this case it con-
sists of two values:  and . The first indicates
the minimum variability and the second the maximum
variability. For example, the  value for a forger is a ran-
dom value in the range:

 
 
 

If the modified value is not in the parameter range, it is
set to its nearest extreme value. The modified parameters
are:
a. As in the case of genuine generation: , , , ,
, , , , ,  and .
Fig. 10. Influence of increasing the kinetic filters length,  and  on the signature readability
10 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, MANUSCRIPT ID
b. Additionally, as the forger does not capture the exact
letter grid from the genuine signature, the letter grid val-
ues 
and 
are also modified by .
c. Finally, as a forger has a different neuromuscular
system, the values of variables, ,
 and  are worked out anew but as
the forger forces his own neuromuscular system to imi-
tate the genuine signature shape the variables , 
and  are modified by  as said above.
Fig. 11 shows different examples of synthetic genuine
and forged signatures obtained by the procedures de-
scribed: it displays signature with both flourish and text
with different complexities, a signature with only text and
another one with just a flourish.
6 EXPERIMENTS
These experiments are aimed at determining the ability
of the synthesizer to generate realistic synthetic da-
tasets. The stability of the genuine signatures and the
skills of the synthetic forgers are customized by adjust-
ing the values of the variables: , ,  and
.
Therefore, two kinds of experiments have been carried
out: perceptual experiments to assess the realism of the
synthetic signature images and performance experiments
on generated synthetic databases to validate in terms of
Equal Error Rate (EER) the synthetic signer variability
and the forgers’ skills.
The performance experiments are carried out in two
steps. The first works out the relation between the EER
with random forgeries and the parameters  and
 which controls the within and between variability of
the synthetic signature database. The second step studies
the sensitivity of the EER for forgers’ skill with respect to
the parameters  and .
The perceptual experiment is carried out by estimating
human ability to distinguish between synthetic and real
signatures through a survey with people outside of the
forensic area.
6.1 Protocol for Performance Experiments
The performance evaluation is computed by using the
verifier proposed in [41]. It is based on texture features
such as the local binary pattern (LBP) [34] and the local
derivative pattern (LDP) [35]. The signature is trans-
formed to the LBP and LDP image which is divided into
12 sectors. The histogram of each sector is worked out,
concatenated and its dimension reduced by using a Dis-
crete Cosine Transform (DCT) to obtain the feature vec-
tor. The classifier is based on a least square support vector
machine (LSSVM) [36].
Following a well-established experimental protocol,
the training set consists of 10 randomly selected genuine
signatures. The remaining genuine signatures are used
for testing. When testing with a specific signer, random
forgery scores are computed by using the genuine test
samples from all the remaining users. Scores for forgers
are computed from the synthetic forgeries of the signer.
All the experiments are repeated 10 times and the aver-
aged results in term of Equal Error Rate (EER) are provid-
ed.
In order to establish a reference for the realism of the
performance results obtained with the synthetic data-
bases, the performance obtained with the real signatures
of the GPDS corpus with 150 users are an EER=0.44% for
random forgeries and EER=15.90% for skilled forgeries.
For the 881 real users from the same database, the EERs
are equal to 0.88% and 23.42% for random and skilled
forgeries respectively.
Fig. 11 . Six possible synthetic identities with three genuine specimens (first three columns) and three possible forged signatures ( last three
columns). The first four signatures are composed of text plus flourish, the fifth example has only text and the sixth is a simple flourish.
Synthetic Genuine instances Synthetic Forgeries
MIGUEL A. FERRER ET AL.: STATIC SIGNATURE IMAGE SYNTHESIS: A NEUROMOTOR INSPIRED APPROACH FOR BIOMETRICS PAGE 11
6.2 Performance Experiments
This section studies the performance sensitivity with
respect to the four parameters that define the database
variability. First we report at Table I the sensitivity with
respect to the parameters that set up the synthesis of gen-
uine samples:  and . The ability of these pa-
rameters to produce datasets with different inner and
between class variability is clear from the range of differ-
ent EERs obtained. It can be seen that reducing the flour-
ish corner ball radius, decreases the synthetic signer vari-
ability and improves the performance. Also the perfor-
mance is more sensitive to  than to . Moreover,
the ability of the procedure to produce realistic databases
is proved by the fact that the synthetic database perfor-
mance is similar to the real GPDS database performance
when   and =30%.
Table II evaluates the ability of the synthetic procedure
to produce forgeries with different skills. This depends on
the following parameters: the inner and outer radius of
the flourish corner ring for forgeries  and
 and the forger text variability . Table II pre-
sents the results for various  and , supposing
for the sake of simplicity that   mm. The
EER reduces when the outer ring radius increases because
a greater  means less skilled forgers. Again,
 influences the performance more than  because
it is the former variable which best describes the forgers’
skills. Similar results to those for a real GPDS database
can be obtained by setting  and
=100%.
In conclusion, the proposed procedure is able to gener-
ate useful customized databases. The different variabili-
ties and therefore performances are tuned according to
only four parameters.
TABLE I
EER (%) FOR RANDOM FORGERIES FOR 150 SYNTHETIC USERS
Within text
variability: 
Ring corner ball radius:  in mm
0.42
1.27
2.12
2.96
3.81
4.66
10 %
0.0000
0.023
0.09
0.33
0.61
1.60
30 %
0.0003
0.010
0.10
0.45
0.79
1.61
50 %
0.0006
0.01
0.11
0.48
0.85
1.74
70%
0.002
0.09
0.19
0.56
1.30
2.17
90%
0.006
0.09
0.28
0.64
1.85
2.38
TABLE II
EER (%) FOR SKILLED FORGERIES WITH
150 SYNTHETIC USERS*
Forger text
variability: 
Outer ring corner ball radius  in mm
5.77
6.28
6.70
7.13
7.55
60 %
18.16
16.86
15.72
15.17
14.56
80 %
16.98
16.17
15.36
14.80
13.66
100 %
16.61
16.09
15.56
14.30
12.53
120 %
15.57
15.24
14.91
13.23
11.91
140 %
14.30
14.38
14.45
12.55
12.97
*The inner ring corner ball is fixed to 
6.3 Perceptual experiments
We conduct perceptual experiments to investigate the
generator’s ability to produce humanlike signatures. In a
similar way to [20] [37][45], this is measured by showing
non-forensic volunteers a set of real and synthetic images.
The volunteers are not told whether the signature is real
or synthetic. They are asked to score between 0 (very sure
synthetic) and 10 (very sure human) the realism of the
presented signature according to their impression,
formed after a quick inspection of the signature.
For this experiment, forty synthetic signatures were
generated with real texts. They were combined with an-
other 40 real signatures randomly selected from GPDS,
MCYT. Real and synthetic signatures were randomly
mixed.
To avoid any background effects, the signatures were
set against the same white background. In addition, the
test was presented on printed sheets to avoid the use of
computer facilities, e.g. the zoom, to help make the deci-
sion. A subset of this experiment is shown in Fig. 12
The realism of the synthetic generator is measured by
calculating two kinds of errors, as in [20] and [37]. We
work out the False Synthetic Rate (FSR): a real signature
is assigned as synthetic if the score is less than 5. We then
work out the False Real Rate (FRR): a synthetic signature
is assigned as real if its score is greater than 5. The final
Average Classification Error (ACE) is calculated as ACE=
(FSR + FRR)/2. The results of the survey of 80 volunteers
are shown in the first three columns of Table III. The av-
erage score of real and synthetic signatures is also given
at Table III along with the average time taken to complete
the experiment.
TABLE III
RESULTS OF THE PERCEPTUAL EXPERIMENT
Error rates (%)
Average score
Average
time (min)
FSR
FRR
ACE
Real
Synthetic
43.02
45.10
44.06
5.38
4.50
8.70
Fig. 12. Subset of signatures used in the Perceptual Experiment to
evaluate the appearance of our signatures. For information, the
synthetic signatures are marked with a cross.
12 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, MANUSCRIPT ID
The value of ACE=44.06% confirms the expected con-
fusion between real and synthetic signatures. This con-
clusion is also supported by the real and synthetic aver-
age score of around 5. Therefore, we conclude that per-
ceptually the synthetic signature generator based on the
motor equivalence approach along with the virtual depo-
sition ink model is able to produce signatures that human
non-expert examiners accept as real.
7 CASE STUDY: ROBUSTNESS AGAINST NUMBER OF
IDENTITIES AND INK VARIABILITY
An advantage of our synthetic signature generator is that
it allows easy checking of the robustness of verification
algorithms according to different scenarios. In this sec-
tion, as a useful example of applying the synthetic algo-
rithm, we analyze the robustness of the signature verifier
to different numbers of users and inks. Five versions of
the same database are generated for the following 5 ex-
periments:
Experiment 1: Generation of a database by assign-
ing a random pen to each sample. Our pen model consid-
ers 18 possible types of pen. The pen diameter varies in
the range  and the ink type
is randomly chosen from solid, viscous and fluid.
Experiment 2: Signature images for all the sam-
ples are generated with a ballpoint of 0.4 mm and solid
ink. This is similar to the pen used for the off-line MCYT
signature database.
Experiment 3: In this case, the images are generat-
ed with a ballpoint of diameter 0.2 mm and viscous ink.
Experiment 4: The images are obtained with a
ballpoint of diameter 0.2 mm and solid ink.
Experiment 5: As in the case of GPDS, the genuine
signature of each synthetic identity is generated using the
same randomly selected pen. The forgeries are synthe-
sized with a randomly selected pen.
By comparing the results of experiments 2 and 4 we
can see the influence of the ballpoint diameter on the
signature verifier. Also, we can see the effect of varying
the ink type by comparing the results from experiments 3
and 4. The influence of the pen can be seen in experiment
5 where the random and simulated forgeries have been
written with a different pen than that used for the genu-
ine signatures. Experiment 1 shows the most realistic case
because each sample is written with a different pen.
TABLE IV
EER FOR RANDOM FORGERIES OF THE SAME SYNTHET IC DB
WITH DIFFERENT PEN CONFIGURATIONS AND NUMBER OF USERS
Number of users in the database
Exp
ballpoint
ink
75
150
300
881
1500
2500
4000
1
random
random
0.76
0.57
0.63
0.79
0.79
0.74
0.79
2
4 mm
solid
0.53
0.52
0.44
0.72
0.72
0.63
0.67
3
2 mm
viscous
0.48
0.51
0.45
0.75
0.70
0.67
0.71
4
2 mm
solid
0.47
0.55
0.54
0.73
0.71
0.64
0.68
5
Random (same for
all the genuine)
0.47
0.47
0.47
0.66
0.62
0.57
0.61
Table IV shows the results of the above experiments
using a different number of identities. Increasing the
number of identities does not display a clear tendency in
the EER. This indicates that the EER depends more on the
identitiesvariability than on their number. On the other
hand, randomly changing the ink decreases the perfor-
mance. From comparing experiment 2 and 4, it seems that
narrower ballpoints make verification easier; and by
comparing the third and fourth experiments, it appears
that the ink type is not relevant in a database when all the
signatures are taken with the same ink type. The compar-
ison of the first experiment (randomly selected inks) with
the second (all users with the same ink as in the MCYT
database) and fifth (each user with one ink type as in
GPDS database) indicates that the results obtained with
the GPDS and MCYT databases are biased positively with
respect to real applications where each signer uses a dif-
ferent pen for each signature.
8 CONCLUSION
This paper proposes a novel method for the generation of
synthetic off-line handwritten signatures inspired by the
human neuromotor model. The proposed method gener-
ates entirely realistic synthetic genuine and synthetic
forged signatures. Additionally, an ink deposition model
is used to generate images with a highly realistic appear-
ance.
The designed synthetic signature generator is based on
the so called internal model which defines the handwrit-
ing action in two steps: the action plan and neuromotor
inverse model. The signature generator imitates the action
plan by using a trajectory plan, i.e. a sequence of target
trajectory points in a grid. The neuromotor path is repre-
sented by a kinematic filter based on a variable length
Kaiser window. The window length is proportional to the
inverse of the pen speed, which is obtained using a scalar
version of the sigma lognormal model. Once the synthetic
signature’s trajectory is worked out, an ink deposition
model is defined to obtain realistic images of the signa-
ture generated.
The parameters we use to define the synthesized signa-
ture are obtained by analyzing the lexical and morpholog-
ical aspects of signatures in the MCYT Off-line signature
and GPDS signature corpus. Parameters such as the num-
ber of words in a real signature, the number of letters per
word, the presence or absence of a flourish or text, text
and flourish relations, etc. have been statistically charac-
terized.
The validation protocol is twofold: performance relat-
ed and perceptual. The performance experiment is aimed
at learning the ability of the synthetic signature generator
to produce databases with different within class variabil-
ity and forgeries with different forger skills. The experi-
ments show that by varying only four variables it is pos-
sible to control the writer stability and the forger skill. It
is possible to find values of these parameters to synthetize
databases with a similar performance to a real database
such as the GPDS.
MIGUEL A. FERRER ET AL.: STATIC SIGNATURE IMAGE SYNTHESIS: A NEUROMOTOR INSPIRED APPROACH FOR BIOMETRICS PAGE 13
The perceptual experiment is addressed at learning the
ability of the synthesizer to generate humanlike signa-
tures. A survey to 80 people shows a near 50% of confu-
sion between real and synthetic signatures which proves
the realism of the generated synthetic signatures.
The novel synthetic generation algorithm has enor-
mous potential for many applications such as perfor-
mance estimation, security evaluation, scalability studies,
ink effect studies, etc. Some of them are evaluated in this
paper. In our on-going research we are adding parame-
ters to test temporal drift to the database to simulate the
effects of multisession signature taking, ageing and neu-
rodegenerative illness. We believe forgery generation can
be also improved by using the ScriptStudio program [46].
ACKNOWLEDGMENTS
This study was funded by the Spanish government’s
MCINN TEC2012-38630-C04-02 research project.
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Miguel A. Ferrer received the M.Sc. degree in
telecommunications, in 1988, and his Ph.D.
degree, in 1994, each from the Universidad
Policnica de Madrid, Spain. He belongs to
the Digital Signal Processing research group
(GPDS) of the research institute for technologi-
cal development and Communication Innova-
tion (IDeTIC) at the University of Las Palmas
de Gran Canaria in Spain where since 1990 he has been an Associate
Professor. His research interests lies in the fields of computer vision, pat-
tern recognition, biometrics, mainly those based on hand and handwrit-
ing, audio quality, mainly for health and condition machinery evalua-
tion and vision applications to fisheries and aquaculture.
Moises Diaz-Cabrera received two M. Tech
degrees in 2010: Industrial Engineering and
Industrial Electronics and Automation Engineer-
ing and holds a M.Sc. in Intelligent Systems and
Numerical Applications in Engineering (2011) as
well as a M.Ed. in Secondary Education (2013),
all from La Universidad de Las Palmas de Gran
Canaria. He is currently pursuing a Ph.D. degree
and his research areas include handwritten signature recognition, pat-
tern recognition and computer vision. Also he has some experience in
Intelligent Transportation Systems through collaborations with CICEI,
at ULPGC, and VI slab, at the University of Parma.
Aythami Morales received his M.Sc. degree in
Telecommunication Engineering in 2006 from
Universidad de Las Palmas de Gran Canaria.
He received his Ph.D degree from La Universi-
dad de Las Palmas de Gran Canaria in 2011.
He performs his research works in the Digital
Signal Processing Group (GPDS) at Las Palmas
de Gran Canaria University and he has under-
taken research visits to the Biometric Research Laboratory at Michigan
State University, the Biometric Research Center at Hong Kong Poly-
technic University and the Biometric System Laboratory at University
of Bologna. His research interests are focused on pattern recognition,
computer vision, machine learning and biometrics signal processing.
He is the author of more than 30 scientific articles published in interna-
tional journals and conferences.
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