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Chapter 1
Modeling the Complexity of Signature and Touch-Screen Biometrics
using the Lognormality Principle
Ruben Vera-Rodriguez, Ruben Tolosana, Javier Hernandez-Ortega, Alejandro
Acien, Aythami Morales, Julian Fierrez and Javier Ortega-Garcia
BiDA Lab Biometrics and Data Pattern Analytics Laboratory, Universidad
Autonoma de Madrid, Madrid, Spain
(ruben.vera, ruben.tolosana, javier.hernandezo, alejandro.acien,
aythami.morales, julian.fierrez, javier.ortega)@uam.es
This paper focuses on modeling the complexity of biomechanical tasks through
the usage of the Sigma LogNormal model of the Kinematic Theory of rapid hu-
man movements. The Sigma LogNormal model has been used for several ap-
plications, in particular related to modeling and generating synthetic handwritten
signatures in order to improve the performance of automatic verification systems.
In this paper we report experimental work for the usage of the Sigma LogNormal
model to predict the complexity of biomechanical tasks on two case studies: 1)
on-line signature recognition in order to generate user-based complexity groups
and develop specific verification systems for each of them, and 2) detection of age
groups (children from adults) using touch screen patterns. The results achieved
show the benefits of using the Sigma LogNormal model for modeling the com-
plexity of biomechanical tasks in the two case studies considered.
1. Introduction
On-line signature verification and other handwritten tasks (drawings, touch pat-
terns, etc.) are experiencing a high development recently due to the technological
evolution of digitizing devices, including smartphones and tablets. Such handwrit-
ten data can be applied to many applications in different sectors such as security,
e-government, healthcare, education, user profiling, advertising or banking.1–4
This paper focuses on modeling the complexity of handwritten information,
which can be a very important factor in different applications related to hand-
writing. We propose to model the complexity of handwritten tasks through the
usage of the Sigma LogNormal model of the Kinematic Theory of rapid human
movements.5The Sigma LogNormal model has been used in the past for several
1
This is a pre-print of an article to be published in the book:
The Lognormality Principle and its Applications, R. Plamondon et al. (Eds.),
World Scientific, 2019.
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2R. Vera-Rodriguez, R. Tolosana, J. Hernandez-Ortega, A. Acien, A. Morales, J. Fierrez and J. Ortega-Garcia
applications. One of the most successful ones has been the synthetic generation
of handwriting, in particular signatures (two examples in6and7). This model has
recently been used in8and9not to generate synthetic signature samples, but to
improve the performance of traditional signature verification systems. In8the au-
thors proposed a skilled forgery detector using some features extracted from the
Sigma LogNormal model whereas in,9a new set of features based on the Sigma
LogNormal model was proposed achieving very good performance.
In this paper we report experimental work for the usage of the Sigma LogNor-
mal model to predict the complexity of biomechanical tasks on two case studies:
1) The first one describes its application to on-line signatures in order to generate
user-based complexity groups (as there are users with very complex signatures
and others with very simple ones). Then, a specific signature verification system
is developed for each complexity group achieving very significant improvements
of verification performance.10 2) On the other hand, the second one describes
its application to detect age groups (children from adults) in touch dynamic tasks
performed on smartphones or tablets,11 as the difference between adults and chil-
dren is mainly caused by the different maturity of their anatomy and neuromotor
system. These are less mature in children, so they have worse manual dexterity
causing rougher movements.5,12
The remainder of the paper is organized as follows. Sec. 2 describes the Sigma
LogNormal model, used in this work to model the complexity of handwritten
tasks. Sect. 3 describes the first case study focused on modeling the complexity
of on-line signatures and its experimental results. Sect. 4 describes the second
case study focused on modeling the complexity of touch dynamic information in
order to detect age groups and its experimental results. Finally, Sec. 5 draws the
final conclusions and points out some lines for future work.
2. The Sigma LogNormal Model
Many models have been proposed to analyze human movement patterns in general
and handwriting in particular. These models allow the analysis of features related
to motor control processes and the neuromuscular response, providing comple-
mentary features to the traditional Xand Ycoordinates related to handwriting
tasks. One of the most well known writing generation models is the Sigma Log-
Normal model.5,13
The Sigma LogNormal model decomposes the complex signals that describe
the speed of muscular movements into simpler ones that can be explained by a
few parameters. These parameters contain information about the activity itself
and about the neuromotor skills of the person.14 In particular, the Sigma Log-
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Modeling the Complexity of Signature and Touch-Screen Biometrics using the Lognormality Principle3
Fig. 1. Trace and velocity profile of one reconstructed on-line signature using the Sigma LogNormal
model. A single stroke of the signature and its corresponding lognormal profile are highlighted in red
colour. Individual strokes are segmented within the LogNormal algorithm.5
Normal model states that the velocity profile of human hand movements can be
decomposed into strokes. Moreover, the velocity of each of these strokes, i, can
be described with a speed signal vi(t)that has a lognormal shape:
|vi(t)|=Di
p2πσi(t−t0i)exp(−(ln(t−t0i)−µi)2
2σ2
i
)(1)
where each of the parameters are described in Table 1. The complete velocity
profile is modelled as a sum of the different individual stroke velocity profiles as:
vr(t) =
N
X
i=1
vi(t)(2)
where Nis the number of lognormals of the entire movement. A complex
action, like a handwritten signature or touch task, is a summation of these lognor-
mals, each one characterized by different values for the six parameters in Table
1. Fig. 1 shows an example of the lognormal velocity profiles extracted for each
stroke of one signature.
3. Case Study 1: On-Line Signature Complexity
Signature verification systems have been shown to be highly sensitive to signature
complexity.15 In,16 Alonso-Fernandez et al. evaluated the effect of the complexity
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4R. Vera-Rodriguez, R. Tolosana, J. Hernandez-Ortega, A. Acien, A. Morales, J. Fierrez and J. Ortega-Garcia
Table 1. Sigma LogNormal parameters description.
Parameter Description
DiInput pulse: covered distance when executed isolated.
t0iInitialization time. Displacement in the time axis.
µiLogtemporal delay.
σiImpulse response time of the neuromotor system.
θsi Initial angular position of the stroke.
θei Final angular position of the stroke.
and legibility of the signatures for off-line signature verification (i.e. signatures
with no available dynamic information) pointing out the differences in perfor-
mance for several matchers. Signature complexity has also been associated to the
concept of entropy, defining entropy as the inherent information content of bio-
metric samples.17,18 In19 a “personal entropy” measure based on Hidden Markov
Models (HMM) was proposed in order to analyse the complexity and variability of
on-line signatures regarding three different levels of entropy. In addition, the same
authors have recently proposed in20 a new metric known as ”relative entropy” for
classifying users into animal groups where skilled forgeries are also considered.
Despite all the studies performed regarding on-line signature as a biometric trait,
none of them have exploited, as far as we are aware, the concept of complexity in
order to develop more robust and accurate on-line signature verification systems.
3.1. Proposed System
The architecture of our proposed system is shown in Fig. 2. Based on the parame-
ters of the Sigma LogNormal model, we propose to use the number of lognormals
(N) that models each signature as a measure of the complexity level of the signa-
ture. Once this parameter is extracted for all available genuine signatures of the
enrolment phase, the user is classified into a complexity level using the majority
voting algorithm (low, medium and high complexity levels). Only genuine signa-
tures are considered in our proposed approach for measuring the complexity level.
The advantage of this approach is that the signature complexity detector can be
performed off-line thereby avoiding time consuming delays and making it feasible
to apply in real time scenarios.
Then, after having classified a given user into a complexity group, a specific
on-line signature verification module based on time functions (a.k.a. local sys-
tem)21 has been adapted to each signature complexity level. For each signature
acquired, signals related to Xand Ypen coordinates are used to extract a set of
23 time functions, similar to22 (see Table 2). The most discriminative and robust
time functions of each complexity level are selected using the Sequential Forward
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Modeling the Complexity of Signature and Touch-Screen Biometrics using the Lognormality Principle5
Identity claim
Low Personal Entropy System
Similarity
Computation
Similarity
Computation
Similarity
Computation
Similarity
Computation
Similarity
Computation
Similarity
Computation
Pre-Processing Time
Funct. Extraction
Low Personal Entropy System
Medium Personal Entropy SystemMedium Personal Entropy System
High Personal Entropy SystemHigh Personal Entropy System
Accepted or
Rejected
Enrollment SignaturesEnrollment Signatures
Sigma LogNormal
Features Extraction
Classif er
Classif er
Personal
Entropy
Detector
Pre-Processing
Pre-ProcessingPre-Processing
Pre-Processing
Pre-Processing
Time
Funct. Extraction
Time
Funct. Extraction
Time
Funct. Extraction
Time
Funct. Extraction
Time
Funct. Extraction
Sigma LogNormal
Features Extraction Decision
Threshold
Decision
Threshold
Decision
Threshold
Decision
Threshold
Decision
Threshold
Decision
Threshold
Fig. 2. Architecture of our proposed methodology focused on the development of an on-line signature
verification system adapted to the signature complexity level.
Feature Selection algorithm (SFFS) enhancing the signature verification system
in terms of EER.
The local system considered in this work for computing the similarity between
the time functions from the input and training signatures is based on DTW algo-
rithm.23 Scores are obtained as:
score =e−D/K (3)
where Dand Krepresent respectively the minimal accumulated distance and
the number of points aligned between two signatures using DTW algorithm.
3.2. Database and Experimental Protocol
In this case, BiosecurID database24 is considered. Signatures were acquired from
a total of 400 users using a Wacom Intuos 3 pen tablet with a resolution of 5080
dpi and 1024 pressure levels. The database comprises 16 genuine signatures and
12 skilled forgeries per user, captured in 4 separate acquisition sessions. Each
session was captured leaving a two month interval between them, in a controlled
and supervised office-like scenario. Signatures were acquired using a pen stylus.
The available information within each signature is: Xand Ypen coordinates and
pressure. In addition, pen-up trajectories are available.
The experimental protocol has been designed to allow the study of different
signature complexity levels in the system performance. Two main experiments
are carried out: 1) evaluation of the signature complexity detector proposed in this
work in order to classify users into different complexity levels, and 2) evaluation
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6R. Vera-Rodriguez, R. Tolosana, J. Hernandez-Ortega, A. Acien, A. Morales, J. Fierrez and J. Ortega-Garcia
Table 2. Set of time functions considered in this work.
# Feature
1 x-coordinate: xn
2 y-coordinate: yn
3 Pen-pressure: zn
4 Path-tangent angle: θn
5 Path velocity magnitude: vn
6 Log curvature radius: ρn
7 Total acceleration magnitude: an
8-14 First-order derivate of features 1-7:
˙xn,˙yn,˙zn,˙
θn,˙vn,˙ρn,˙an
15-16 Second-order derivate of features 1-2: ¨xn,¨yn
17 Ratio of the minimum over the maximum speed over a 5-
samples window: vr
n
18-19 Angle of consecutive samples and first order difference: αn,
˙αn
20 Sine: sn
21 Cosine: cn
22 Stroke length to width ratio over a 5-samples window: r5
n
23 Stroke length to width ratio over a 7-samples window: r7
n
of the proposed approach based on a separate on-line signature verification system
adapted to each signature complexity level.
For the first experiment, our proposed signature complexity detector is ana-
lyzed using all available users from BiosecurID. For the second experiment, the
BiosecurID database is split into development dataset (40% of the users) and eval-
uation dataset (the remaining 60% of the users). The development dataset is con-
sidered in order to select the most discriminative and robust time functions for
each signature complexity level using the SFFS algorithm whereas the evaluation
dataset is considered for the evaluation of the proposed system. Both skilled and
random forgeries are considered using the 4 signatures from the enrolment session
as reference signatures and the remaining 12 genuine signatures and 12 skilled
forgeries signatures as the test. The final score is obtained after performing the
average score of the four one-to-one comparisons.
3.3. Results
3.3.1. Analysis of the Signature Complexity Detector:
The first experiment was designed to evaluate the proposed approach for signature
complexity detection. For this, the signature complexity detector was performed
in two different steps. First, each user of the BiosecurID database was manu-
ally labelled in a signature complexity level (low, medium, high). This process
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Modeling the Complexity of Signature and Touch-Screen Biometrics using the Lognormality Principle7
0 10 20 30 40 50 60
Number of Lognormals
0
0.05
0.1
0.15
Probability Density Function
Low Complexity
Medium Complexity
High Complexity
Fig. 3. Probability density function of the number of lognormals for each complexity level using all
genuine signatures of the BiosecurID database. The three proposed complexity-dependent decision
thresholds are highlighted by black dashed lines.
was carried out by manually labelling the image of just one genuine signature
per user. This was performed by two annotators and two times each in order to
keep consistency on the results. Three different complexity levels were consid-
ered based on previous works.20 Users with signatures longer in writing time and
with an appearance more similar to handwriting were labelled as high-complexity
users whereas those users with signatures shorter in time and with generally sim-
ple flourish with no legible information were labelled as low-complexity users.
This first stage served as a ground truth. Following this stage, the Sigma Log-
Normal parameter Nwas extracted for each available genuine signature of the
BiosecurID database (i.e. a total of 400 ×16 = 6400 genuine signatures). Then,
we represented for each complexity level their corresponding distribution of log-
normals according to the ground truth performed during the first stage. Fig. 3
shows the distributions of the number of lognormals obtained for each complexity
level using all genuine signatures of the BiosecurID database. The three proposed
complexity-dependent decision thresholds are highlighted by black dashed lines
and were selected in order to minimize the number of misclassifications between
different signature complexity levels. Signatures with lognormal values equal or
less than 17 are classified as low-complexity signatures whereas those signatures
with more than 27 lognormals are classified into the high-complexity group. Oth-
erwise, signatures are categorized into medium-complexity level. Fig. 4 shows
some of the signatures classified into each complexity level.
We now analyse each resulting complexity level following the same proce-
dure proposed in:20 analysing the system performance for different complexity
groups considering only Xand Ypen coordinates. It is important to remark that
each user is classified into a complexity level applying the majority voting algo-
rithm to all available enrolment signatures of the user. Table 3 shows the system
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8R. Vera-Rodriguez, R. Tolosana, J. Hernandez-Ortega, A. Acien, A. Morales, J. Fierrez and J. Ortega-Garcia
Fig. 4. Signatures categorized for each complexity level using our proposed signature complexity
detector. From top to bottom: low, medium and high complexity.
performance for each complexity level in terms of EER(%). The results show dif-
ferent system performance regarding the signature complexity level. Users with a
high complexity level have an absolute improvement of 4.3% compared to users
categorized into a low complexity level for skilled forgeries. Therefore, the idea
of considering a different optimal on-line signature verification system for each
signature complexity level is analysed in next sections in order to select the most
discriminative and robust time functions for each complexity group and reduce
the system performance.
3.3.2. Time-Functions Selection for the Complexity-based Signature
Verification System:
First we analyse which are the most discriminative and robust time functions for
each signature complexity level using the SFFS algorithm over the development
dataset. The following three cases are studied:
(1) Time functions selected for all three signature complexity levels.
(2) Time functions selected only for medium and high signature complexity lev-
els.
(3) Time functions selected only for low and medium signature complexity levels.
For the first case, the time functions ˙zn,˙anand vr
n(see Table 2) have been
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Modeling the Complexity of Signature and Touch-Screen Biometrics using the Lognormality Principle9
Table 3. Experiment 1: System performance results (EER
in %) of the BiosecurID database of each personal complex-
ity level.
Low C. Medium C. High C
Skilled forgeries
Random forgeries
22.2
3.6
21.7
2.4
17.9
2.6
selected in all systems as robust time functions regardless of the signature com-
plexity level. These time functions are the variation of pressure, variation of ac-
celeration and ratio of the minimum over the maximum speed and provide general
and valuable information to all signature verification systems about the knowledge
and speed of the users performing their signatures. For the second case, the time
functions ˙vn,¨ynand ˙αnhave been selected for both medium and high signature
complexity levels. These time functions provide information related to the vari-
ation of the velocity, vertical acceleration and variation of angle, time functions
more related to the geometry of characters and therefore, with the handwriting. Fi-
nally, the time function cnis the only one selected for the third case and provides
information related to the angles as signatures with low and medium complexity
level are usually categorized for having simple flourishes with no legible informa-
tion. It is important to highlight that the time function ¨ynis not selected for users
with low signature complexity level. In other studies such as,25 this time function
was selected in most optimal systems. However, the vertical acceleration seems
not to be very discriminative for users with low signature complexity level as their
signatures are usually simpler and not related to handwriting.
3.3.3. Experimental Results of the Complexity-based Signature Verifica-
tion System:
The second part of the experimental work was focused on developing a specific
verification system for each group of signature complexity. For this, the SFFS
algorithm was applied to the development dataset in order to find the most dis-
criminative time functions for each complexity group. Then, the evaluation of the
proposed system was compared to a baseline system based on DTW and the same
system (same time functions) for all complexity groups, similar to the baseline
system presented in.8
Table 4 shows the evaluation results achieved considering our proposed
approach based on personal entropy on-line signature verification systems.
Analysing the results obtained, our Proposed Systems achieve an average abso-
lute improvement of 2.5% EER compared to the Baseline System for the case of
skilled forgeries. It is important to note that for the most challenging users (users
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10R. Vera-Rodriguez, R. Tolosana, J. Hernandez-Ortega, A. Acien, A. Morales, J. Fierrez and J. Ortega-Garcia
Table 4. Experiment 2: System performance results (EER in %) on the evaluation dataset for each
signature complexity level.
Low C. Medium C. High C.
Baseline Proposed Baseline Proposed Baseline Proposed
Skilled forgeries
Random forgeries
13.8
1.5
10.1
1.3
7.5
0.7
5.2
0.5
6.2
0.9
4.6
0.9
with high personal entropy level), our proposed approach achieves an absolute
improvement of 3.7% EER compared to the Baseline System. Analysing the re-
sults obtained for the random forgery cases, our Proposed Systems also achieves
improvements for all personal entropy levels. For this case, the improvement has
been lower than for skilled forgery cases due to its low values and the way that the
SFFS algorithm was applied during the training of the systems (focused on skilled
forgery cases). Results obtained after applying our proposed approach based on
personal entropy on-line signature verification systems outperform the results of
the state-of-the-art for the BiosecurID database. In,8the authors achieved an ab-
solute improvement of 1.0% EER for skilled forgery cases whereas our proposed
approach achieves an average absolute improvement of 2.5% EER compared to
the same Baseline System.
Fig. 5. Experiment 2: Analysis of the False Rejection Rate (FRR) at different values of False Ac-
ceptance Rate (FAR) for both Proposed and Baseline Systems on the whole evaluation dataset.
For completeness, Fig. 5 shows the performance of the Baseline and Proposed
Systems considering all personal entropy levels together in terms of the false re-
jection rate (FRR) at different values of false acceptance rate (FAR). Our Proposed
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Modeling the Complexity of Signature and Touch-Screen Biometrics using the Lognormality Principle11
Systems achieve a final value of 5.8% FRR for a FAR = 5.0% and 3.9% FRR for
a FAR = 10.0%. These results show the importance of considering different sig-
nature verification systems for each personal entropy level in order to enhance the
verification systems with more robust time functions.
4. Case Study 2: Predicting Age Groups from Touch Patterns
Age groups prediction based on handwritten touch patterns acquired from touch-
screen devices such as smartphones or tables is a recent and important challenge.
Touchscreen devices provide mobile access to an unlimited number of digital con-
tents and services (e.g. more than a half of YouTube visits come from mobile de-
vices and this percentage is increasing26). Digital services are used by people from
everywhere, all ages, all ethnicities and all socioeconomic status. In this context,
the classification of users according to geographic and demographic attributes is
crucial for service personalization (e.g. recommender systems, parental control,
security).27 Some of these attributes can be obtained from metadata associated
to the device (e.g. IP address, language selection, GPS location) or can be in-
ferred from the user behavior (e.g. browsing history, social network contents, and
keystroke dynamics).28 We want to highlight the spread of the use of this kind of
devices by young children. The study in29 reveals that 97% of US children under
the age of four use mobile devices, regardless of family income.
In this case study we analyze a way to classify users of touch panels according
to two age groups (children and adults). The age is a key attribute in user pro-
filing with direct application on several automatic systems (e.g. parental control,
recommender systems, advertising). Three examples of use cases are: i) lock-
ing content and/or applications: locking some services in tablets and smartphones
when children are using them, i.e. buying new applications or sensitive content;
ii) user’s age study by service providers: this way service providers could develop
new content that fits better to their actual audience; iii) real-time interface adapt-
ing: as children have worse control of their fine movements than adults, changing
default interfaces to special tailored ones could be beneficial.
The most popular method to reveal the age of the user is based on an online
questionnaire in which the user directly answers questions about his age. How-
ever, this solution assumes: i) honesty on the response of the users, and ii) users
can read. Both assumptions cannot be guaranteed because of many practical rea-
sons. Besides the fact that people lie, nowadays children start to use digital plat-
forms and services before learning to read.
In the existing literature, there are many experiments exploring the use of tech-
nology by children, seeking how to improve the design of adapted interfaces and
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12R. Vera-Rodriguez, R. Tolosana, J. Hernandez-Ortega, A. Acien, A. Morales, J. Fierrez and J. Ortega-Garcia
applications.30 However, modeling and characterizing mathematically how chil-
dren interact with touch devices and how their conduct differs from the adult’s
one is a field that has not been studied deeply enough. A work related to this topic
is31 where they analyzed different types of touching tasks like tap, rotate or drag
and drop, and they found that children have different success rates when trying to
perform different tasks. Simple tasks - for example tapping - can be done by all
children without any problem, but the more complex ones are very difficult to be
completed by very young children.
In,32 they measured the touch patterns of children and compared it to patterns
from adults. They discovered that children have a larger miss rate than adults when
trying to hit small targets. In33 tap tasks are used to extract time and precision-
based features. They designed two different approaches, using only one tap for
classification and using 7 consecutive tasks. They get high accuracy rates: 86.5%
in the one tap approximation, and 99% of accuracy using 7 consecutive taps to
combine their scores. Even though they get good results using tap tasks, we de-
cide to use drag and drop tasks because the differences between the neuromotor
development of users can be manifested in a better way. The direct comparison
between approaches is not fair because we are using different tasks/information
to classify users. However, in our work we demonstrate that using a very com-
mon and fast action (e.g. unlock screen based on drag and drop) we can achieve
higher classification rates that those achieved in33 for the one task approach (the
second approach has not been implemented yet). In our opinion, both approaches
are complementary, have very different nature, and can be combined to achieve
higher performances.
The difference between adults and children is mainly caused by the differ-
ent maturity of their anatomy and neuromotor system. These are less mature in
children, so they have worse manual dexterity causing rougher movements.12,34
In order to characterize the interaction of children and adults with touchscreen
devices, we propose to use a model of the human neuromotor system. The Sigma
LogNormal theory of rapid human movements represents complex movements
with an analytic model that describes some physical and cognitive features of hu-
man beings.35,36 Studies like14 have proved that the Sigma LogNormal model can
be used to characterize children handwriting. They conclude that there are two
main groups of children separable by looking at their learning stage. Children’s
neuromotor skills become more similar to the adults’ skills when they grow up,
namely, when they finish their preoperational stage. At age 10 children know how
to activate each little muscle properly to produce determinate fine movements.37
As they are based on the same neuromotor skills, the principles applied to hand-
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Modeling the Complexity of Signature and Touch-Screen Biometrics using the Lognormality Principle13
Table 5. Sigma LogNormal features extracted.
Space-based features Time-based features
f1=Dif8= ∆t0=t0i−t0i−1
f2=µif9=v2=|vi(t2i)|
f3=σif10 =v3=|vi(t3i)|
f4= sin(θsi)f11 =v4=|vi(t4i)|
f5= cos(θsi)f12 =δt05 =t5i−t0i
f6= sin(θei)f13 =δt15 =t5i−t1i
f7= cos(θei)f14 =δt13 =t3i−t1i
f15 =δt35 =t5i−t3i
f16 =δt24 =t4i−t2i
f17 = ∆t1=t1i−t1i−1
f18 = ∆t3=t3i−t3i−1
writing models can be also used to model touchscreen patterns.
In this case study we propose the use of the Sigma LogNormal model to de-
tect age groups as simple application of the model to drag and drop touch tasks
showed large differences between adults and children velocity profiles. In par-
ticular, this case study is focused in age classification of users into two groups:
children under 6 years old and adults. We use information of simple touch tasks
collected from 119 people (89 children and 30 adults) using two different types of
devices: a smartphone and a tablet. Single-sensor and cross-sensor scenarios have
been evaluated. The results show accuracies over 90% in several scenarios with
top correct classification rate of 96% for the data obtained from tablets.
4.1. Proposed System
In this case, a more complex system was developed compared to Case Study 1 in
order to predict age groups from drag and drop touch tasks, as the main focus here
was to optimize the final classification result.
The parameters of the Sigma LogNormal model (as described in Sect. 2)
were used to calculate 18 different features per lognormal (see Table 5) as de-
scribed in.35 These features can be classified into two groups: space-based and
time-based. Space-based features are those that give information about the spa-
tial distribution of the strokes, such as Di,µi,σi, and other features based in θsi
and θei (see Table 1). Time based features are composed by the values of speed at
some relevant points of the strokes like their maximum or inflexion points; and the
time-offsets between those points. The task time and the number of lognormals in
each task have been added as additional features.
It is worth noting that the lognormals with amplitude value lower than a thresh-
old were discarded. Then, the 18 features from35 are computed for each stroke,
and each parameter is averaged across strokes. The 18 averaged parameters are
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14R. Vera-Rodriguez, R. Tolosana, J. Hernandez-Ortega, A. Acien, A. Morales, J. Fierrez and J. Ortega-Garcia
Fig. 6. Comparison between Sigma LogNormal speed profiles for (a) an adult and (b) a child follow-
ing the same task.
augmented with the task time and the number of strokes to generate the final fea-
ture vector of size 20.
Regarding the classification of the age of the user, quite often it is possible to
differentiate between children and adults by simply looking at the velocity pro-
file of a touch screen task. In Figure 6, an example of these types of profiles is
presented, consisting in performing a drag and drop task in both cases. A visual
comparison between children and adults velocity profiles shows that children’s
signals are usually composed by a higher number of strokes than the adults’ ones,
and therefore have a higher degree of complexity.
Figures 7(a) and 7(b) show the histograms of two features (Covered distance
f1, and Logtemporal delay f2) for children and adults. These two features are
highly discriminative as their histograms are clearly separated, showing differ-
ences between both classes and therefore suggesting the potential for the classifi-
cation task.
As a classifier we use a SVM (Support Vector Machine) with a RBF (Radial
Basis Function) kernel because of its good general performance in binary classifi-
cation tasks and the few number of parameters to configure.
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Modeling the Complexity of Signature and Touch-Screen Biometrics using the Lognormality Principle15
0.4999 0.49995 0.5 0.50005 0.5001 0.50015 0.5002
Covered distance "D" (f1)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Probability Density Function
TABLET
children
adults
0.49985 0.4999 0.49995 0.5 0.50005 0.5001 0.50015
µ (f2)
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Probability Density Function
TABLET
children
adults
Fig. 7. Probability Density Functions for two features (f1and f2). These are highly discriminative
features as histograms are separated.
4.2. Database and Experimental Protocol
The database used is publicly available and was presented in.37 It is comprised
with data from touchscreen activity of both children and adults performing pre-
designed tasks in an ad-hoc app. In the present work, we have used the data from
singletouch and multitouch drag and drop activities. Drag and drop activities con-
sist of picking one object on the device screen and moving it to a target area.
Multidevice information is available as the users have completed the tasks both
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16R. Vera-Rodriguez, R. Tolosana, J. Hernandez-Ortega, A. Acien, A. Morales, J. Fierrez and J. Ortega-Garcia
Table 6. Accuracy results for the 20 lognormal features. The accuracy is measured as the rate of correct classifications considering
both classes.
Testing samples
Phone Singletouch Tablet Singletouch Phone Multitouch Tablet Multitouch
Phone Singletouch 93.6% 95.0% 88.0% 92.1%
Tablet Singletouch 93.7% 96.3% 88.9% 94.0%
Phone Multitouch 94.1% 95.9% 88.0% 92.8%
Traning samples
Tablet Multitouch 93.0% 96.3% 87.9% 94.6%
in a smartphone and in a tablet. Both single-sensor and cross-sensor tasks are
analyzed.
The dataset is composed by 89 children between 3 and 6 years old and 30
young adults under 25 years old. The mean age of the children is 4.6 years. The
total number of drag and drop tasks is 2912 for children and 1157 for adults (see37
for more details).
As the experimental protocol, the database was divided randomly into training
(60%) and testing (40%). The random selection was repeated 50 times and the
final performance is presented in terms of averaged correct classification accuracy.
4.3. Results
Table 6 shows the accuracies obtained according to the different scenarios. They
are presented in terms of correct classification accuracy (percentage of samples
from both classes correctly classified).
The mean value of accuracy having into account all the evaluated scenarios
is 92.8%. The classification rates are over 96% in a single-sensor setting and
over 95% in a cross-sensor scenario. The best results are obtained with tablets as
sensors, while using smartphone’s data slightly degrades the results.
Compared with33 where they get an accuracy rate of 86.5% using one tap task
for classification and with a single-sensor aproximation (using smartphone’s data),
our system performs better, getting a 93.6% of accuracy using only data from
smartphones, and over 96% using data from tablets. Another conclusion that can
be extracted from Table 6 is that the data obtained from multitouch tasks get worse
results than the singletouch cases. The best multitouch scenario is obtained using
tablet’s data for both training and testing, with a 94.6% of accuracy, compared
with its singletouch counterpart that gets a 96.3%. This may be caused by the less
developed control of the left hand by right-handed people and vice versa. The
main reason for using the Sigma LogNormal model is that adults have a better
control of fine movements than children, what is translated to different values for
the model parameters.37
The cross-sensor scenarios get results not too far from the single-sensor sce-
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Modeling the Complexity of Signature and Touch-Screen Biometrics using the Lognormality Principle17
narios. The results obtained using smartphone singletouch data for training, and
tablet singletouch data for testing (95.9% of accuracy) are quite similar to those
obtained using only tablet singletouch data (96.3% of accuracy). This fact makes
this type of systems very suitable for real applications due to its high independence
of the device used.
Due to the higher number of children in the database compared to adults, se-
lecting a percentage of the total users make the two scenarios unbalanced. Ex-
periments balancing the number of both classes in training and testing have been
made. The results show small variations around 1% of accuracy with respect to
the presented results.
Figure 8 shows histograms of the scores calculated in the classification pro-
cess. It can be seen that the scores from children and adults are visibly sepa-
rated into two different zones, making possible to obtain high accuracy rates (over
96%). There are also other zones where the scores distributions overlap. These
regions are the source of incorrect classifications. Combining scores from several
tasks of the same user could make possible to reduce the overlap areas, increasing
even more the accuracy rate.
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18R. Vera-Rodriguez, R. Tolosana, J. Hernandez-Ortega, A. Acien, A. Morales, J. Fierrez and J. Ortega-Garcia
Fig. 8. Histograms of scores using the Sigma LogNormal model features. Left figure represents the
scores for single-sensor scenario, using tablet singletouch data for both training and testing. Right
figure shows the histogram for a cross-sensor scenario, using phone singletouch data for training and
tablet multitouch data for testing the classifier.
5. Conclusions
This work has reported experimental results on modeling the complexity of
biomechanical tasks through the usage of the Sigma LogNormal model of the
Kinematic Theory of rapid human movements. Two different case studies have
been analyzed.
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Modeling the Complexity of Signature and Touch-Screen Biometrics using the Lognormality Principle19
The first case study has focused on applying the Sigma LogNormal model to
develop an on-line signature complexity detector. Just by using the number of
strokes of the signatures was enough to obtain very good results differentiating
between three different signature complexity groups (low, medium and high). As
a second stage, a specific signature verification system was developed for each
signature complexity group by carrying out a time functions selection process.
Very significant improvements of recognition performance have been shown when
comparing the proposed system with a baseline, being both based on DTW and
time functions as features. For future work, the approach considered in this work
will be further analysed using the e-BioSign public database38 in order to consider
new scenarios such as the case of using the finger as the writing tool. Novel sys-
tems based on the usage of Recurrent Neural Networks (RNNs)39 and the fusion
of different systems40 will be considered. Also, different types of presentation
attacks to signature recognition systems41 will be considered analysing how sig-
natures with different complexity levels are affected.
On the other hand, the second case study has focused on age group predic-
tion (children from adults) from handwritten touch patterns acquired from touch-
screen devices such as smartphones or tables. Applying the Sigma LogNormal
model to some examples of drag and drop tasks from children and adults showed
that children had a more complex velocity profiles with a larger number of sigma
lognormals. The proposed approach is based on 20 features extracted from the
model, and results achieved were very promising with classification rates over
96% in a single-sensor setting and over 95% in a cross-sensor scenario. Future
work includes the analysis of touchscreen data to continuously monitor the user
behaviour.42
Acknowledgements
This work has been supported by project TEC2015-70627-R MINECO/FEDER,
Bio-Guard (Ayudas Fundacin BBVA a Equipos de Investigacin Cientfica 2017)
and by UAM-CecaBank Project. Ruben Tolosana and Alejandro Acien are sup-
ported by a FPU Fellowship from Spanish MECD, and Javier Hernandez by a FPI
Fellowship from UAM.
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