Yanushkevich S.N., Wang P.S.P., Gavrilova M.L., Srihari S.N. (eds.) Image Pattern Recognition. Synthesis and Analysis in Biometrics
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28 Synthesis and Analysis in Biometrics
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Chapter 2
Signature Analysis, Verification and Synthesis in
Pervasive Environments
Denis V. Popel
Biometric Technology Group,
Computer Science Department, Baker University,
P.O. Box 65, Baldwin City, KS 66006, USA
denis.popel@bakeru.edu
Despite the wide appreciation of biometric principles in security
applications, biometric solutions are far from being affordable and
available “on demand” anytime and anywhere. Many security biometric
solutions require dedicated devices for data acquisition delaying their
deployment and limiting the scope. The chapter focuses primarily
on analysis of data taken from a human signatures for his/her
authentication or identification. Also the chapter introduces a system
developed to identify and authenticate individuals based on their
signatures and/or handwriting. The issues of pervasive services are
addressed (i) by integrating unique data acquisition and processing
techniques which are capable of communicating with a variety of off-
the-shelf devices such as pressure sensitive pens, mice, and touch pads,
(ii) by using sequence processing techniques (like matching, alignment
or filtering) for signature analysis techniques and comparison, (iii) by
using the self-learning database solutions for achieving accurate results,
and (iv) by utilizing signature synthesis techniques for benchmarking
and testing.
Contents
2.1. Introduction ................................... 32
2.2. SignatureRepresentation............................ 34
2.3. SignatureComparison ............................. 36
2.3.1. SequenceAlignment.......................... 37
2.3.2. AlgorithmandExperimentalResults ................ 43
2.4. SignatureSynthesis............................... 47
2.4.1. SignatureSynthesisTechniques ................... 47
2.4.2. Statistically Meaningful Synthesis . . . . . . . . . . . . . . . . . . 48
2.4.3. Geometrically Meaningful Synthesis . . . . . . . . . . . . . . . . . 49
31
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32 Synthesis and Analysis in Biometrics
2.4.4. AlgorithmandExperimentalResults ................ 54
2.5. SystemArchitecture .............................. 55
2.6. Concluding Remarks and Future Work . . . . . . . . . . . . . . . . . . . . 59
Bibliography ....................................... 62
2.1. Introduction
The research in signature biometrics is traditionally interdisciplinary and
includes such fields as data retrieval and scanning, sequence processing
and understanding physical properties, image processing and pattern
recognition, and even physiology and psychology. Signature processing
deals with behavioural human characteristics, and can be classified as
behavioural biometrics
[
5
]
. These characteristics can be captured by various
input devices such as scanners and tablets. Currently there is no universal
standard to represent signature biometrics. The variety of input devices
with their own formats complicates the situation for data storage and
processing. Human involvement with societal and legal issues, such as
protection of privacy and legality of information gathering, makes the
situation even more complicated.
There are many techniques used (see
[
3,5,10,9,15,16
]
for details) to
acquire and process signatures and/or handwriting depending on the
target application area (e.g. user authentication or document automation),
signature and handwriting producer (e.g. written by an ink pen or gyro-
pen) and image acquisition devices (e.g. flat scanners or pressure sensitive
tablets). Further, there is no standard representation for this wide variety
of signature images. However, our preliminary study
[
8,11
]
suggests
that this question is answerable by an appropriate architecture of the
system which integrates mathematical models, formats, and self-learning
databases. Our research demonstrates that the majority of contour images
should be modelled using graph-based approaches, or, at the very least,
using approaches derived from continuous or multiple-valued (as opposed to
binary) logic
[
14
]
. Some known modeling systems discard graph information
by preserving only sequential representations. This explains many obvious
limitations of current systems such as the lack of a unified approach for
image transformation operations, strong dependence on the resolution of
image acquisition systems, and the inability of software to make use of the
originally graph-based nature of some images. By using proper formats,
the tasks below can be accomplished faster, easier, and at a lower cost.
Some biometric characteristics, such as irises, retinas, and fingerprints,
do not change significantly over time, and thus they have low in-class
variation. The in-class variations for signatures can be large meaning
that signatures from a single individual tend to be different. Even forensic
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Signature Analysis, Verification and Synthesis 33
experts with long-term experience cannot always make a decision whether
a signature is authentic or forged
[
1
]
. Signatures are easier to forge than,
for example, irises or fingerprints. However, the signature has a long
standing tradition in many commonly encountered verification tasks, and
signature verification is accepted by the general public as a non-intrusive
procedure while hand prints and fingerprint verification, on the other hand,
are associated with criminal investigations. It is assumed in automated
signature processing that an individual’s signature is unique. The state-of-
the-art tools for automated signature analysis and synthesis rely partially
or totally on methods of artificial intelligence. Some of these methods are
mentioned in this chapter.
There are two types of automated signature processing: off-line and
on-line. Off-line signature processing is used when a signature is available
on a document. It is scanned to obtain its digital representation. On-line
signature processing relies on special devices such as digitizing tablets with
pens and/or gyropens to record pen movements during writing. In on-line
processing, it is possible to capture the dynamics of writing, and, therefore,
it is difficult to forge. Even with an image of the signature available,
dynamic information (kinematics) pertinent to a signature is not as readily
available to a potential forger as is the shape of signature (geometry).
Skilled forgers can reproduce signatures to fool the unskilled eye. Human
experts can distinguish genuine signatures from the forged ones. Modeling
the invariance in the signatures and automating the signature recognition
process pose significant challenges.
Aiming to solve some critical problems in pervasive signature processing,
this chapter describes a system built to analyze and simulate human
signatures. It is accomplished by (i) introducing some widely used signature
descriptions, (ii) outlining a method for aligning sequences of multi-
valued and continuous data for signature verification, and (iii) describing
a methodology of automated signature generation for testing. It also
introduces an efficient algorithm based on matching principles which is
capable of measuring distances between signatures and aligning them to
fulfil maximum correlation requirement. Overall, the system exploits
the complete cycle of signature processing which includes representation,
analysis, modeling, matching, and simulation.
This chapter is structured as four main blocks: an overview of signature
representation methods is given in Section 2.2, signature comparison
methods and algorithms for sequence alignment and matching are outlined
in Section 2.3, some techniques for signature synthesis are introduced in
Section 2.4, the overall architecture of the system as well as implementations
issues are given in Section 2.5. Section 2.6 concludes the chapter and
presents possible extensions.
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34 Synthesis and Analysis in Biometrics
2.2. Signature Representation
Many types of images like signatures can be classified as contour images
or line objects stored on paper or electronic media. Line objects carry
both geometric and kinematic information and cannot be handled in the
same manner as raster or 2D images. In signatures, the line shape as well
as its thickness, and other characteristics along the contour, which can be
retrieved from the completed image, represent geometric information, while
characteristics such as speed of writing or exerted pressure along the line
drawn can only be retrieved in the process of creating the image and thus
represent kinematic information.
Example 2.1. Both geometric and kinematic characteristics can be merged
into a single 3D representation. The 3D representation of a signature is
given in Fig. 2.1.
X
Y
Pressure
Fig. 2.1. 3D view of the on-line signature: the plain curve is given by the two-tuple
(X, Y ), the pressure is associated with the Z axis, the speed of writing is depicted by
the shade of the curve, where darker is slower speed (Example 2.1).
The simplest form of the handwriting is represented by a plane curve.
There are three commonly used descriptions of plane curves:
Implicit form: f(x, y)=0;
Explicit form: y = f(x), considered as a function graph;
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Signature Analysis, Verification and Synthesis 35
Parametric form: r(t)=(x(t),y(t)), using Cartesian parametric
equations x = x(t)andy = y(t).
The latter form has been selected for further plane curve description of
handwriting. Such a selection is justified by the nature of data which is
acquired in a parameterized format. We use the following characteristics
of the plane curve representing handwriting with an arbitrary parameter t
(Fig. 2.2): position, velocity, speed, and acceleration.
(x(t),y(t))
r'=(x'(t),y'(t))
I
x
y
t
0
t
Position: r(t)=(x(t),y(t));
Velo c ity :
r
(t)=(x
(t),y
(t));
Speed:
|r
(t)| = |x
(t),y
(t)|;
Acceleration:
r
(t)=(x
(t),y
(t)).
Fig. 2.2. Characteristics of the plane curve representing handwriting with an arbitrary
parameter t.
If t ∈ [t
0
,t] → r(t) with velocity v(t)=r
(t) and speed |v(t)|,then
s(t)=
t
t
0
|v(t)|dt (2.1)
is called the arc lengthof the curve. For a plane curve:
s(t)=
t
t
0
x
(t)
2
+ y
(t)
2
(2.2)
The arc length is independent of the parameterization of the curve. The
value
ds(t)
dt
= s
(t)=
x
(t)
2
+ y
(t)
2
indicates the rate of change of arc
length with respect to the curve parameter t.Inotherwords,s
(t)gives
the speed of the curve parameterization.
For convenience, we also parameterize the curve with respect to its arc
length s: r(s)=(x(s),y(s)). The parameterization defines a direction along
the curve on which s grows. Let t(s)betheunit tangent vectorassociated
with the direction. Denote by ϕ(s) the angle between the tangent at a
point (x(s),y(s)) and the positive direction of the axis x.Thecurvature
measures the rate of bending as the point moves along the curve with unit
speed and can be defined as
k(s)=
dϕ(s)
ds
. (2.3)
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36 Synthesis and Analysis in Biometrics
The curvature is the length of the acceleration vector if r(t) traces the curve
with constant speed 1. A large curvature at a point means that the curve
is strongly bent. Unlike the acceleration or the velocity, the curvature does
not depend on the parameterization of the curve (Fig. 2.3).
s
(x(s),y(s))
I
x
y
t
0
t
k
(
s
)
=d
I
/
ds
Unit tangent vector:
t(t)=
(r)
(t)
|r
(t)|
Curvature: k(t)=
|t
(t)|
|r
(t)|
k(t)=
|r
(t)×r
(t)|
|r
(t)|
3
Fig. 2.3. The curvature measures.
Curvatures are used in the statistical analysis of some contour shapes
[
4
]
.
Curvature possesses the useful beneficial features for signature processing:
• Invariant to shifting (transition) and rotation;
• Gives a unique representation of the curve up to rigid motion; and
• Inversely proportional to scaling: the curve cα(t) has the curvature
k(t)
c
for c>0.
But the most important feature is that the computation of curvature is a
reversible operation: by performing the reverse sequence of steps (numerical
integration), it is possible to restore the original image. This fact has been
used in the comparison method presented below where signature matching
is performed by graph comparison and sequence matching and alignment.
2.3. Signature Comparison
There are two approaches to signature comparison: static and dynamic.
In the static signature comparison, only geometric (shape) features such
as curvatures and angles are used for authentication of identity. Typically,
the signature impressions are normalized to a known size and decomposed
into simple components (strokes). The shapes and stroke relationships are
used as features forming a graph structure. In the dynamic signature
comparison, not only the shape features are used for authentication of
the signature but the dynamic features like pressure and velocity are
also employed. The signature impressions are processed as in the static
signature comparison. Invariants of the dynamic features augment the
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Signature Analysis, Verification and Synthesis 37
static features, making forgery difficult since the forger must know not only
the impression of the signature but also the way the impression was made.
The following sequential characteristics recorded along the trajectory are
used for sequence matching: curvature (geometric), pressure (kinematic),
and velocity (kinematic).
2.3.1. Sequence Alignment
Let us introduce the following notation that will represent the sequence
(vector) of n values A = {a
1
,a
2
,...,a
n
}. Another vector of size m that
will be used for comparison is B = {b
1
,b
2
,...,b
m
}. The parametric
arrangement of these sequences is based on an order index (e.g., a time
stamp).
An alignment of two sequences, A and B, is a pairwise match between
the characters of each sequence. Three arrangements are possible for
comparing two sequences: global alignment which returns the similarity
score for entire vectors; local alignment which finds the longest common
subsequence; and semiglobal alignment which compares a short sequence
and a longer sequence without considering both ends of the sequence. The
focus of this section is on global alignment methods only. Three kinds of
changes can occur at any given position within a sequence: (i) a mutation
that replaces one value with another; (ii) an insertion that adds one or
more positions; or (iii) a deletion that eliminates one or more positions.
Since there are no common rules for value insertion or deletion in the
sequences of curvatures or velocities, gaps in alignments are commonly
added to reflect the occurrence of this type of change. The pairwise
alignment for the sequences A and B results in a two-row matrix built
in a way such that removing all gaps (‘-’) from the first row gives A,and
removing gaps from the second row gives B. A column with two gaps is
not allowed.
The problem of finding the optimal matching or alignment can be solved
using dynamic programming, which is described by using a matrix M with
n rows and m columns. One sequence is placed along the top of the matrix
and the other sequence is placed along the left side. The process of finding
the optimal matching between two sequences is the process of finding an
optimal path from the top left corner to the bottom right corner of the
matrix. Any step in any path can only be done to the right, down or
diagonal. Every diagonal move corresponds to match or mismatch, whereas
a right move corresponds to the insertion of a gap in the vertical sequence,
and a down move corresponds to the insertion of a gap in the horizontal
sequence.