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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58 Synthesis and Analysis in Biometrics
decision making tools. The engine is a robust and scalable technology
designed to support behavioural authentication mechanisms based on
handwritten electronic signatures for identification and verification.
The core of the engine is a database which adjusts the levels of
accuracy and the speed of processing depending on the amount and
quality of inserted data. The database integrates designed input/output
formats, improves searching and matching capabilities, and establishes
intermodular connections among signature processing tools. At the testing
stage, the database is populated with artificially generated signatures (see
Section 2.4). This permits a complete look at the robustness of the signature
processing toolbox and accuracy of matching assuming that noise and
various resolutions or writing conditions could adversely affect the overall
performance of the system.
Most methods for detecting images in the database that are similar to
a query image check every image in the database for similarity, a process
that is very slow for very large data sets. While techniques do exist that
speed up the search by indexing the database, they fail to restrict the
search to a small portion of the database when applied to our problem.
Such an approach to image searching has two major strengths. First, the
measures of image similarity are robust to the common transformations
performed on images, e.g. rotation, translation, scaling, cropping, filtering,
compression, etc. Second, the measure of similarity is adjustable to gain
maximum selectivity. New comparison metrics are created to demonstrate
a compromise between robustness and selectivity. The database includes
advanced indexing techniques. The self-learning database allows us to
perform multi-factor optimization for speed and accuracy.
Online implementation. The online implementation of the system
includes (i) signature acquisition tools, (ii) a searchable signature database
(the engine), and (iii) an online interface. The system currently supports
pressure sensitive tablets which allow recording both geometric (signature
contours, shapes, etc.) and kinematic/dynamic characteristics (pressure,
time stamps, etc.), touch pads and mice for collecting human handwriting
and strokes. This implementation has been successfully tested on PDA
devices and smart-phones where signatures are produced by a stylus pen.
Overall, the system is a flexible and viable solution for many pervasive
environments.
The web-based interface has six basic modules: login, upload, list,
draw and search, verify,andidentify. The database is protected
against any unauthorized access by the login module. After the successful
login, the user is given administrative rights to the upload and list functions.
The upload module allows the user to upload a signature image providing
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Signature Analysis, Verification and Synthesis 59
a descriptive keyword (e.g. a person’s name), and to choose a file type from
the drop down list (see Fig. 2.15, first panel). After clicking submit,theweb
script updates the database and generates all the necessary distributions
for the given image.
The list script creates a table, listing all the data from the database.
For signature images, the data are listed in the form of thumbnails (see
Fig. 2.15, second panel). A button labelled regenerate is also available
for administrative users to automatically regenerate distributions for all
signatures. This is especially useful when a new classification feature is
added to the engine. By clicking regenerate, all previously stored data are
recalculated for every signature in the database. Images can be inspected
and deleted when necessary.
The only functions accessible to non-administrative users are draw and
search, verify and identify, because they do not alter the database.
Identify is a module that allows the user to upload a signature image,
generate distribution data, and compare the generated data against the
data of all images in the database (see Fig. 2.16, first panel). The
verification module collects the keyword label from the user and compares
the generated data against a limited set of images. Both modules create a
table displaying the testing signature and listing the top ten signatures from
the database along with similarity ratings (see Fig. 2.16, second panel). The
draw and search module allows to use real-time signature acquisition from
the browser window.
2.6. Concluding Remarks and Future Work
In this section, we provided an outline of a complete cycle of signature
processing techniques ranging from various signature representations,
signature analysis and comparison, as well as signature synthesis. This cycle
is implemented in a system used for identification and authentication of
signatures and human handwriting in pervasive environments. The system
changes the mechanism of data collection and processing, and concentrates
on a very specific area of personal authentication and identification based
on signature input. The system can verify, compare, and organize both the
visual appearance of a signature and the behavioural characteristics of the
signature including the speed of writing and pressure. Our proprietary
technology is based on a unique mixture of sequence processing and
statistical techniques.
In general, the system uses drivers to integrate with many off-the-
shelf image acquisition devices and standardized software platforms, and
connectors to interface with legacy and commonly used authentication
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60 Synthesis and Analysis in Biometrics
Fig. 2.15. Screenshots of the upload and list modules.
systems and applications. The system will have applicability in all areas
where signature identification or verification is desirable or required. Using
the system, businesses, practitioners and researchers will gain access to a
robust, automated and scalable system that renders behavioural biometrics
available for analysis and will be able to build a dynamically configurable
knowledge base for the design of future pervasive systems or data
exploration. Additionally, the system can complement existing software
packages in security technologies and enhance their functionality across
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Signature Analysis, Verification and Synthesis 61
Fig. 2.16. Screenshots of the identification and draw and search modules.
a wide range of products including personal access, online transactions,
banking and financial transactions, secure document automation, etc.
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62 Synthesis and Analysis in Biometrics
Possible extensions can include voice processing and fusion of voice and
image biometrics. An information-theoretic approach can be utilized to
speed-up the prediction of possible alignments for continuous sequences
(see, for example,
[
12
]
).
Acknowledgments
We express our appreciation to Drs. Vlad P. Shmerko and Svetlana
N. Yanushkevich for valuable discussions, as well as to Joshua Strohm
and Scott Alexander, former students, for critical comments and data
preparation.
Bibliography
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Math. Stat., 28, pp. 823–838.
3. Dimauro, G., Impedovo, S., Modugno, R. and Pirlo, G. (2002). Analysis
of stability in hand-written dynamic signatures, Proc. 8th International
Workshop on Frontiers in Handwriting Recognition, pp. 259–263.
4. Dryden, I. and Mardia, K. (1998). Statistical Shape Analysis, John Wiley &
Sons, Chichester.
5. Jain, A., Griess, R. and Connell, S. (2002). On-line signature verification,
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6. Kuiper, N. (1962). Tests concerning random points on a circle, Proceedings of
the Koninklijke Nederlandse Akademie van Wetenschappen, A63, pp. 38–47.
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the search for similarities in the amino acid sequence of two sequences, J.
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8. Nikitin, A. and Popel, D. (2004). signmine algorithm for conditioning
and analysis of human handwriting, Proc. Int. Workshop on Biometric
Technologies, Calgary, Canada, pp. 171–182.
9. Parker, J. R. (2006). Composite Systems for Handwritten Signature
Recognition, this issue.
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recognition: a comprehensive survey, IEEE Trans. Pattern Analysis and
Machine Intelligence, 22, pp. 63–84.
11. Popel, D. (2002). A compact graph model of handwritten images: Integration
into authentification and recognition, Proc.IAPRInt.Workshopon
Structural and Syntactic Pattern Recognition, Lecture Notes in Computer
Science 2396, pp. 262–270.
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Signature Analysis, Verification and Synthesis 63
12. Popel, D. (2003). Conquering uncertainty in multiple-valued logic design,
Artificial Intelligence Review, Kluwer, 20, pp. 419–443.
13. Popel, D. and Popel, E. (2004). Controlling uncertainty in discretization of
continuous data, Proc. IEEE Int. Symp. on Multiple-Valued Logic, pp. 288–
293.
14. Popel, D. and Popel, E. (2005). bioGlyph: Biometric identification in
pervasive environments, Proc. IEEE Int. Symp. on Multimedia, pp. 713–718.
15. Shmerko, V., Phil Phillips, Kukharev, G., Rogers, W., Yanushkevich, S.
Biometric technologies, Proc. Int. Conf. The Biometrics: Fraud prevention,
Enchanced Service, Las Vegas, Nevada, pp. 270–286, 1997.
16. Shmerko, V., Phil Phillips, Rogers, W., Perkowski, M., Yanushkevich, S.
Bio-Technologies, Bulletin of Institute of Math-Machines, Warsaw, Poland,
ISSN 0239-8044, no.1, pp. 7–30, 2000
17. Smith, T. and Waterman, M. (1981). Identification of common molecular
subsequences, Journal of Molecular Biology, 147, pp. 195–197.
18. Yanushkevich, S., Shmerko, V., Stoica, A. and Popel, D. (2005). Inverse
Problems of Biometrics, CRC Press/Taylor & Francis Group, Boca Raton,
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Chapter 3
Local B-Spline Multiresolution with Example in Iris
Synthesis and Volumetric Rendering
Faramarz F. Samavati
∗,‡
, Richard H. Bartels
†,§
,LukeOlsen
∗
∗
Department of Computer Science,
University of Calgary, Calgary, Alberta,
T2N 1N4, Canada
†
School of Computer Science,
University of Waterloo, Waterloo, Ontario,
N2L 3G1, Canada
‡
samavati@cpsc.ucalgary.ca
§
rhbartel@uwaterloo.ca
Multiresolution has been extensively used in many areas of computer
science, including biometrics. We introduce local multiresolution filters
for quadratic and cubic B-splines that satisfy the first and the second
level of smoothness respectively. For constructing these filters, we use
a reverse subdivision method. We also show how to use and extend
these filters for tensor-product surfaces, and 2D/3D images. For some
types of data, such as curves and surfaces, boundary interpolation is
strongly desired. To maintain this condition, we introduce extraordinary
filters for boundaries. For images and other cases in which interpolating
the boundaries is not required or even desired, we need a particular
arrangement to be able to apply regular filters. As a solution, we propose
a technique based on symmetric extension. Practical issues for efficient
implementation of multiresolution are discussed. Finally, we discuss
some example applications in biometrics, including iris synthesis and
volumetric data rendering.
Contents
3.1. Introduction ................................... 66
3.2. Wavelets and Multiresolution Background . . . . . . . . . . . . . . . . . . 67
3.3. ReviewofConstruction............................. 70
3.4. OtherB-SplineMultiresolutionFilters .................... 75
3.4.1. ShortFiltersforCubicB-Spline................... 75
3.4.2. Cubic B-Spline Filters: Inverse Powers of Two . . . . . . . . . . . 75
65
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66 Synthesis and Analysis in Biometrics
3.4.3. ShortFiltersforQuadraticB-Spline................. 76
3.4.4. WideFiltersforQuadraticB-Spline................. 76
3.5. Extraordinary (Boundary) Filters . . . . . . . . . . . . . . . . . . . . . . . 76
3.5.1. Boundary Filters for Cubic B-Spline . . . . . . . . . . . . . . . . 77
3.5.2. Boundary Filters for Short Cubic B-Spline . . . . . . . . . . . . . 80
3.5.3. Boundary Filters for Short Quadratic B-Spline . . . . . . . . . . . 80
3.5.4. Boundary Filters for Wide Quadratic B-Spline . . . . . . . . . . . 80
3.6. EfficientAlgorithm ............................... 80
3.7. Extensions .................................... 82
3.7.1. Periodic(Closed)Curves....................... 82
3.7.2. TensorProductSurfaces ....................... 84
3.7.3. 2DImages ............................... 84
3.7.4. 3DImages ............................... 88
3.8. Results, Examples and Applications . . . . . . . . . . . . . . . . . . . . . . 88
3.8.1. ExampleApplications......................... 89
3.8.2. IrisSynthesis ............................. 91
3.8.3. Real-Time Contextual Close-up of Volumetric Data . . . . . . . . 93
3.9. Conclusion .................................... 95
Bibliography ....................................... 95
3.1. Introduction
Multiresolution provides a tool for decomposing data into a hierarchy of
components with different scales or resolutions. This hierarchy can be
used for noise removal, compression, synthesizing and recognition of the
objects. An efficient and economical multiresolution is associated with
wavelets. Therefore, this kind of multiresolution has been employed in
many areas such as image processing
[
13
]
,biomedical
[
21
]
and computer
graphics
[
18
]
.
Noise removal, data synthesis and feature recognition are common
problems in biometrics. Multiresolution techniques have been employed
in iris identification
[
7,9,23
]
,irissynthesis
[
22
]
, feature extraction from
fingerprints and irises
[
3,10,14
]
, and for detecting faces in images
[
24
]
.
To date, Haar wavelets have primarily been used in biometric
applications due to their simplicity. Haar wavelets are based on zero-degree
B-splines. Unfortunately, zero-degree B-spline functions and their wavelet
functions are not even continuous and consequently they are not well suited
when we need a “smooth multiresolution representation” for data.
In this chapter, we introduce multiresolution representations for
quadratic and cubic B-spline that satisfy the first and the second level
of smoothness respectively. To keep the simplicity and efficiency of the
resulting techniques, we build and describe local multiresolution filters from
a condition for biorthogonal wavelets using the general approach of reverse
April 2, 2007 14:42 World Scientific Review Volume - 9in x 6in Main˙WorldSc˙IPR˙SAB
Local B-Spline Multiresolution 67
subdivision. Consequently, the purpose of this work is not only describing
the construction method (Sections 3.3–3.5), but also discussing practical
implementation issues (Sections 3.6–3.8).
3.2. Wavelets and Multiresolution Background
Multiresolution operations are specified by a set of filter matrices A
k
, B
k
,
P
k
and Q
k
. Consider a given discrete signal C
k
, expressed as a column
vector of samples. A lower-resolution sample vector C
k−1
is created by a
down-sampling filter on C
k
. This process can be expressed as a matrix
equation
C
k−1
= A
k
C
k
.
The details D
k−1
lost through the down-sampling are captured using B
k
D
k−1
= B
k
C
k
.
The pair of matrices A
k
and B
k
are called analysis filters and the process
of splitting a signal C
k
into C
k−1
and D
k−1
is called decomposition.
Recovering the original signal C
k
is called reconstruction.Itinvolves
refinement of the low-resolution sample C
k−1
and details D
k−1
using the
synthesis filters P
k
and Q
k
, which reverse the operations of A
k
and B
k
C
k
= P
k
C
k−1
+ Q
k
D
k−1
.
The matrices A
k
, B
k
, P
k
and Q
k
form the core of the multiresolution
approach, and the efficiency of the resulting techniques depends on the
structure of these matrices. For an efficient and useful representation, the
following properties are desired:
• All matrices should be banded, with repetitive row/column entries.
• C
k−1
is a good approximation for C
k
.
• The storage requirement for storing C
k−1
and D
k−1
is not more than
that of C
k
.
• The time required to decompose and reconstruct the signal is linearly
dependent on the size of C
k
.
Decomposition and reconstruction operations take place in some
underlying function spaces V
k−1
⊂V
k
wherein C
k
defines some function
f
k
=
i
c
k
i
φ
k
i
in the large space, C
k−1
defines an approximation f
k−1
=
i
jc
k−1
j
φ
k−1
j
to that function in the smaller space, and D
k−1
defines the
difference g
k−1
=
i
jd
k−1
j
ψ
k−1
j
in the complement space V
k
\V
k−1
.The