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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178 Synthesis and Analysis in Biometrics
for which it was devised. Using prior information it is possible to more
accurately estimate the relative distances between the ranked classifications
and use these to calculate better weights for resolving the rankings in a
Borda fashion
[
7
]
.
What is being proposed is a variable weighting of the ranked items.
One suggestion is to use the measured properties of the classifier directly
to assign a value to each rank position. For the 5 classifier/3 class problem
above the count computed for class a would be
k(a)=
5
i−1
P
i
(a)f
a
,
where Pi(a) is the measured probability of classifier i issuing a classification
of a, and fa is a scale value. This scale value could be a constant (e.g. R−1)
or a function of the rank of a, as two examples. This will be called the a
posteriori Borda count,orAPBorda in the ensuing discussion
[
15
]
.
A second idea is to ignore the specific probabilities and assign simple
non-uniform values to the ranked items. These weights could still be based
on the typical observed distances between classes in a given classification,
or could be constructed to achieve a specific goal. For example, again using
the 5 classifier/3 class problem above, recall that the problem was that
there was a conflict between the majority vote and the Borda count. Now
use a weight of R − 1 on the first ranked class, (R − 2) × w on the second,
and (R − 3) × w
2
(= 0) on the third. It is now possible to find a weight w
such that the winner found by summing the weights over all classifiers is
the majority winner. In this latter instance the weight would be w =0.67;
this could be thought of as a weighted Borda count, referred to as wBorda
in further discussion.
In all of these cases the initial ranking is found by sorting the classes
based on the measured probabilities for the classifier involved.
6.5.6. Empirical Evaluation
One of the problems with the empirical evaluation of classifier combination
algorithms is the need for vast amounts of data. In this case, the data
consists of classifier output from many different classifiers and a great many
individual classification tasks. This means that the input data, with ground
truth, must exist, and the classifiers must be correctly implemented. Even
if sufficient data can be found, it has certain pre-defined properties that
can’t be altered. A classifier has a given recognition rate for a given type
of data, and it may not be possible to provide all desired combinations
of characteristics. For example, a classifier combination algorithm may
work well when all individual classifiers operate at over 90% recognition,
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Composite Systems for Handwritten Signature Recognition 179
or when the classifiers have nearly the same rates. It is important to be
able to determine benefits and limitations, either from a theoretical basis
or empirically.
6.6. Conclusions
We have presented some new signature features and classifiers, and
have combined them with existing ones to create a composite signature
recognition scheme having high reliability. We have also discussed classifier
combination in the context of signature recognition in a general way, hoping
to inspire further work in this area.
The simplest way to merge multiple methods is using a voting scheme.
While it may be possible to improve things a little more using a more
complex scheme, such as a rank based vote, a very large amount of
data based on past performance is required to gain an accurate confusion
matrix from which rankings can be extracted. So, a simple majority vote
was constructed using the temporal distance, slope histogram, and global
relative distance methods. The graph in Fig. 6.8 shows the result of this
combining process for different numbers training signatures and shows the
temporal distance graph overlaid on this. In no case is the result better
than that achieved by simple temporal distance. The graph in Fig. 6.8
shows the result of this combining process for different numbers training
signatures and shows the temporal distance graph overlaid on this. In no
case is the result better than that achieved by simple temporal distance.
The graph does show, along with Fig. 6.7, how the success depends
on training set size; a more robust algorithm will have a relatively flat
graph, although it is clear that smaller training sets will invariably give
poorer results. The temporal distance method is the most robust method
presented, according to this definition, and robustness is unimproved by
using multiple algorithms.
Adding a fourth method to the mix changes things a little. When the
shadow mask algorithm is included in the vote the success rate overall can
be made to reach 99.14%. Since there are four components in each vote a
parliamentary majority vote is used, in which the target receiving the most
votes, rather than the majority of votes, is selected. Thus, two votes are
needed to select a winner; if there are two items receiving two votes each, we
have a tie, and reject the signature. In actual practice this happened once
in the 1400 signatures recognized, and there were fifty cases of a vote being
determined by two agreeing votes. In no case did one of these two-votes
misclassify a signature.
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180 Synthesis and Analysis in Biometrics
Temporal Distance
Three-Way Vote
Number of Training Signatures
Success Rate
30
40
50
60
70
80
90
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Fig. 6.8. Results for the voting technique. A three method vote, simple majority,
compared against the simple temporal distance algorithm.
The global relative distance method works as well as many published
algorithms, and has the advantage of being quite simple and obvious. An
accelerated version is fast enough for actual use, but and has a slightly
lower success rate.
The temporal distance method is very successful, giving a solo success
rate of 98.6%. It is fast and easy to compute. It can be performed directly
on point data without the need to create an image, and the exemplars can
be saved as feature vectors, speeding up the recognition process.
A simple direct comparison between signatures is possible, and has a
high success rate. It has been combined with other methods by using simple
voting to improve the success rate to over 99%.
Acknowledgments
This work was partly supported by the Natural Science and Engineering
Research Council of Canada (NSERC). I would like to thank Mark
Baumback and Lani Bateman, former students who contributed significantly
to the work. Thanks also to Dr. Marina Gavrilova and Dr. Svetlana
Yanushkevich.
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Composite Systems for Handwritten Signature Recognition 181
Bibliography
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18. Parker, J. R., Bateman, L. and Baumback, M. (2002). Scale effects in shadow
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Vegas, USA, June 24–27.
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182 Synthesis and Analysis in Biometrics
19. Riba, J., Carnicer, A., Vallmitjana, S. and Juvells, I. (2000). Methods for
invariant signature classification, Proc. ICPR, Barcelona, Spain. pp. 957–
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20. Sabourin, R., Cheriet, M. and Genest, G. (1993). An extended shadow code
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Chapter 7
Force Field Feature Extraction for Ear Biometrics
David Hurley
Analytical Engines Ltd.,
61 Meon Crescent, Chandlers Ford,
Eastleigh, Hampshire, SO53 2PA, UK
djh@analyticalengines.co.uk
The overall objective in defining feature space is to reduce the
dimensionality of the original pattern space, whilst maintaining
discriminatory power for classification. To meet this objective in the
context of ear biometrics a new force field transformation is presented
which treats the image as an array of mutually attracting particles that
act as the source of a Gaussian force field. Underlying the force field
there is a scalar potential energy field, which in the case of an ear takes
the form of a smooth surface that resembles a small mountain with
a number of peaks joined by ridges. The peaks correspond to potential
energy wells and to extend the analogy the ridges correspond to potential
energy channels. Since the transform also turns out to be invertible, and
since the surface is otherwise smooth, information theory suggests that
much of the information is transferred to these features, thus confirming
their efficacy.
We describe how field line feature extraction, using an algorithm
similar to gradient descent, exploits the directional properties of the
force field to automatically locate these channels and wells, which then
form the basis of the characteristic ear features. We also show how an
analysis of this algorithm leads to a separate closed analytical description
based on the divergence of force direction.
The technique is validated by performing recognition on a database
of ears selected from the XM2VTS face database, and by comparing the
results with the more established technique of Principal Components
Analysis (PCA). This confirms not only that ears do indeed appear to
have potential as a biometric, but also that the new approach is well
suited to their description.
183
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184 Synthesis and Analysis in Biometrics
Contents
7.1. Introduction ................................... 184
7.2. EarTopology .................................. 186
7.3. TheForceFieldTransforms .......................... 187
7.3.1. Transformation of the Image to a Force Field . . . . . . . . . . . 188
7.3.2. The Energy Transform for an Ear Image . . . . . . . . . . . . . . 190
7.3.3. AnInvertibleLinearTransform ................... 192
7.4. ForceFieldFeatureExtraction......................... 192
7.4.1. FieldLineFeatureExtraction .................... 193
7.4.2. Dome Shape and Brightness Sensitivity . . . . . . . . . . . . . . . 194
7.4.3. Convergence Feature Extraction . . . . . . . . . . . . . . . . . . . 195
7.5. EarRecognition................................. 199
7.5.1. Experiment Results and Analysis . . . . . . . . . . . . . . . . . . 201
7.6. Conclusions ................................... 204
Bibliography ....................................... 204
Glossary
CCR — Correct Classification Rated
FFE — Force Field feature Extraction
Log — Laplacian of Gaussian operator
PCA — Principal Components Analysis
7.1. Introduction
The potential of the human ear for personal identification was recognized
and advocated as long ago as 1890 by the French criminologist Alphonse
Bertillon
[
1
]
. In machine vision, ear biometrics has received scant attention
compared to the more popular techniques such as automatic face, eye, and
fingerprint recognition
[
2,3
]
. However, ears have played a significant role in
forensic science for many years, especially in the United States, where an
ear classification system based on manual measurements has been developed
by Iannarelli, and has been in use for more than 40 years
[
4
]
, although the
safety of ear-print evidence has recently been challenged in the Courts.
[
5
]
Ears have certain advantages over the more established biometrics; as
Bertillon pointed out:
“The ear, thanks to these multiple small valleys and hills which furrow
across it, is the most significant factor from the point of view of
identification. Immutable in its form since birth, resistant to the
influences of environment and education, this organ remains, during the
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Force Field Feature Extraction for Ear Biometrics 185
entire life, like the intangible legacy of heredity and of the intra-uterine
life.”
The ear does not suffer from changes in facial expression and is firmly fixed
in the middle of the side of the head so that the immediate background is
predictable whereas face recognition usually requires the face to be captured
against a controlled background.
Collection does not have an associated hygiene issue, as may be the
case with direct contact fingerprint scanning, and is not likely to cause
anxiety, as may happen with iris and retina measurements. The ear is
large compared with the iris, retina, and fingerprint and therefore is more
easily captured.
The technique provides a robust and reliable description of the ear
without the need for explicit ear extraction. It has two distinct stages:
(a) Image to force field Transformation, and
(b) force field Feature Extraction.
Firstly, the entire image is transformed into a force field by pretending that
each pixel exerts a force on all the other pixels, which is proportional to the
pixel’s intensity and inversely proportional to the square of the distance to
each of the other pixels. It turns out that treating the image in this way is
equivalent to passing it through an extremely powerful low pass filter which
transforms it into a smooth undulating surface, but with the interesting
property that the new surface retains all the original information.
Operating in the force field domain allows us to access to a wealth of
established vector calculus techniques to extract information about this
surface. For example, we will show how the divergence operator may
be used to extend this algorithmic approach leading to an even richer
mathematical description.
The powerful smoothing also affords valuable resistance to noise and
surface matching is also greatly facilitated when the surfaces are smooth.
Also, because it is based on a natural force field, there is the prospect of
implementing the transform in silicon hardware by mapping the image to
an array of electric charges.
The smooth surface corresponds to the potential energy field underlying
the vector force field and the directional properties of the force field can
be exploited to automatically locate a small number of potential wells and
channels which correspond to local energy peaks and ridges respectively
which then form the basis of the new features.
Information theory would also suggest that these are good features as
follows. A smooth surface is easier to describe than a complicated one
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186 Synthesis and Analysis in Biometrics
and therefore requires less information; in the extreme, a hemisphere can
be described just by its radius. At the other extreme, a surface made
up of random noise would be very hard to describe and therefore would
require much more information. The total image information is conserved
in the transformation, so we argue that there must be a redistribution
of information density away from the smoothest parts towards the salient
channels and wells which break up the monotony of the otherwise smooth
surface.
It is worth noting that the force field is derived directly from the entire
image without any pre-processing whatsoever; we effectively smooth the
entire image with a gigantic 1/r kernel, which is more than four times the
area of the original image, thus obliterating all fine detail such as edges,
yet preserving all the image information. The target application is ear
biometrics where we would expect measurement conditions such as diffuse-
lighting and viewpoint to be carefully controlled and we shall assume that
the subject will be looking directly ahead, sideways to the camera view.
The resulting camera projection will be taken as the subject’s ear image
for biometric purposes, even if the ears should protrude excessively. We
do not seek pinna-plane tilt invariance simply because there is no reason
why the tilted version of a given pinna should not correspond to another
subject’s ear.
A selection of samples taken from each of sixty-three subjects drawn
from the XM2VTS face profiles database
[
11
]
has been used to test the
viability of the technique. A classification rate of 99.2% has been achieved
so far, using just simple template matching on the basic channel shapes,
demonstrating the merit of the technique at least at this scale.
It can reasonably be expected that the use of more sophisticated channel
matching techniques would lead to even better results. We also do a head-
to-head comparison with PCA which also helps to demonstrate the implicit
extraction inherent in the technique. As such, a new low-level feature
extraction approach is demonstrated with success in a new application
domain.
7.2. Ear Topology
The ear does not have a completely random structure, it is made up of
standard features just like the face. The parts of the ear are less familiar
than the eyes, nose, mouth, and other facial features but nevertheless are
always present in a normal ear. These include the outer rim (helix), the
ridge (antihelix) that runs inside and parallel to the helix, the lobe, and
the distinctive u-shaped notch known as the intertragic notch between the
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Force Field Feature Extraction for Ear Biometrics 187
ear hole (meatus) and the lobe. Figure 7.1 shows the locations of the
anatomical features in detail.
“The ear does not have a
completely random structure, it is
made up of standard features just
like the face.”
Fig. 7.1. Topology of the human ear. Just like the face, the ear has standard constituent
features consisting of the outer and inner helices, the concha — named for its shell-like
appearance, the inter-tragic notch and of course the familiar ear-lobe.
7.3. The Force Field Transforms
This section gives a brief description of the mathematical foundations
of the new transforms. The basic concepts used can be found in
various introductory works on physics
[
12,13
]
and electromagnetics.
[
14,15
]
We consider how faster computation can be achieved by applying
the convolution theorem in the frequency domain. The question of
transform invertibility is considered as this establishes that the transforms
are information preserving. Further details of invariance, including