FAST NON-LINEAR NORMALIZATION ALGORITHM FOR IRIS
RECOGNITION
Wen-Shiung Chen, Jen-Chih Li, Ren-He Jeng
VIPCCL, Department of Electrical Engineering, National Chi Nan University, Puli, Nantou, Taiwan
Lili Hsieh
Department of Information Management, Hsiuping Institute of Technology, Dali, Taichung, Taiwan
Sheng-Wen Shih
Department of Computer Science and Information Engineering, National Chi Nan University, Puli, Nantou, Taiwan
Keywords: Biometrics, Non-linear Normalization, Law of Cosine.
Abstract: In biometrics, human iris recognition provides a high-level security. However, the size of eye pupil always
varies with different illumination, resulting in the iris texture deformation. Thus, how to precisely predict
the deformation degree of the iris is an important issue. A fast algorithm simply using the law of cosine is
proposed to make Yuan and Shi’s non-linear normalization model used in iris recognition suitable for real-
time personal authentication applications.
1 INTRODUCTION
In biometric-based automatic identity authentication
techniques, the iris recognition is one of the most
reliable methods. Iris texture possesses a lot of
distinctive information helpful for discriminating
people's identity. Nowadays the existing iris
recognition systems have a very good performance
(J. Daugman, 1993; R. Wildes, 1997; L. Ma et al.,
2003; L. Ma et al., 2004). However, the iris texture
can be deformed due to variation of pupil size
resulting from different illumination. How to
compensate the effect of pupil size variation
becomes an important issue. In most of the iris
recognition techniques, a normalization process is
always performed.
In general, the human eye pupil's diameter is of
about 1.5mm ~ 7mm, and always varies with
different illumination from exterior into eye. The
human iris is an annular region circumjacent the
pupil, and having the width of around 12mm. The
iris is an enormous complex meshwork of pectin ate
ligament tissue resulting in patterns of almost
infinite variety. The pupil size varies with different
illumination, as a result the iris deforms, such as
contract or expand, even torture, caused by papillary
variations. The purpose of normalization is to
facilitate the subsequent processing (e.g., feature
extraction), and most importantly, to restore
precisely various degrees of deformation of the iris
structure in a minimal state of distortion. Among the
normalization methods, The approach, proposed by
Daugman (J. Daugman, 1993), is the most popular
and widely used in many systems, in which iris is
assumed to be homogenous 'rubber-sheet' model. In
this approach the annular iris region is linearly
mapped or transformed into a fix-sized rectangular
block via the following formulas:
,
1
,
1
(1)
where
,
and
,
are the
polar coordinates of the inner and outer boundary
points in the direction ,
,
are the Cartesian
coordinates. However, the model is not entirely
accurate since it assumes the stretch of iris tissue in
radial direction is linear as the pupil size changes.
507
Chen W., Li J., Jeng R., Hsieh L. and Shih S. (2010).
FAST NON-LINEAR NORMALIZATION ALGORITHM FOR IRIS RECOGNITION.
In Proceedings of the International Conference on Computer Vision Theory and Applications, pages 507-510
DOI: 10.5220/0002840905070510
Copyright
c
SciTePress
Under the environment with uniform
illumination, the size of pupils varies slightly so that
the performance can be good. However, on the other
hand, a non-uniform illumination scenario always
results in the variation of pupil size vastly. In such
case, the linear mapping cannot correctly predict the
deformation so that the performance becomes
degraded. Therefore, to develop a non-linear
normalization method for resolving iris texture
deformation is necessary.
H. J. Wyatt's work (H. J. Wyatt, 2000) focuses
on the construction of a meshwork of 'skeleton' that
can minimize 'wear-and-tear' of iris as pupil size
varies. By following, Yuan and Shi adopted the idea
in (H. J. Wyatt, 2000) as a basic model. They
simplified it and developed a non-linear
normalization model for iris recognition (X. Yuan et
al., 2005). The modified approach was applied to
overcome the non-linear deformation on the iris
texture caused by pupil variations in iris recognition.
It has been shown that this modified approach
achieves a relatively good performance. However,
the model needs to solve two simultaneous equations
so that it is complicated to get the sampling points
and the time complexity is high. When the size of
image needed to be normalized increases, the
computing time becomes too large. The iris
recognition system must be realized in real-time for
the authentication applications. Therefore, it needs
to propose a fast algorithm which can construct the
nonlinear normalization model quickly for
implementing iris recognition.
2 NON-LINEAR
NORMALIZATION REVISITED
In 2005, Yuan and Shi proposed a non-linear
normalization model (X. Yuan et al., 2005), as
shown in Figure 1, with the prior defined parameter
λ
through the solution of two simultaneous
equations to solve the iris deformation caused by
pupillary variations problem. First of all we
construct the gap of 90-degree between points P and
I that is connected by the arc
PI
. Such an arc
defined in the H.J. Wyatt (H. J. Wyatt, 2000) is
known as “fiber.” Then we define the virtual pupil
radius
that constructs the same arc
between the points P and I connected by the
arc
PI
.
2
o
1
o
r
ref
r
R
1
r
2
r
)(
2
iΔ
1
()iΔ
Figure 1: The non-linear normalization model proposed by
Yuan and Shi.
The arc
PI
is part of the circle of:
(2)
where
2
⁄
(3)
and
2
⁄
,
(4)
and arc
PI
is part of the circle of:
(5)
where
2
⁄
(6)
and
2
⁄
.
(7)
Then the arc
PI
is uniformly sampled along
the radial direction. When the pupil radius changes
from to
,
the non-linear relationship between
arc
PI
and arc
PI
is used to solve the non-linear
deformation of the iris texture patterns.
Suppose the point A is on the i-th sampling
circle. Then A
and A
can be solved by:
∆
(8)
where
∆
1
,0,1,2,…,1.
(9)
Its corresponding point A on the arc
PI
can be
solved by:
VISAPP 2010 - International Conference on Computer Vision Theory and Applications
508
A
A
(10)
where
A
A
⁄
.
(11)
By solving these two simultaneous equations (4)
and (5), the Cartesian coordinates, A
and A
, of the
point A are obtaind. Since it needs to solve two
equations simultaneously, the computing time must
be high. In the next section a simple and fast
approach is then proposed to reduce the computing
time tremendously.
Algorithm 1: Non-linear Normalization Algorithm.
for 0 to 1 do
begin
Generate eq.(4);
Solve eq.(4) by newton’s method;
Generate eq. (5);
Solve eq.(5) by newton’s method;
en
d
3 FAST ALGORITHM OF
NON-LINEAR
NORMALIZATION
2
o
1
o
r
ref
r
R
1
r
2
r
)(i
r
θ
)(
2
iΔ
1
()iΔ
)(i
k
θ
Figure 2: Observation.
According to the non-linear normalization model
mentioned above, we realize that the final goal is to
find out the Cartesian coordinates A
and A
of the
sampled point A, indirectly by first knowing the
coordinates of the virtual point A. If we know the
length of OA
between the point A and the pupil
center O, and the angle
between OA
and -
axis, the coordinates of the point A may be
determined. It is observed from Figure 1 that the two
points A and A are colinear, so OA
and OA have the
same angle
. Obviously, the three points, the
point A, the pupil center O and the center
of
arc
PI
, form a triangle ∆AO
, as shown in
Figure 2. Since the lengths of three sides of the
triangle are known, the angle
can be
determined according to the law of cosine.
Similarly, the three points, the point A, the pupil
center O and the center
of arc
PI
, form another
triangle ∆AO
, as shown in Figure 2. In this
triangle only OA
is unknown. According to the law
of cosine and the law of sine, the length of OA
may
be determined from
which might be obtained
from ∆AO
. Trivially, the coordinates, A
and A
,
of the sampled point A are computed by
A
∆
sin
A
∆
cos
(12)
where
cos
∆
2
∆
(13)
and
∆
2
cos
⁄
.
Finally, we adopt the Cartesian coordinates of all
of the sampled point A on arc
PI
to construct a
non-linear normalization model directly. The
detailed procedure is shown in algorithm II.
Algorithm 2: Fast Non-linear Normalization Algorithm.
for 0 to 1 do
begin
Compute
;
Compute ∆
;
A
∆
sin
;
A
∆
cos
;
en
d
4 EXPERIMENTAL RESULTS
In this section, two different non-linear
normalization algorithms are compared.
4.1 Speed Comparison
The time consumption of Yuan's algorithm and
proposed algorithm in computing 32 sampling points
FAST NON-LINEAR NORMALIZATION ALGORITHM FOR IRIS RECOGNITION
509
of fiber are shown in Table 1.
Table 1: Computing Speed Comparison.
Yuan and Shi’s
algorithm
The Proposed
algorithm
Speed
100
0.14
Figure 3
shows the relationship of the sampling
point of fiber and the computing time in different
algorithms.
Figure 3: The relationship of the number of sampling
points of fiber and the computing time of different
methods.
4.2 Performance Comparison
We implemented two iris recognition systems in
which the same pre-processing, feature extraction,
classification, except the normalization, are used.
We collected an iris image database (denoted as
DB1) in different illumination. It contains 18 classes
and each class contains 9 images. The image
samples of three subjects are shown in
Figure 4.
Figure 4: The eye image samples.
Then we evaluate the performances with linear
and non-linear normalization on DB1. The ROCs
(receiver of operating curves) are shown
in Figure 5.
Figure 5: ROC curves with linear and non-linear
normalization.
5 CONCLUSIONS
In this paper, we proposed a fast and simple non-
linear normalization algorithm. Even if the
normalization of image size increases, the
computing time is not increased rapidly, and it is
also very simple and easy to achieve. The
experimental results show the computing time is
reduced by 100 ms, and the equal error rate (EER) is
decreased by 0.94% as compared with linear
normalization.
REFERENCES
J. Daugman, 1993. High confidence personal visual
recognition of person by a test of statistical
independence. IEEE Trans. on Pattern Analysis and
Machine Intelligence, vol. 15, no. 11, pp. 1148-1161.
R. Wildes, 1997, Iris recognition: An emerging biometric
technology. Proceedings of the IEEE, vol. 85, no. 9,
pp. 1348-1363.
L. Ma, T. Tan, Y. Wang and D. Zhang, 2003. Personal
identification based on iris texture analysis. IEEE
Trans. on Pattern Analysis and Machine Intelligence,
vol. 25, no. 12, pp. 1519-1533.
L. Ma, T. Tan, Y. Wang and D. Zhang, 2004. Efficient iris
recognition by characterizing key local variations.
IEEE Trans. on Image Processing, vol. 13, no. 6, pp.
739-750.
H. J. Wyatt, 2000. A 'minimum-wear-and-tear' meshwork
for the iris. Vision Research, vol. 40, pp. 2167-2176.
X. Yuan and P. Shi, 2005. A non-linear normalization
model for iris recognition. Advances in Biometric
Person Authentication, pp. 135-141.
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