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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