Journal of Signal and Information Processing, 2011, 2, 274-278
doi:10.4236/jsip.2011.24039 Published Online November 2011 (http://www.SciRP.org/journal/jsip)
1
A New Partitioning Method in Frequency Analysis
of the Retinal Images for Human Identification*
Masoud Sabaghi, S. Reza Hadianamrei, Ali Zahedi, Maziyar Niyakan Lahiji
Nuclear Science and Technology Research Institute (N.S.T.R.I), Tehran, Iran.
Received August 8th, 2011; revised September 10th, 2011; accepted September 25th, 2011.
ABSTRACT
Retinal image is one of the robust and accurate biometrics methods to recognize a person. In this article we present a
new biometric identification system based on Fourier transform and angular partitioning of the spectrum. In this
method, at first, the optical disc is localized using template matching techniqu e and used for rotating the retin al image
into the reference position . It compensates the rotation effects which might o ccur during the scanning process. Fourier
transform coefficient and angu lar partitioning of these coefficients are used for the purpose of feature definition in our
method. The extract features are rotation invariant and robust against noise. Finally we employ Euclidean distance for
feature matching. The proposed algorithm was tested using 40 images from DRIVE database and experimental results
showed the efficiency of the propos ed algorithm for the identification of retinal images with noise and rotation.
Keywords: Biometric, Retina, Image Processing, Frequency Analysis, Partitioning
1. Introduction
Biometric is the use of distinctive biological or behave-
ioral characteristics to identify people. Biometric systems
are now being used in large national and corporate secu-
rity projects, and their effectiveness rests on an under-
standing of biometric system and data analysis [1]. Some
of the common identifications method include: voice,
fingerprint, face, hand geometry, facial thermo gram, iris,
retina [2]. Little changes in vessels’ pattern during the
lifetime, high security, more reliability and stability are
the important features which exist in retinal image [2,3].
These traits make retina as a robust approach in person
identification. Different algorithms have been utilized for
human identification. In [4] vessels’ pattern is extracted
and then 2 level Daubechies wavelet is used for decom-
position and extraction of wavelet energy as a feature. In
[5] we presented an approach based on localizing the
optical disc using Haar wavelet and active Contour mo-
del which is used for rotation compensation. Ten we used
Fourier-Mellin transform coefficients and complex mo-
ment magnitudes of the rotated retinal image for feature
definition. In [3] vessel’s pattern is extracted and the
vessels in the vicinity of optical disc is selected, and then
whit (or with?) polar transformation the vessels in Carte-
sian coordinate trans form into the polar coordinate.
Multi scale analysis was used for separating the vessels
into the groups of large, medium and small. Finally, the
angle between the vessel and the horizontal axis is calc-
ulated for feature vector construction. Ortega et al. [6]
used a fuzzy circular Hough transform to localize the
optical disc in the retinal image. Then, they defined feat-
ure vectors based on the ridge endings and bifurcations
from vessel obtained from a crease model of the retinal
vessels inside the optical disc. For matching, they ado-
pted a similar approach as in [7] to compute the parame-
ters of a rigid transformation between feature vectors
which gives the highest matching score. This algorithm is
more computationally efficient in comparison with the
algorithm presented in [7]. However, the performance of
the algorithm has been evaluated using a very small dat-
abase including only 14 subjects.
As mentioned before, pre-processing based on blood
vessel extraction increases the computational cost of the
algorithm. In this paper, a new robust feature extraction
method without any pre-processing phase has been pro-
posed to reduce computational time and complexity. This
proposed method is based on angular partitioning of the
frequency spectrum information of retinal image by a new
special structure. In our method, we have used angular
partitioning with the special structure on magnitude and
phase spectrum of retinal image for feature extraction.
This article is in 5 sections as follow: Section 2 desc-
*This work was supported in part by N.S.T.R.I, Tehran, Iran.

A New Partitioning Method in Frequency Analysis of the Retinal Images for Human Identification275
ribes the Anatomy of the retina. In Section 3, the method
for localizing the optic disc and removing rotation effect
is discussed. Sections 4 represents Fourier transform coe-
fficient and partitioning this coefficient to obtain feature
vector. Experimental results appear in Section 5 and we
conclude the paper in Section 6.
2. Retinal Anatomy
The retina is a multi-layered sensory tissue that lines the
back of the eye. It contains millions of photoreceptors
that capture light rays and convert them into electrical
impulses. These impulses travel along the optic nerve to
the brain where they are turned into images. Optic disc is
brighter than the other parts of the retina and is normally
circular in shape and has a diameter of almost 3 mm. It is
also the entry and exist point for nerves entering and
leaving the retina to and from the brain. Fovea or the
“yellow spot” is a very small area at the center of retinal
that is most sensitive to light and is responsible for our
sharp central vision [5]. Blood vessels are continuous pa-
tterns with little curvature, branch from optic disk and
have tree shape on the surface of retina. The mean diam-
eter of the vessels is about 250 μm [3]. Figure 1 shows
the surface anatomy of retina.
3. Compensation of Undesired Rotation
Before Because of anatomic movement during imaging
process, some rotation occurr in retinal images. These
rotations cause some problem in feature extraction and
matching phase of retinal image recognition. To achieve
a robust method, rotation compensation is needed.
To determine the rotation angle of the retinal image, at
first, optical disc has been localized by template match-
ing technique. Template matching is a technique in digi-
tal image processing for finding small parts of an image
which match a template image. The basic method of
template matching uses a correlation mask (template),
tailored to a specific feature of the search image, which
we want to detect. In this case, the template is the optic
disc and the search image is the green part of retinal im-
age. For this purpose, the green plane of retinal image is
used and a template image is considered. The template
Figure 1. Retinal anatomy.
image is constructed by selecting a rectangular region
around the optical disc. The template is generated by av-
eraging rectangular region containing OD in our retinal
image database [3]. Retinal image is correlated to the
template image to find the brightest region in the retina,
as shown in Figure 2. This point is an approximation of
the center of the optical disc position [8].
In the second step, the center of the optical disc and the
image center of the mass are used to determine the re-
quired rotation angle and then the undesired rotation of the
scanned image of retina is compensated by applying the
opposite rotation. To locate the image center of the mass
for an M

N image, the following equation is used:


11
11
,
,
MN
xy
MN
xy
x
fxy
x
f
xy







11
11
,
,
MN
xy
MN
xy
yfx y
y
f
xy





(1)
After the localization of OD and the center of mass
points, we calculate the angle between the baseline and
the line passing these two points as shown in Figure 3.
We then compensate for the rotation by applying the op-
posite rotation into input image.
4. Feature Extraction
After Our proposed feature extraction method is based on
Fourier transform of retinal images and a special parti-
tioning of Fourier spectrum. The block scheme for fea-
ture extraction of retinal image is shown in Figure 4.
First, without any preprocessing, Fourier transform has
been applied to raw retinal images. Two-dimensional
discrete Fourier transform of input image is calculated
using the following equation [9]:
 

11
2π
00
1
,,
e
MN

j
ux MvyN
xy
Fuvf xy
MN
 

 (2)
Where f(x,y) is image intensity of size M N and the
variable u and v are the frequency variables [8]. Fourier
spectrum and phase angle are defined as following:

 
1/2
22
,,,FuvR uvIuv




 (3)
 

1,
,,
I
uv
uv tgRuv 





y

(4)
Where R(u,v) an I(u,v) are the real and imaginary parts
of F(u,v), respectively.
Then we used Fourier spectrum and phase angle in-
formation. The Fourier spectrum energy and the sum of
the phase angle are, respectively, defined as:
 
22
11
2
,
lk
xlyk
EFx

 (5)

,uv  

A New Partitioning Method in Frequency Analysis of the Retinal Images for Human Identification 276
Figure 2. Template matching technique for optical disc lo-
calization (a) original image (b) template (c) correlated im-
age.
Figure 3. The result of rotation compensation (a) retinal
image after localizing the center of mass and optical disc (b)
the calculated angle (c) compensation for image rotation.
Figure 4. Complete flow diagram for feature extraction
process in the proposed system. (a) Retinal image after ro-
tation compensation (b) Fourier spectrum (c) phase angle (d)
partitioning the Fourier spectrum and phase angle (e) cal-
culate energy of Fourier spectrum and the sum of the phase
angle in per partition (e) future vector construction.
So the feature vector is as:
(E,

) (6)
The energy spectrum and the sum of the angles reflect
the strength of the images’ details in different frequen-
cies. The details of retinal images are in the blood ves-
sels.
As we mentioned above, the vectors computed from
“Equation (6)” are global features of a blood vessel.
These features extracted from the whole images do not
preserve the information concerning the special location
of different details, so their ability to describe a retina is
weak [4].
To solve this problem, we introduce a new partitioning
based on dividing the Fourier spectrum and phase angle
into several half circles with the same centre which is the
centre of spectrum that include segments with same area
and same degree arc as shown in Figure 5. Purposed
partition in this method (Figure 5(c)) includes a combi-
nation of two partitions shown in Figure 5(a) and Figure
5(b). As shown in Figure 5(a), the spectrum and phase
angle are divided into different ranges of high and low
frequency information. Whereas the thick vessels are of
low frequency patterns and the thin vessels are of high
frequency patterns, thus this partitioning shows the crite-
rion of the thickness of the vessels, and while Figure 5(b)
that includes the same frequency range, has information
about vessels in different directions, Figure 5(c) has in-
formation about the thickness and the direction of the
vessels.
The pixels near the centre of the spectrum are of no
value because these pixels include only low frequency
information of the image that depends on average gray
level of the image. Also the pixels that have a distance of
more than 105 pixels from the centre of the spectrum do
not carry any useful information. Because of the symm-
etrical property of the spectrum, partitioning for feature
extraction only includes the upper half circle of the spec-
trum and the lower half circle have been neglected to
decrease the dimension of feature vector.
 
22
11
2
,
lk
xlyk
EFxy




,uv  

The magnitude spectrum and phase angle of image
were divided into N parts with the same area called parti-
tion as described previously. The radius of the selected
half circle ranged from 5 to 105 pixels. The number of
the partitions can be varied for the best result. After par-
titioning the spectrum image of the retina, the energy and
sum of the phase angle of each partition was used for
constructing the feature vector. Finally, the vector is no-
rmalized by total energy and sum of the phase. This no-
rmalized vector is named Fourier spectrum and phase
Feature (FSPF). Our proposed identification system in-
cludes the following phases. In the registration phase of
the persons, a number of images are scanned from each
person, then after rotation compensation of the captured
retinal image, FSPF of all image are extracted and regis-
tered in a Data Base.
In the test phase, FSPF of the test retinal image is co-
mputed, and then compared with all FSPF retinal images
in the Data Base; finally, we find the image in Data Base
by the minimum Euclidean distance and select it as the
identified person.

A New Partitioning Method in Frequency Analysis of the Retinal Images for Human Identification277
Figure 5. Partitioning process. (a) Partitioning for selecting
the different ranges of frequency information. (b) Parti-
tioning for vessels information in different direction. (c)
Final partition includes the combination of the partitions in
Figures 5(a) and (b).
5. Experimental Results
The proposed algorithm was tested on a database of 160
retinal images from 40 subjects. For each subject we use
4 images. First image is noisy one and two next images
were rotated images by a random angle. White Gaussian
noise is added to the original images to generate a noisy
image and the 4th image is a noisy and rotated one. Im-
ages are green channel of input color image. To employ
the proposed method, each Fourier spectrum and phase
angle of retinal image included 4 nested half circles and
each half circle was divided into parts with 45 degree
angle, and therefore, each spectrum of the retinal image
was divided into 16 parts and feature vector had 32 ele-
ment. These numbers of partitions were selected after
making 8, 12, 16, 24 partitions.
The proposed method is evaluated by a test routine as
follow: Euclidean distance between each retinal feature
vector and all of the others in feature vector data base
were calculated. Identified person is determined as corr-
esponding a minimum distance. To evaluate the rejection
ability of the proposed method, we import 20 images
from STARE database [10] and 16 images from personal
database as reject data, and the system recognizes this
entire image as rejects data. Figure 6 shows in-class and
out-class histograms to determine this system reliability.
The accuracy of the identification process is presented in
Table 1. According to the results in table I, we can see
the average identification rate with amplitude and phase
partitioning is better than amplitude partitioning.
6. Conclusions
In this article, a method is proposed for human identi-
fication system based on retinal image processing, using
new special partitioning for amplitude and phase of Fou-
rier transform. This approach is robust to rotation and
noise. In addition, it is simple and has low computational
00.01 0.02 0.03 0.04 0.05 0.06 0.070.08
0
100
200
300
400
500
600
700
800
900
DISTANCE
PROBABILITY DENSITY
AMPLITUDE & PHASE
GENUINE
IMPOSTOR
Figure 6. In-class and out-class histograms.
Table 1. Comparison between results of identification.
Identification
Noise (20 db)
Average identification
rate with amplitude
partitioning
Average identification rate
with amplitude and phase
partitioning
without noise 96% 100%
with noise 92% 100%
complexity. Feature vector generated in this method has
useful information about vessel density and vessels di-
rection in the image.
REFERENCES
[1] T. Dunstone and N. Yager, “Biometric System and Data
Analysis,” Springer, New York, 2008, pp. 529-548.
[2] S. Nanavati, M. Thieme and R. Nanavati, “Biometrics
Identity Verification in a Networked World,” John Wiley
& Sons, Inc., New York, 2002.
[3] H. Farzin, H. A. Moghaddam and M. S. Moin, “A Novel
Retinal Identification System,” EURASIP Journal on
Advances in Signal Processing, Vol. 2008, 2008, Article
ID: 280635.
[4] M. Shahnazi, M. Pahlevanzadeh and M. Vafadoost,
“Wavelet Based Retinal Recognition,” 9th International
Symposium on Signal Processing and Its Applications
(ISSPA), Sharjah, February 2007, pp. 1-4.
[5] H. Tabatabaee, A. Milani-Fard and H. Jafariani, “A Novel
Human Identifier System Using Retina Image and Fuzzy
Clustering Approach,” Proceedings of the 2nd IEEE In-
ternational Conference on Information and Communica-
tion Technologies (ICTTA06), Damascus, April 2006, pp.
1031-1036.
[6] M. Ortega, C. Marino, M. G. Penedo, M. Blanco and F.
Gonzalez, “Biometric Authentication Using Digital Reti-
nal Images,” Proceedings of the 5th WSEAS International
Conference on Applied Computer Science (ACOS06),
Hangzhou, April 2006, pp. 422-427.
[7] Z. W. Xu, X. X. Guo, X. Y. Hu and X. Cheng, “The
Blood Vessel Recognition of Ocular Fundus,” Proceed-
ings of the 4th International Conference on Machine

A New Partitioning Method in Frequency Analysis of the Retinal Images for Human Identification 278
Learning and Cybernetics (ICMLC05), Guangzhou, Au-
gust 2005, pp. 4493-4498.
[8] R. C. Gonzalez and R. E. Woods, “Digital Image Proc-
essing,” Pearson Education Inc., New Delhi, 2003, pp.
548-560.
[9] J. Staal, M. D. Abramoff, M. Niemeijer, M. A. Viergever
and B. van Ginneken, “Ridge-Based Vessel Segmentation
in Colorimages of the Retina,” IEEE Transactions on
Medical Imaging, Vol. 23, No. 4, 2004, pp. 501-509.
doi:10.1109/TMI.2004.825627
[10] A. Hoover, V. Kouznetsova and M. Goldbaum, “Locating
Blood Vessels in Retinal Images by Piecewise Threshold
Probing of a Matched Filter Response,” IEEE Transac-
tions on Medical Imaging, Vol. 19, No. 3, 2000, pp.
203-210. doi:10.1109/42.845178