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Abstract— This paper presents a novel method using discrete transforms to segment exudates and blood vessels in
retinographies. Illumination correction is previously done based on a homomorphic filter due to uneven illumination in
retinographies. To distinguish foreground objects from the background, we propose a family of super-Gaussian filters in
the discrete cosine transform domain and we analyze the difference between Butterworth and super-Gaussian band-pass
filters. The filters are applied on the green channel since it has the relevant information to segment pathologies. To detect
exudates in the filtered image, a gamma correction is first applied to enhance foreground object. Then, Otsu’s global
thresholding method is used, after which, a masking operation over the effective area of retinographies is performed to
obtain final segmentation. For blood vessels, the negative of the filtered image is first calculated, and then a median filter is
applied to reduce noise and artifacts followed by gamma correction. Again, Otsu’s global thresholding method is applied
for image binarization. Next a morphological closing operation is employed and a logical masking operation gives the
resulting segmentation. Illustrative examples taken from a worldwide free clinical database are included to demonstrate the
capability of the proposed segmentation method.
Index Terms— Butterworth filter, discrete cosine transform, image segmentation, super-Gaussian filter.
I. INTRODUCTION
Millions of people across the world live with varying degrees of irreversible vision loss because they have an
untreatable, degenerative eye disorder, which affects the retina [1]. Under these conditions, the delicate layer of
tissue that lines the inside back of the eye is damaged, affecting its ability to send light signals to the brain. When
the blood vessels are damaged by high blood sugar levels and initially become defective, later they may become
blocked. The defective vessels can lead to hemorrhages (spots of bleeding), fluid, and exudates (fats) to escape
from the blood vessels over the retina. The blocked vessels can starve the retina from oxygen (ischemia), leading
to the growth of new abnormal vessels in the retina.
Actually, there are several screening eye exams that help to find any illness, among the exams are the amsler grid,
auto fluorescence, dilated eye exam, fundoscopy or ophthalmoscopy, eye fundus photography, fluorescence
angiography, optical coherence tomography, and tonometry [2], [3]. In recent researches, diverse techniques such
as the Hough transform, mathematical morphology, illumination correction, and histogram equalization [4]-[9]
have been applied to eye fundus photography to find blood vessels, exudates, or hemorrhages. Other works
enhance the image using Gaussian filters as well as the watershed transform [10]-[12]. In this paper, we use the
databases known as DIARETDB0 and DIARETDB1 (Standard Diabetic Retinopathy Database Calibration Level
{0,1}) from Lappeenranta University in Finland [13], where each image in these databases has a size of 1152 ×
1500 pixels. Knowing that the area of the optic disk is 2.47 mm2
(radius = 0.887 mm), the corresponding
approximate spatial resolution is about 4.746 µm per pixel.
The purpose of this research work is to extract exudates and blood vessels in eye fundus color images. Basically,
our proposal consists of the following steps. First, a binary image mask is created to obtain the boundary of the eye
fundus in the acquired color image by clipping the effective area taken by the camera. Second, a homomorphic
filter in the discrete cosine transform (DCT) [14] or Fourier transform domain is applied to homogenize image
illumination, after which a super-Gaussian band-pass filter in the frequency DCT domain is used to distinguish
between foreground objects and eye fundus image background. Then, two procedures are proposed for the
different types of pathologies mentioned earlier. The first procedure that determines exudates employs gamma
correction to enhance contrast, Otsu’s global thresholding method serves to binarize the image, and a logical
operation between the binary mask and the thresholded image is realized to get the segmented image.
The second procedure is for blood vessels. First the negative of the filtered image is obtained, then a median filter
A super-Gaussian discrete cosine transform filter
for the detection of pathologies in retino graphies Luis David Lara-Rodríguez and Gonzalo Urcid
Optics Department, National Institute of Astrophysics, Optics, and Electronics (INAOE)
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is applied to reduce noise and artifacts, again a gamma correction is applied to enhance contrast, and image
thresholding (Otsu’s method) is performed using global statistics to obtain the desired object regions including
their edges. Final segmentation of blood vessels is obtained by morphological closing followed by a logical
operation between the binary mask and the thresholded image. Our paper is organized as follows: Section II
explains in detail the different image processing steps involved in the proposed frequency DCT filtering based
method for the segmentation of the aforementioned pathologies including several representative examples.
Section III presents the segmentation results obtained as well as the proposed segmentation algorithm in pseudo
code format. We close the paper with Section IV of conclusion and some pertinent comments.
II. SEGMENTATION OF EXUDATES AND BLOOD VESSELS
A. Theoretical Background
A binary mask is designed to delete the effective area taken by the eye fundus camera, an example of a mask is
shown in Fig. 1. The desired mask is obtained by extracting the red, green and blue channels, then a quotient
between the red and green channel is calculated. To the resulting image a median filter is applied to reduce noise
and Otsu’s global thresholding method is used to get the final mask.
Fig. 1. a), b) eye fundus color images of right and left eyes respectively; c), d) associated binary masks.
In a segmentation process, it is possible to discriminate objects of interest from the background by dividing the
image in regions that satisfy certain conditions [15]. In general, due to the presence of non-uniform illumination in
eye fundus images, we propose the use of a Fourier or DCT homomorphic filter to homogenize illumination. The
discrete cosine transform (DCT) is a finite sequence of data points in terms of a sum of cosine functions
oscillating at different frequencies and amplitudes. DCT’s are important in numerous applications in science and
engineering. Formally, the DCT is a linear and invertible operator that can be identified with an array of M × N
elements. Mathematically, the two dimensional DCT is given by,
1
0
1
0 2
)12(cos
2
)12(cos,
,2,
M
x
N
y N
vx
M
uxyxf
MN
vuvuC
,
(1)
where is the two-dimensional Kronecker’s delta. If u = v = 0, then δ = 1; if u,v ≠ 0, then δ = 0. On the other
hand, recall that the two dimensional discrete Fourier transform (DFT) is given by,
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1 1
2 / /
0 0
, ,M N
i ux M vy N
x y
F u v f x y e
,
(2)
Where, is an input image of size M × N , u = 0,1,…, M − 1, and v = 0,1,…, N – 1, for both transforms. If
is multiplied by the transform is centered and its DFT is computed with a fast Fourier
transform (FFT) algorithm. The filtered image, denoted by , is given by,
, IDFT , ,g x y F u v H u v , or (3)
, IDCT , ,g x y C u v H u v (4)
Where, in (3), IDFT is the inverse discrete Fourier transform and is the DFT of the input image .
In (4), is the DCT of the input image . Note that the inverse discrete cosine transform (IDCT) has
the same expression as (1) with u and v changed by x and y, respectively. Besides, is a specific
homomorphic filter in the Fourier or DCT domain. For numerical computation, the functions C, F, H, and g are
matrices of the same size as the given image. A high-pass Butterworth homomorphic filter (HF) is defined by [15],
4
HF H L L
0
,,
n
D u vH u v
D
,
(5)
Where, the filter order n determines the slope of the function between the low (γL < 1) and high (γH > 1) gamma
bounds. In (5), the particular values used for DFT filtering of the eye fundus color images are set to γL = 0.75, γH =
1.75, n =2, and D0 = 10 is the chosen cutoff spatial frequency. In similar fashion, the values used for DCT filtering
of the eye fundus color images are set to γL = 0.75, γH = 1.75, n = 2, and D0 = 20 is the cutoff spatial frequency. An
example of illumination correction for an RGB eye fundus color image is shown in Fig. 2.
Fig. 2. a) Eye fundus color image, b) illumination corrected color image using DFT, c) illumination corrected color
image using DCT.
We can observe in Fig. 2 that the homomorphic filtered image using the DCT looks better since illumination is
more uniform than the DFT filtered image. For that reason we work with the DCT instead of the DFT filtered
image. Once the illumination is corrected, filtering with the discrete cosine transform is used to intensify the
foreground objects against the surrounding background of the corresponding green channel.
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We introduce a super-Gaussian function as a novel filter for processing images in the frequency domain [16]. The
advantages of this type of filter is explained next in comparison with a Butterworth filter. Table I gives the
defining expressions of the types of super-Gaussian filter frequency functions, i.e., low-pass, high-pass, band-pass
and band- reject that can be used for image processing.
Table I. Mathematical expressions of the four types of Butterworth and super-Gaussian filters.
Low-pass
1
2
BLP 1 /n
oH r D D
(6a)
2
02
SGLP
nr
DH r e
(6b)
High-pass
1
2
BHP 1 /n
oH r D D
(7a)
2
02
SGHP 1
nr
DH r e
(7b)
Band-pass
12
2 2
BBP 0, 1 /n
H r W D D WD
(8a)
22 2
0
SGBP ,
nr D
rWH r W e
(8b)
Band-reject BBR BBP, 1 ,H r W H r W (9a) SGBR SGBP, 1 ,H r W H r W
(9b)
In equations (6a) through (8b), is the filter order, W is the band-pass width, is
the Euclidean distance from the center of the filter (the origin), and D0 is the cutoff spatial frequency in the DCT
domain. An analysis between a super-Gaussian band-pass filter and a Butterworth band-pass filter in terms of
slope and bandwidth rates is discussed next. Specifically, we determine the ratio between slope variations of both
filters to find out which one has a major slope in or near the cutoff frequency. Also, we find the ratio between
band-pass widths variations of both filters to find which filter has the narrower bandwidth or is more selective.
Therefore, partial derivation of both filter expressions, first with respect to r (radial distance) and second with
respect to W (band-width) is displayed in the following equations. Note that subscript SGBP refers to a band-pass
super-Gaussian filter and subscript BBP is an abbreviation for a band-pass Butterworth filter.
The slope variation for the BBP and SGBP filters, in (8a) and (8b), is determined as follows,
2 22 2 2 2
0 02 12 2 2 2
0 0SGBP SGBP 2
2 12 2 2 2
0 0
BBP BBP2 22 22 2
02 2
0
, , 2 ,
21, 1 , .
1
n nr D r Dn
rW rW
n
nn n
r D r DH r W e H r W n e
r rW r W
nW r D rW r DH r W H r W
rrW r D rWr D
Hence, the corresponding slopes ratio, denoted by ρS(r,W), is found to be,
22 2
022 22 2SGBP
0
4BBP
, .
nr D
n n rW
S n
Hr D rW e
rr WH rW
r
(10)
Using (10), we now prove that in a neighborhood of the cutoff frequency D0, the slope of a SGBP filter is greater
than or equal to the slope of a BBP filter with the same order while keeping a fixed bandwidth. First, let r = D0,
then, ρ(D0) = 1; second, consider r = r1 ≈ D0 then,
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222
122 2 2 SGBP BBP
1 0 1 4
1
0 , 1 or .
nn
nn
S n
a rW H Hr D a r W
r rrW
Similarly, from (8a) and (8b), the bandwidth variation for the SGBP and BBP filters is given, respectively by,
2
2 202
2 2
SGBP 0
22 2
BBP
2 2 2 2
0 0
2 and
21 .
nr Dn
rW
n n
H r Dne
W W rW
H n rW rW
W W r D r D
From the previous two expressions, the bandwidths ratio ρW(r,W) results in the following expression,
22 2
022 22 2SGBP
0
4BBP
,
nr D
n n rW
W n
Hr D rW e
Wr WH rW
W
(11)
Next, based on (11), we verify that within the band limits DL and DH, the band-pass width of a SGBP filter is
strictly less than the band-pass width of a BBP filter of the same order. Recall that, DL = D0 – W/2 and DH = D0+
W/2; also, if we let r = DL or r = DH, then we have,
2 22 20 0
2 22 2 2 2 2
112 2
2 2 22 2
4 4
2224 44
4 4
0
,
1 .
n n
L
L L
nn
n nn
L o H o
D D D
n nD W Dn n
L L
W L n n
L L
nn nL
L SGBPBBP
n n
L L
D D D D a
a D W e a D W eD W
D W D W
e a D W e D W HH
W WD W D W
From the ratio analysis based on (10) and (11) between filter types, we can observe that the super-Gaussian
band-pass filter exhibits a higher slope and a more selective band-pass width (delimiting fall-off frequencies).
Therefore, it should be clear that a super-Gaussian filter with tunable order n establishes a balanced frequency
response between those displayed by a simple Gaussian and Butterworth filters. Figure 3 shows the 1D profiles of
super-Gaussian high and low-pass filters along positive frequencies, computed using the values (in pixels), D0 =
105, n = 1,..,5, and W = 35, over the interval r = 0,...,511. Analogously, Fig. 4 displays the 1D profiles for
super-Gaussian band-reject and band-pass filters.
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Fig. 3. a) SGHP filters, b) SGLP filters; D0 = 105 and n = 1,…,5 over the pixel subrange r = 0,…,350.
Fig. 4. a) SGBR filter, b): SGBP filter; D0 = 105, n = 1,…,5, and W = 35 over the pixel subrange r = 0,…,200.
Furthermore, for a visual comparison, Fig. 5 shows several Butterworth band-pass and super-Gaussian band-pass
filter profiles of different orders in the DCT domain, with parameters values set to D0= 200 (cutoff frequency) and
W = 150 (bandwidth) for both filters.
As can be seen in the given graphs, the band width value is better delimited with a super-Gaussian filter since its
curve is steeper than the corresponding curve of a Butterworth filter, where the values of D, D0, W are given in
pixels. In the discussion that follows, we use a super-Gaussian band-pass (SGBP) filter given by (8b) in Table I.
In the present study, the design parameter values of a super-Gaussian band-pass filter are set to n = 2, W = 275,
and D0 = 100. The filtered image, after inversion with the IDCT, is given by the equivalent spatial expression,
SGBP HF SGBP, , , , .Gg x y I x y h x y h x y
(12)
In (12), * denotes convolution. The DCT filtering stage is the same for segmenting exudates as well as blood
vessels and the specific steps to segment each type of pathology are described in the following subsections.
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Fig. 5. a) Butterworth and b) super-Gaussian band-pass filter 1D profiles; c) Butterworth and d) super-Gaussian
band-pass filter 3D contours for n = 2.
B. Segmentation of Exudates
For this type of pathology, a 3 × 3 median filter is first applied over the whole image with the purpose to
preserve exudates edges; then, a gamma correction with value 2 is applied to to enhance
contrast, and Otsu’s method, based on global and local statistics [15], is used to compute a global threshold value
denoted by LOtsu. Specifically, the binary output image is determined as
SGBP EOtsu
E
if
otherwise
0 g ,,
1
x y LB x y
,
(13)
Where, the E sub index label refers to exudates. The segmented image is found by masking the previous image
with the initial binary mask M, i.e., SE = BE ∧ M, where ∧ is the logical AND or minimum matrix operation (cf.
Case construct in Algorithm DTBS, Sec. III). An illustrative example of exudates segmentation is displayed in
Fig. 6.
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Fig. 6. a) Eye fundus color image with hard and soft exudates (database: diaretdb0−v1−1/image007) with enhanced
illumination, b) super-Gaussian band-pass filtered enhanced image, c) binary image showing segmented hard and soft
exudates.
C. Segmentation of Blood Vessels
In order to emphasize blood vessels, the negative image, of the previous
filtered image is first computed, where L is the maximum value of the corresponding grayscale dynamic range. In
our case, L = 256, since we are using the usual 8-bit coded grayscale. Then, as in the case of exudates, a 3 × 3
median filter is passed over image to preserve edges, followed by a gamma correction of value 3 applied to
. In similar fashion, thresholding is performed using Otsu’s method to obtain a binary image
based on the global threshold value LOtsu. Specifically, the binary output image is computed as,
NSGBP VOtsu
V
if
otherwise
0 g ,,
1
x y LB x y
,
(14)
where, the V sub index label refers to blood vessels. Once the binary image in (14) is computed, a morphological
closing operation is used to connect object edges in the corresponding regions of , i. e.,
, where S is a structuring element selected as an isotropic square of size 3 × 3 on-pixels
[17]. In other words, image BV (x,y) is first eroded and then dilated by S thus first eliminating artifacts or spikes
smaller than S and then restoring the overall objects shapes. Finally, the segmented image SV containing the blood
vessels is obtained by masking the previous image. Hence, SV = BV ∧ M , where ∧ is the logical AND or minimum
matrix operation (cf. corresponding Case construct in Algorithm DTBS, Sec. III). An representative example of
blood vessels segmentation is depicted in Fig. 7. We remark that using the same technique as described in this
subsection, it is possible to segment other pathologies such as aneurysms, which are localized blood filled balls of
variable size in the wall of a blood vessel [18].
III. IMAGE SEGMENTATION RESULTS
To test our proposed segmentation technique, we use six eyes fundus color images taken from the free domain
databases DIARETDB0 and DIARETDB1. The first database consists of 130 eye fundus color images, of which 20
are normal and 110 contain signs of diabetic retinopathy such as hard exudates, soft exudates, micro aneuyrysms,
hemorrhages, and neovascularization. The second database consists of 89 eye fundus color images, from which 84
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images contain at least mild non-proliferate signs of diabetic retinopathy. The other five images are considered
normal since these do not contain any signs of diabetic retinopathy. The aforementioned clinical characteristics
are based on the expert’s knowledge who participated in the overall evaluation of both databases.
Fig. 7. a) Eye fundus color image with blood vessels and aneurysms (database:diaretdb0−v1−1/image005) with
enhanced illumination, b) super-Gaussian band-pass filtered and contrast enhanced image, c) segmented binary image
showing segmented pathologies.
The eye fundus color images were captured using the same 50 degree field-of-view digital fundus camera with
varying imaging settings [19]. As mentioned earlier, each image has a size of 1152 × 1500 pixels, with an
approximate spatial resolution of 4.756 micrometers per pixel. We remark that the global threshold value obtained
by applying Otsu’s method is different for each image. Figures 8 to 13 show illustrative examples of exudates and
blood vessels segmentations. Table II gives the segmentation parameter numerical values (gamma correction and
Otsu’s global threshold) used for exudates and blood vessels. In the exudates segmented images, we can observe
that the optic disk has a similar color as exudates; however, our technique does not segment the optic disk. In Figs.
10 to 12, in addition to segmented blood vessels, aneurysms are also distinguished in the segmentation and
correspond to small amorphous regions not connected to the blood vessels. Algorithm DTBS gives in
pseudo-code format the sequence of instructions to implement of our filtering based segmentation technique.
Table II. Gamma correction and threshold values for segmenting exudates and blood vessels.
Exudates (γ = 2) Blood Vessels (γ = 3)
Figure No. : Pathology type Figure No. : Pathology type
5 : hard & soft exudates 0.20 6 : blood vessels & aneurysms 0.32
7 : hard exudates 0.19 9 : blood vessels & aneurysms 0.27
8 : hard exudates 0.16 10 : blood vessels & aneurysms 0.25
11 : blood vessels 0.29
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Fig. 8. a) Eye fundus color image with hard exudates (database: diaretdb1−v02−1/image015), b) binary image with
segmented hard exudates.
Fig. 9. a) Eye fundus color image with hard exudates (database: diaretdb1−v02−1/image019), b) binary image with
segmented hard exudates.
Fig. 10. a) Eye fundus color image with blood vessels and aneurysms (database: diaretdb1−v02−1/image033),
b) binary image with segmented blood vessels and aneurysms.
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Fig. 11. a) Eye fundus color image with blood vessels and aneurysms (database: diaretdb0−v01−1/image054),
b) binary image with segmented blood vessels and aneurysms.
Fig. 12. a) Eye fundus color image with blood vessels (database: diaretdb1−v01−1/image093), b) binary image with
segmented blood vessels.
hom hom
0 0 L H 0
hom hom hom
0 0 L H
ho
- Discrete Transform Based Segmentation for Exudates and Blood Vessels
, ,
G
D n D n W M S
H HF D n
g IDCT DCT I H
Algorithm DTBS
Input parameters , , , , , ,
Illumination correction
, , ,
m
SGBP 0
SGBP SGBP
SGBP SGBP
E SGBP EOtsu
NSGBP
1
H HBP D n W
g IDCT DCT g H
g GammaCorrection MedFilter g
S Binarize Minimum g L M L
g Ne
DCT Filtering
, ,
Case : Exudates Segmentation
,
, ,
Case : Blood Vessels Segmentation
SGBP
NSGBP NSGBP
V NSGBP VOtsu
1
gative g
g GammaCorrection MedFilter g
S Binarize Minimum g L M L S
,
, ,
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Soft exudates as shown in Fig. 6, are nerve fiber layer infarcts or pre-capillary arterial occlusions. On the other
hand, hard exudates as illustrated in Figs. 6, 8, and 9, represent the accumulation of lipid in or under the retina
secondary to vascular leakage; this is due to the aqueous portion of the fluid that is absorbed more quickly than the
lipid component. Thus, the lipid that builds up in or under the retina becomes visible as yellowish deposits. In
Figs. 7 and 10 to 12, we can observe the segmentation of blood vessels (temporal arcades) whereas aneurysms,
that look like small islands and are easily seen where the macula is located, are displayed in Figs. 7, 10, and 11.
The confusion matrix contains information about actual and predicted classifications realized by a pattern
recognition system [20]. Performance of such systems is commonly evaluated using the data in the matrix shown
in Table III.
Table III. Confusion matrix.
Positive test True positive
TP
False positive
FP
Negative test False negative
FN
True negative
TN
Total TP + FN FP + TN
The confusion matrix has four entries which are, the number TP of correctly detected objects that a test group
sample gives positive, the number TN of incorrectly detected objects that a test group sample gives negative, the
number FP of correctly detected objects classified erroneously (negative), and the number FN of incorrectly
detected objects classified as positive.
The confusion matrix help us to find the true positive rate (TPR), also known as sensitivity, which refers to the
proportion of objects that give positive test results, and the true negative rate (TNR), also known as specificity,
which refers to the proportion of objects that give negative test results, (14) gives these proportions,
and TP TN
TPR TNRTP FN TN FP
(15)
To obtain the sensitivity and specificity rates of our test image examples, twenty eye fundus color images hand
marked of exudates and blood vessels were used as ground-truth. In Table IV, the values of sensitivity and
specificity of the method proposed (DTBS) are compared with other methods taken from the technical literature,
both for the segmentation of exudates and blood vessels.
Table IV. Sensitivity and specificity rates for the segmentation of exudates and blood vessels in eye fundus color images
between various segmentation techniques versus the proposed method DTBS.
Exudates sensitivity and specificity Blood vessels sensitivity and specificity
Method proposed by Method proposed by
Jaafar [4] 0.8930 0.9930 Saleh [9] 0.8423 0.9658
Garaibeh [6] 0.9210 0.9910 Niemeijer [22] 0.6898 0.9696
Welfer [7] 0.7048 0.9884 Oloumi [23] 0.8579 0.9000
Kande [21] 0.8600 0.9800 Staal [24] 0.7194 0.7793
DTBS (in this work) 0.9412 0.9910 DTBS (in this work) 0.8517 0.9832
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IV. CONCLUSION
In this work, we have introduced a discrete cosine transform based filtering approach to the problem of extracting
exudates and blood vessels (including aneurysms) in eye fundus color images. A Fourier transform or DCT
homomorphic Butterworth type filter is proposed for illumination correction of input images and a binary mask of
the effective area of the retinography is constructed as a quotient between the red and green channels.
An important step of the proposed method is the DCT spatial frequency domain processing using a
super-Gaussian band-pass filter with carefully selected parameters. This novel type of filtering achieves an
adequate contrast of the foreground objects against the background. We choose the DCT over the Fourier
transform since its computation deals only with real values instead of complex numbers; in addition, the results
obtained with the corresponding homomorphic DCT based filter are visually better. For blood vessels, a negative
of the filtered image is first obtained, then a median filter is applied for both pathologies to reduce background
noise and artifacts, and a gamma correction is applied to enhance the resulting image contrast. Then, a binary
image is determined using Otsu’s statistical method. However, before the final masking operation is realized, an
intermediate operation is used in the case of detecting blood vessels. In particular, a closing morphological
operation is required with an appropriate structuring element. Several illustrative examples are provided to
demonstrate the segmentation results obtained with the proposed method. Based on the commonly used confusion
matrix in the medical clinical realm, notice that high sensitivity and specificity rate values have been obtained in
our segmentation examples in comparison with other techniques described in the technical literature.
Future work contemplates two aspects. First, to extend the number of tests using the DTBS method on other
clinical databases available such as DRIVE [25] and STARE [26]. Second, to introduce the necessary additions to
our base algorithm in order to include the segmentation of other known pathologies such as hemorrhages or retinal
neovascularization, considering for example, the image samples taken from the database used here (DIARETDB).
A further enhancement of our DCT based proposal will consider the design and implementation of an automatic
pattern recognition system for classifying eye fundus pathologies as a tool for assisted medical diagnosis, capable
of distinguishing, e.g, diabetic retinopathy from maculopathy.
ACKNOWLEDGMENT
Luis D. Lara-Rodríguez thanks the National Council of Science and Technology (CONACYT) for doctoral
scholarship CVU 332238. Gonzalo Urcid is grateful with the National Research System (SNI-CONACYT) for
financial support through grant No. 22036.
REFERENCES [1] Netdoctor, explanation of eyes diseases. www.netdoctor.co.uk.
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ISSN: 2319-5967
ISO 9001:2008 Certified International Journal of Engineering Science and Innovative Technology (IJESIT)
Volume 5, Issue 3, May 2016
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AUTHOR BIOGRAPHY
Luis David Lara-Rodríguez received his B.E. (2007) from Puebla Institute of Technology (ITP), Mexico, and his
M.Sc. (2011) from the Benemeritus Autonomous University of Puebla (BUAP), Mexico. He is a Ph.D. student in the
Optics Department at the National Institute of Astrophysics, Optics, and Electronics (INAOE) in Tonantzintla,
Mexico. His present research interests include 3D modeling, digital image processing and analysis, optical systems
simulations, and computer programming.
Gonzalo Urcid received his B.E. (1982) and M.Sc. (1985) both from the University of the Americas in Puebla,
Mexico, and his Ph.D. (1999) in optics from the National Institute of Astrophysics, Optics, and Electronics (INAOE)
in Tonantzintla, Mexico. He holds the appointment since 2001 of National Researcher from the Mexican National
Council of Science and Technology (SNI-CONACYT), and currently is an Associate Professor in the Optics
Department at INAOE. His present research interests include applied mathematics, digital processing of multichannel
images, artificial neural networks based on lattice algebra, and pattern recognition.