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Abstract—Optic Disc (OD) localization is an important pre-processing step that significantly

simplifies subsequent segmentation of the OD and other retinal structures. Current OD localization

techniques suffer from impractically-high computation times (few minutes per image). In this work,

we present a fast technique that requires less than a second to localize the OD. The technique is

based on obtaining two projections of certain image features that encode the x- and y- coordinates

of the OD. The resulting 1D projections are then searched to determine the location of the OD. This

avoids searching the 2D image space and thus enhances the speed of the OD localization process.

Image features such as retinal vessels orientation and the OD brightness are used in the current

method. Four publicly-available databases, including STARE and DRIVE, are used to evaluate the

proposed technique. The OD was successfully located in 330 images out of 340 images (97%) with

an average computation time of 0.65 seconds.

Index Terms—Optic disc, localization, projection, image features

I. INTRODUCTION

With the new advances in digital modalities for retinal imaging, there is a progressive need of image

processing tools that provide fast and reliable segmentation of retinal anatomical structures. The optic

disc (OD) is a major retinal structure that usually appears in retinal images as a circular bright object [1].

This work is supported by a grant from Center for Informatics Science (CIS), Nile University (NU), Egypt.

A. E. Mahfouz is with the Medical Imaging & Image Processing Lab, Nile University, Egypt (e-mail: ahmed.mahfouz@nileu.edu.eg).

A. S. Fahmy, PhD. is with the School of Communication & Information Technology, Nile University, Egypt (phone: 002-02-35342069; fax: 002-02-35392350; e-mail: asfahmy@nileuniversity.edu.eg).

Fast Localization of the Optic Disc Using

Projection of Image Features

Ahmed E. Mahfouz and Ahmed S. Fahmy*

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It is the region where the optic nerve and the retinal and choroidal vessels emerge into the eye [2]. A large

number of algorithms have been proposed in literature to segment the OD; this includes the use of Hough

Transform [3]–[5], active contour models [6], and Gradient Vector Flow (GVF) [7] and [8]. Nevertheless,

the success and efficiency of these algorithms depend mainly on determining a seed point inside the OD,

i.e. localization of the OD [6]–[8]. Although manual localization of the OD is sufficient, the process can

be prohibitively cumbersome when dealing with large number of images. This has stimulated several

research groups to develop algorithms for automatic localization of the OD [1], [2] and [9]–[12]. OD

localization can also be useful for a number of applications. For example, the OD location can serve as a

landmark for localizing and segmenting other anatomical structures such as the fovea (where the distance

between the OD center and the center of the fovea is roughly constant) [2]. The location can also be used

to classify left and right eyes in fovea-centered retinal images [13]. In addition, the detection of OD

location is sometimes necessary for computing some important diagnostic indices for hypertensive

retinopathy based on vasculature such as Central Retinal Artery Equivalent (CRAE) and Central Retinal

Vein Equivalent (CRVE) [10]. Also, since the OD can be easily confounded with large exudates and

lesions, the detection of its location is important to remove it from a set of candidate lesions [9].

In normal eyes, automatic localization of the OD is simple because it has well-defined features.

Nevertheless, developing fast and robust methods for automatic localization of the OD could be very

challenging due to the presence of retinal pathologies that alter the appearance of the OD significantly

and/or have similar properties to the OD [3]. OD localization methods can be classified into two main

categories, appearance-based methods and model-based methods. Appearance-based methods identify the

location of the OD as the location of the brightest round object within the retinal image. These methods

include techniques such as intensity thresholding [4] and [5], highest average variation [14], matched

spatial filter [12], and principle component analysis [10]. Although these methods are simple and have

high success rates in normal images, they fail to correctly localize the OD in diseased retinal images

where the pathologies have similar appearance properties to the OD.

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Model-based methods depend mainly on extracting and analyzing the structure of the retinal vessels

and defining the location of the OD as the point where all the retinal vessels originate [9], [1] and [2].

Techniques such as geometrical models [9], template matching [11], and convergence of vasculature [1],

[2] have a relatively high success rate in diseased images, but they are computationally very expensive

because they require segmentation of the retinal vessels as an initial step of the localization process. For

example, the geometrical model-based method proposed by M. Foracchia et al. [9] achieves a success rate

of more than 97.5%, but it takes an average computation time of 2 minutes to localize the OD in a given

image. Another OD localization method based on vasculature convergence has been described by A.

Youssif et al. [2]. The method achieves an accuracy of more than 98.77%, but it takes an average

computation time of 3.5 minutes per image to correctly locate the OD.

In this work, a novel fast technique for OD localization is proposed. The new method can be classified

as a model-based method in which the OD is considered the region where the main retinal vessels

originate in a vertical direction. The computational time of the localization process is significantly

enhanced by reducing the problem from one 2D localization problem to two 1D problems that does not

require segmentation of the retinal vessels. The remaining sections of this manuscript are organized as

follows; Section 2.1 describes the “easy-to-compute” image features that can be used to decompose the

image into two 1D signals. Section 2.2 contains the methodologies of determining the horizontal and the

vertical locations of the OD from the resulting two 1D signals. Section 2.3 proposes a geometry-based

method that can be used to enhance the robustness of the localization process. Section 3 contains the

detailed algorithm that can be used to implement the proposed technique and reproduce the results which

are displayed in Section 4. Sections 5 and 6 contain a discussion of the results and the conclusion

respectively.

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II. THEORY AND METHODS

A. Projection of Image Features

Searching for the OD location in a 2D space (image space) renders any localization algorithm highly

expensive in terms of computational time. The main objective of this work is to propose a localization

algorithm with significantly enhanced speed by converting the typical 2D localization problem into two

1D localization problems, i.e. reducing the dimensionality of the problem. This reduction of

dimensionality is achieved by projecting certain features from the retinal image onto two orthogonal axes

(horizontal and vertical). The resulting two 1D signals are then searched to determine the horizontal and

vertical coordinates of the OD location. The key factor needed for the success of the dimensionality

reduction process is to obtain two meaningful 1D signals that can be used to determine the coordinates of

the OD location. A meaningful horizontal (or vertical) signal can be defined to be a signal whose

maximum value occurs at the horizontal (or vertical) location of the OD. In order to produce such 1D

signals, the set of retinal image features to be projected on either axis should be carefully determined.

Two features are used to create the two 1D projection signals. The first, and the most fundamental

feature, is based on the simple observation that the central retinal artery and vein emerge from the OD

mainly in the vertical direction and then progressively branch into main horizontal vessels, see fig. 1(a).

These main horizontal vessels branch further in all directions to feed most of the retina. This vasculature

structure of the retina suggests that a vertical window (with height equal to the image height and a proper

width) would always be dominated by vertical edges (vertical vessels) when centered at the OD. Although

the window may contain vertical edges at other locations, e.g. small vascular branches and lesions, it will

always be populated by strong horizontal edges as well, i.e. the edges of the two main horizontal branches

of the retinal vessels. Given the above retinal vessels structure, the integration of the difference between

the vertical and horizontal edges, over a region represented by the pre-described vertical window, is a

possible scoring index of the horizontal location of the OD. Simple gradient operators (the kernel [1 0 -1]

and its transpose) are used to produce the vertical and horizontal edge maps of the image.

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The second feature used in this work is the intensity profile of the region containing the OD. The OD is

usually a region that is brighter than its surroundings with a thin dark vertical slice in the center

(representing the vertical vessels inside the OD). Sections 2.3 and 2.4 give details on how to incorporate

this feature into the proposed technique.

B. OD Localization

In order to localize the OD, the process is split into two steps. In the first step, the image features are

projected onto the horizontal axis to determine the horizontal location of the OD. In the second step, the

horizontal location, determined from step 1, is searched for the correct vertical location of the OD. The

following two sections show these two steps in detail.

It is worth noting that the areas outside the camera aperture (circular region) are excluded using a

binary mask generated by thresholding the red component of the image based on the method described in

[3].

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Fig. 1. (a) A retinal image showing the sliding window at two different locations, sliding direction and

projection direction. (b) Plot of the 1D signal resulting from projecting the image features onto the

horizontal axis (Hprojection).

Horizontal Localization of the OD

In order to follow the approach described in the preceding two sections to determine the horizontal

location of the OD, define a horizontally sliding window whose width and height are equal to double the

thickness of a main vessel and the image height, respectively. Let this window scan the retinal image

from left to right and project the image features within it onto a horizontal axis to form the first 1D signal,

used later for horizontal localization. Assume that the image features of interest, the features to be

projected, are: (1) the absolute difference between image's vertical and horizontal edges, and (2) the

image‟s intensity values.

Fig. 1(a) shows a retinal image with the horizontally sliding window placed at two different locations

(location1 & location 2). When the window is located over the OD (location 1), it encloses a large number

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of vertical edges and almost no horizontal edges; that is the projection of the integration of the difference

between the vertical and horizontal edges produces a maximum value. Also at the location of the OD, the

projection of pixels' intensity within the same window returns a minimum value, because the window

contains a large number of vertical vessels (represented by low intensity pixels). When the window is

centered at any other location in the retinal image (location 2 for example), it may enclose a significant

number of vertical edges (representing small vascular branches and/or lesions), but it will always contain

a high population of horizontal edges (representing the two main horizontal branches of the retinal

vessels).

Fig. 1(b) shows the 1D signal resulting from projecting the two features described above on the

horizontal axis. The value of the signal at each horizontal location is the ratio between: (1) the projection

of the difference between the vertical and horizontal edges, and (2) the projection of the intensity values

within the window, when centered at this horizontal location. Notice that the horizontal location of the

optic disc is easily identified as the location of the maximum peak of the resulting 1D signal.

It is worth Noting that the vessels thickness and the OD diameter are calculated automatically from the

image resolution; assuming that the average OD diameter in adults is 1.5mm and the main vessels

thickness is 15% of the OD diameter [15]. Small variations in these values don‟t alter the resulting signal

significantly.

Vertical localization of the OD

Assuming that the approach followed in the previous section has successfully identified the horizontal

location of the OD, the objective now is to search this horizontal location for the correct vertical location

of the OD. Define a vertically sliding window whose width and height are equal to the diameter of the

OD. Let this window, centered at the horizontal location determined from the previous section, scan the

retinal image from top to bottom and project the image features within it onto a vertical axis to form the

second 1D signal, used later for vertical localization. The image features of interest, features to be

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projected, are: (1) the summation of the image's vertical and horizontal edges, and (2) the image‟s

intensity values.

Fig. 2. (a) A retinal image showing the vertically sliding window, sliding direction and projection

direction. (b) Plot of the 1D signal resulting from projecting the image features onto the vertical axis

(Vprojection).

Fig. 2(a) shows the same retinal image of fig. 1 with the vertically sliding window centered at the

horizontal location of the OD, determined in the previous section. When this vertically sliding window is

located over the OD, it encloses a large number of both vertical and horizontal edges. Also at this

location, the projection of pixels‟ intensity values within the window has a maximum value, i.e. the

window contains a maximum number of bright pixels. At any other location along the vertical line

defining the pre-determined horizontal location of the OD, the window encloses fewer vertical and

horizontal edges and fewer bright pixels. This follows the fact that the possibility of having lesions in the

regions above or below the OD is very small, because no retinal vessels are present in these regions.

Fig. 2(b) shows the 1D signal resulting from projecting the features described above on the vertical

axis. The value of the signal at each vertical location is the multiplication of two quantities: (1) the

projection of the summation of the vertical and horizontal edges and (2) the projection of the intensity

values within the window, when the window is centered at this vertical location. Notice that the vertical

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location of the optic disc is easily identified as the location of the maximum peak of the resulting 1D

signal.

C. Improving the Robustness

Consider the horizontal signal of the image shown in fig. 3. It can be shown that the true peak

corresponding to the OD horizontal location, peak 2 in fig. 3, is not the maximum peak. This is due to the

image artifact that appears as a bright spot to the left of the image. If we follow the algorithm described

above, the estimated OD location will be at a point that, by intuition, cannot belong to an optic disc (e.g.

belongs to a non-circular structure). On the other hand, if the second peak of the horizontal signal is

considered a candidate horizontal location for the OD, the estimated OD location will correspond to the

true location of the OD.

This observation can be used to improve the total accuracy of the technique. That is, instead of

considering the maximum peak of the horizontal signal only, a candidate list of possible horizontal OD

locations is used. The candidate list contains the locations of the maximum n peaks and the algorithm is

repeated for each candidate horizontal location. This results in n possible (2D) candidate locations of the

OD. In order to determine the final location, a set of image features is used to score each candidate

location. Then, the final location of the OD is taken as the candidate with the maximum scoring index.

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Fig. 3. (a) The vertical localization signals corresponding to Peak 1, (b) A retinal image showing the two

candidate OD locations, (c) the vertical localization signals corresponding to Peak 2, (d) horizontal

localization signal.

In this work, the candidate list contains two locations. The scoring index is calculated as the peak

strength of the horizontal signal at the candidate location multiplied by a weighing factor. The weighting

factor incorporates some a priori knowledge of the typical geometric and appearance properties of the

OD.

To calculate the weighting factor, a square window (with edge equal to twice the OD diameter) is

centered at the candidate OD location. Then, 10% of the brightest pixels within this window are

segmented. If an object (large cluster of bright pixels) exists at the candidate location, the eccentricity,

defined as the ratio of the object‟s minor axis length to the object‟s major axis length [16], of this object is

calculated. If no object exists, the eccentricity of the candidate location is set to a very small value (e.g.,

0.1). Then, the weighting factor of this location is set equal to the calculated eccentricity.

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III. ALGORITHM

STEP 1: Get image features

1. Get an image of horizontal edges (Eh) and an image of vertical edges (Ev)

2. Calculate EdgeDiff = |Ev| - |Eh|; where |.| is the absolute operator

3. Calculate EdgeSum = |Ev| + |Eh|

STEP 2: Projecting the image features on the horizontal axis

1. Define Whrz as a rectangular window of size (image height, 2×main vessel width) and centered at a

horizontal location x

2. Slide the window Whrz over the retinal image from left to right, and for each x:

- Calculate Fhrz = sum of EdgeDiff inside the window Whrz

- Calculate Ghrz = sum of pixels’ intensity values inside the window Whrz

- Calculate the ratio Hproj (x) = Fhrz / Ghrz

3. The horizontal location of the OD, HRZ_CAND, is the location of the maximum peak of Hproj

STEP 3: Projecting the image features on the vertical axis

1. Define Wver as a rectangular window of size (OD diameter, OD diameter) and centered at the

horizontal location HRZ_CAND and a vertical location y

2. Slide the window Wver over the image from top to bottom, and for each y:

- Calculate: Fver = sum of EdgeSum inside the window Wver

- Calculate Gver = sum of pixels’ intensity values inside the window Wver

- Calculate the value Vproj = Fver Gver

3. The vertical location of the OD, VER_CAND, is the location of the maximum peak of Vproj

STEP 4: Improving the robustness

1. For every candidate location (HRZ_CAND, VER_CAND), select a region of interest (ROI) of size

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(2 × OD diameter, 2 × OD diameter)

2. Segment the brightest 10% pixels within each ROI

3. Group neighboring pixels into objects

4. Calculate the eccentricity of the largest object

eccen. = minor axis length / major axis length

5. Calculate the Scoring Index of each candidate location as:

Scoring Index(HRZ_CAND, VER_CAND) = Hproj(HRZ_CAND) × eccen(HRZ_CAND, VER_CAND)

6. Select the final OD location as the location with the largest Scoring Index

IV. RESULTS

Four publicly available databases are used to evaluate the accuracy and the computation time of the

proposed technique. The four databases are: (1) STARE database (81 images, 605 700 pixels) [17], (2)

DRIVE database (40 images, 565 584 pixels) [18], (3) Standard Diabetic Retinopathy Database

'Calibration Level 0' (DIARETDB0) (130 images, 1500 1152 pixels) [19] and (4) Standard Diabetic

Retinopathy Database 'Calibration Level 1' (DIARETDB1) (89 images, 1500 1152 pixels) [19]. The

diseased images in the four databases contain signs of DR, such as hard exudates, soft exudates,

hemorrhages and neo-vascularization (NV). The accuracy and computation time results of evaluating the

proposed method using these databases are summarized in Table 1. The table includes the results of

applying the method without constructing the candidate list (the maximum peak of the horizontal

localization signal is selected as the correct location) and also the results with the list containing two

candidates.

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Fig. 4. Success and failure cases in 6 images selected from Stare database. (a) – (l) show successful OD localization samples. (m) – (o) show a sample of failure in OD localization. The white „X‟ indicates the location of the OD as detected by the proposed method.

Table 1. Accuracy and computation time of the proposed OD localization technique.

Database STARE DRIVE DIARETDB0 DIARETDB1 Total

Normal Images 31 33 20 5 89

Diseased Images 50 7 110 84 251

Number of Images 81 40 130 89 340

Success Rate 89% 100% 94.6% 96.6% 94.4%

Success Rate

(with improvement) 92.6% 100% 98.5% 97.8% 97%

Computation Time 0.46 sec. 0.32 sec. 0.98 sec. 0.98 sec.

The proposed method was implemented using Matlab® (The MathWorks, Inc.). The results shown in

Table 1 are acquired by running the developed code on a PC (2.66 Intel® Core 2 Due and 4 GB RAM).

The detected location of the OD is considered correct if it falls within 60 pixels of a manually identified

OD center, as proposed by A. Hoover et al. in [1], M. Foracchia et al. in [9] and A. Youssif et al. in [2].

The center of the OD is manually identified as the point from which all the retinal vessels emerge.

The proposed method achieved a total accuracy of 97% when tested using the four databases, i.e. the

OD was correctly located in 330 images out of the 340 images tested. The OD was correctly located in 75

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images out of STARE‟s 81 images (92.6% accuracy) with an average computation time of 0.46 seconds

per image and an error of 14±15 pixels (mean ± Standard Deviation). In addition, the OD was correctly

located in all the 40 images of DRIVE database (100% accuracy) with an average computation time of

0.32 seconds per image and an error of 11±11 pixels. Fig. 3 shows the results of applying the proposed

method to selected retinal images from the four databases.

V. DISCUSSION

A new method for OD localization is presented. The method achieves fast localization by reducing the

dimensionality of the search space from a 2D space (image space) to two 1D spaces (two 1D signals). The

process of dimensionality reduction is achieved through the projection of certain image features onto two

orthogonal axes (horizontal and vertical). In this work, two features are selected for projection. The first

one is the directionality of the retinal vessels (represented by the horizontal and vertical edge maps of the

image). The second feature is the intensity profile of the OD (a bright circular region with a thin dark slab

in the middle).

The robustness of the novel technique is guaranteed by evaluating the method using four databases

(340 images); most commonly used for evaluation by currently available techniques [1], [2] and [9]. The

method achieved a relatively high success rate in the four databases (97%) with all the parameters of

algorithm maintained at constant values (except for linear scaling of the sizes of the used projection

windows according to the image resolution). That is, there is no need to tailor the algorithm parameters

for different databases.

The step of reducing the dimensionality of the search space resulted in a significantly reduced

computation time (less than one second), compared to currently available techniques (3.5 minutes in [2]

and 2 minutes in [9]). The key factor that greatly enhanced the speed of the method is that the

directionality of the retinal vessels, weather vertical or horizontal, is described by the directionality of

their corresponding edges in the vertical and horizontal edge maps of the retinal image. The process of

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convoluting the image with a 3 1 gradient mask to produce the edge maps is the most computationally

demanding operation in the algorithm, but this operation is negligible if compared to the initial step of

extracting the retinal vessels that is required in all model-based techniques. The latter is usually achieved

by applying a 2D matched filter (typically a 10 15 mask for the resolution of STARE images) with

several orientations (typically at 12 different angles) [20].

The accuracy of the proposed technique is highly dependent on the accuracy of the horizontal

localization process, because searching for the OD‟s vertical location is restricted by a window centered

at the estimated horizontal location. Hence, to increase the accuracy of the proposed technique, two

candidate locations of the OD are estimated and additional scoring of these candidates is done by

incorporating the appearance and geometric properties of the candidate OD. By investigating these two

candidate locations, instead of one location only, the total accuracy of the technique increased from

94.4% to 97%. Note that the process of investigating two candidate locations was applied to all the

images with no significant computation overhead, i.e. a negligible step in terms of computational time.

As shown in fig. 3, even in the presence of retinal pathologies and/or image artifacts, the selected

features were unique to the OD and thus allowed proper localization with relatively high accuracy. Fig 3

(a) – (l) show different images from the four databases where the OD location was detected correctly. Fig

3(m) – (o) show three retinal images in which the proposed method failed to locate the OD.

VI. CONCLUSION

A novel OD localization technique is presented. The new technique achieves accurate results relative to

currently available techniques, but with a significant reduction in the computation time. The main idea

proposed is to reduce the dimensionality of the search space. This is achieved by decomposing the 2D

problem into two 1D problems by projecting certain image features (vessels structure and OD

appearance) onto two orthogonal axes.

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