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Automated Optic Disc Detection in Retinal Images

by Applying Region-based Active Aontour Model

in a Variational Level Set Formulation

Jihene Malek, Mariem Ben Abdallah, Asma Mansour Electronics and

MicroelectronicsLaborotory

Rached Tourki Electronics and

Microelectronics Laborotory

University of Monastir University of Monastir Email: jihenemalek@yahoo.fr

Abstract-An efficient optic disk localization and segmentation are important tasks in an automated retinal image analysis system. General-purpose edge detection algorithms often fail to segment the optic disk due to fuzzy boundaries, inconsistent image contrast or missing edge features. This paper presents a method to automatically locate and boundary detect of the optic disk. The detection procedure comprises two independent methodologies. On one hand, a location methodology obtains a pixel that belongs to the OD using iterative thresholding method followed by Principal Component Analysis techniques (PCA) and, on the other hand, a boundary segmentation methodology estimates the OD boundary by applying region-based active contour model in a variational level set formulation (RSF). The method uses an improved geometric active contour model which can not only solve the boundary leakage problem but also is less sensitive to intensity inhomogeneity The results from the RSF method were compared with conventional optic disk detection using a geometric active contour models (ACM) and later verified with hand-drawn ground truth. Results indicate 89 % accuracy for identification and 95.05 % average accuracy in localizing the optic disc boundary.

Keywords - Fundus images; Optic disk detection; fundus images; peA; a variational level set method.

I. INTRODUCTION

Optic disc (OD) detection is an important step in developing systems for automated diagnosis of various serious ophthalmic pathologies. It is a key preprocessing component in many algorithms designed to identify other fundus features automatically. The relatively constant distance between the OD and the fovea can be used to help estimate the location of the latter [1] The OD region is removed before identifying retinal exudates [2], which are used to assess and grade risk of Macular Edema . The optic disk dimensions are also used to measure abnormal features due to glaucoma. Glaucoma is identified by recognizing the changes in shape, color, or depth that it produces in the OD. Thus, its segmentation and analysis can be used to detect evidence of Glaucoma automatically. OD detection is not an easy matter. Besides the variations in OD shape, size, and color pointed out previously, there are some additional complications to

take into account. Contrast all around the OD boundary is usually not constant or high enough piecewise due to outgoing vessels that partially obscures portions of the rim producing shadows. The optic disk is located by PCA based model. The pixel with the minimum distance in the candidate regions among all the scales is located as the center of optic disk [3] Hoover and Goldbaum [4], [5] located the center of the OD using the vasculature origin. They determined where all the vessels converged by means of a voting-type algorithm called fuzzy convergence. Another method that uses the convergence method of the vessels to detect the OD center was proposed by Foracchia et al.[6]. Youssif et al. [7] presented an OD location method based on a vessels direction matched filter.

The approximate center of optic disc is detected in the retinal image using iterative thresholding method followed by connected component analysis [8]. Several methods for localizing optic disk boundary have been reported in the literature Aquino [9] used a new template-based methodology for segmenting the OD from digital retinal images. This methodology based on morphological and edge detection techniques followed by the Circular Hough Transform to obtain a circular OD boundary approximation. Xu et al applied in [10] a deformable-model approach for robust detection of optic disk and cup boundaries. Osareh et al[ll] located the OD center by means of template matching and extracted its boundary using a snake initialized on a morphologically enhanced region of the OD. In this work, the optic disk boundary is determined by a new region-based active contour model in a variational level set formulation described in [12]. A data fitting energy is defined in terms of a contour and two fitting functions that locally approximate the image intensities on the two sides of the contour. This energy is then incorporated into a variational level set formulation[13] with a level set regularization term, from which a curve evolution equation is derived for energy minimization. This study, inspired by the work of Li and Chutatape [14], Siddalingaswamy and Gopalakrishna [8], and

978-1-4673-1274-5/12/$31.00 ©2012 IEEE

Li et al[I2], presents a method for the automatic detection of the OD. The proposed method comprises several steps. First, the approximate center of optic disc is detected in the retinal image using iterative thresholding method followed by A Principal Component Analysis. PCA very powerful in the detection of a similar shape to the trained shapes; Then, active contour models in a level set formulation is employed to obtain accurate optic disc boundary.

A. Methods

The aim of this work is to introduce a new methodology for OD boundary detection. It needs as initial information the coordinates of a pixel located within the OD. In order to place the first Snake on an image, the approximate location needs to be found. A Principal Component Analysis (PCA)-based model was chosen to serve this purpose.

1) Methodology for Automated Location of the aD: The optic disk is the brightest part in the normal fundus image, it is identified by the largest area of pixels having highest gray level in the images and it is observed that it appears most contrasted in the green channel compared to red and blue channels in RGB image Therefore, only the green channel image is used for the effective thresholding of the optic disc. The principle of this method is to evaluate the unique threshold T for any image with a bimodal histogram, by assuming the threshold to be [15]

T = fJo + fJ1

2 (1)

The fJo and fJl, are the means of each of the two components of the histogram separated by the threshold. To obtain an optimal threshold, histogram derived from the source image is scanned from highest intensity fJ1 value to lower intensity value. The scanning stops at the intensity level fJo which has at least a thousand pixels with the same intensity resulting in a subset of histogram. Then, the two means for the two distributions on either side of the threshold are calculated· a new threshold is obtained by averaging these means. Th� process continues until the value of the threshold value does not change any more. Optimal threshold thus calculated results in maximization of gray level variance between object and background. Applying a threshold on the green image results in number of connected components such as part of optic disc, some noise and other bright features (see Fig.I).shows the result of thresholding on one of the test image resulting in number of isolated connected regions. The component having the maximum number of pixels is assumed to be having the optic cup part of the optic disc and it is considered to be the primary region of interest.

Then the PCA (Principal Component Analyses) based model approach is applied to the candidate regions to give the final location of optic disk. First applying a simple clustering method on the intensity image to find the candidate regions where optic disk may appear and then PCA is applied only on these candidate regions to locate the optic disk. PCA is

(a) Input image (b) Threshold image

Figure 1. Optic Disc localization.

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a powerful tool in the recognition of an identical shape to the trained shapes. The PCA based method has been widely explored in the application of face recognition [16] .The problem of optic disk location is similar to face detection in certain respects in that both of them can be supported by knowledge-based methods. The PCA based approach includes three steps. Firstly, the Eigen vectors are calculated from the training images. Then, a new fundus image is projected to the space specified by the Eigen vectors. Finally, the distance between the fundus image and its projection is calculated. The subspace defined by eigenvectors is termed as disk space. The model obtained by PCA statistical analysis is put to use in the localization of the optic disk in fundus images and explained in full detail as follows: Thirty optic disk images are carefully selected as the training set. A square sub-image around the optic disk is manually cropped from each fundus image as training data. The sub­images are resized to L L pixels and their intensities are adjusted linearly to the same range to form a training set Fig.2. Each training image can be considered as a vector of L2. L is the set to 90 according to the size of optic disk. The technique of PCA is applied to the training set to get the modes of variation around the average image. The training set of optic disk images is denoted as vector 71,72, ... , 7M, where M is the set to 30.

(a) T1 (b) T2

••• ===? (c) T3 (d) T4 (e) average

vector

Figure 2. The training set of OD image and their average vector.

The average image of the training set is defined by Eqn.(2) as demonstrated in Fig.2., and the set of deviation from the average vector cP = [cPl, cP2, .... cPMJis also defined with Eqn.(3):

(2)

(3)

The vector Uk, and Ak, defined by Eqn.(5)are the eigenvec­tor and corresponding eigenvalue of the covariance matrix C which is defined in Eqn.( 4).

M

C = � '" <I><I>T M � t t

i=l (4)

(5)

The subspaces defined by the eigenvector Ui, is called as disk space and eigenvector as eigen disk. The eigenvector Ui,

is a linear combination of the original training-image vectors and arranged in descending order according to its associated eigenvalue. First eight eigen disks are shown in the Fig.3

Figure 3. First eight eigen disks obtained by applying PCA to the training set.

The L x L sub-image new is obtained by cropping an L x L square with the center pixel (x, y). To project the sub-image Tnew to disk space, the mean image 'IjJ should be subtracted:

cPnew - 'IjJ. The sub-image new is projected against the disk space by the following transformation:

Wk = uI cPnew k = 1, 2, .... M (6)

Where Wl,W2,W3, ... Wn are n new disk spaces and n is a number of selected dominant Eigen vectors. A pre-processed image is reconstructed by using its disk spaces and Eigen disks of the training set using equation:

n cPr = LWkUk

k=l (7)

Where cPr is a reconstructed image and n is the number of dominant Eigen disks. The distance between the original image and its projection (reconstruction) onto the disk space is calculated to measure the likeness of optic disk. The point with the acceptably small distance indicates the existence of optic disk. The Euclidian distance E at pixel (x, y) is calculated as:

Cnew = IlcPnews - cPrll (8)

The pixel with the smallest Cnew in the retinal image is located as the center of optic disk.

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B. Methodology for Automated Segmentation of the OD Boundary

The detection of accurate boundary of the optic disc is important for the detection and diagnosis of Glaucoma where the variation in the shape and size of the optic disk is used to detect and measure the severity of disease. Difficulty in finding the optic disc boundary is due to its highly variable appearance in retinal images. The method proposed in this paper is performed on an RGB sub-image of the original retinography. By this way, robustness and efficiency in OD segmentation are increased as it reduces the search space and decreases the number of artifacts and distractors present in the whole image. So, as a first step, a 400 * 400 RGB sub­image is extracted centered on an OD pixel provided by the OD location methodology previously presented FigA

(a) (b)

(c) (d)

Figure 4. Optic disc location in the retinal image.(a)Input image.(b)Threshold image.(c) Localized optic disc.(d)Enlarged optic disc area.

1) elimination of blood vessels: The optic disc region is usually split into multiple sub regions by blood vessels that have similar gradient values. Hence it cannot be directly segmented. A mean filter for smoothing is employed to remove the blood vessels to create a fairly constant region before applying a RSF method. The closing of an image is defined as dilation followed by erosion and it removes small dark details. The definitions for dilation (Id) and erosion (Ie) in the proposed simple colour morphology domain are defined by Eqn.(9) and Eqn.(lO).

(I ffi S) (x, y) = maXj,k [1 (x - j, y - k) + S (j, k)] (9)

(I8 S) (x, y) = minj,k [I(x + j, Y + k) - S (j, k)] (10)

Fig.5 illustrates the gray scale morphology closing result on retinal image. Dilation operation is done remove the blood vessels and then an erosion is done to restore the boundaries to their former position.

(a) (b) (c)

Figure 5. (a) sub-image extracted from original.(b)sub-image extracted from the green channel.( c) Vessel elimination and smoothing

2) Boundary Detection: In order to handle intensity in­homogeneity within the active contour framework, in [12] recently proposed a novel region-based active contour model in a variational level set formulation. Given a gray level image I : n c R2 -7 R, let C be a closed contour in the image domain n, which separates n into two regions: n1 = inside( C) and n2 = outside( C) For a given point x E n, the energy functional they tried to minimize is [12]:

2 c(C,h (x) ,h (X))=L Ai J

i=l (11)

[r K(J(x - y) 1 I(y) - fi(X) 12 dy]dx + viC 1 Jn1

Where Al and A2 are positive constants (fixed usually as 1), and h(x) and h(x) are two values that approximate locally the image intensities in n1 and n2, respectively. The aim of the kernel function K(J is to put heavier weights on points y which are close to the center point x. For simplicity, a Gaussian kernel with a scale parameter (J > 0 was used:

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c�(¢, h (x), h(x)) = t Ai J K(J(x - y)II(y)-i=l (14)

fi(X)12 Mt'(¢(y))dy

Is the region-scalable fitting energy, Mf(¢) = Hc(¢) and M2(¢) = 1 - HE(¢)' Hcis a smooth function approximating the Heaviside function H which is defined by:

1 2 X HE(X) = - [1 + -arctan( -)] 2 7r E

(15)

In order to preserve the regularity of the level function , they used a level set regularization term [17]

(16)

Therefore, the energy functional they proposed to minimize is :

F(¢, h, h) = CE(¢' h, h) + J-lp(¢) (17)

Where J-l is a positive constant. To minimize this energy functional, the standard gradient

descent method is used. By calculus of variations, for a fixed level set function ¢, the optimal functions h(x), h(x» that minimize F( ¢, h, 12 are obtained by:

f,(x) = K(J * [M1(¢(x))I(x)] o K(J(x) * Mt(¢(x)) , i = 1, 2. (18)

For fixed hand 12, the level set function ¢ that minimizes

(12) F( ¢, h, h) can be obtained by solving the following gradient flow equation:

As in level set methods [13], the contour C c n is represented by the zero level set of a level set function c.p : n -7 R.Thus, the energy c in Eqn.(11) can be written as:

Where

CE(¢' h, h) = J c�(¢, h(x), h(x))dx+

v J 1 \l HE(¢(X)) 1 dx, (13)

where OE is the derivative of HE' and ei (i defined as:

(19)

lor 2) is

ei = J K(J(Y - x) 1 I(x) - fi(Y) 12 dy, i = 1, 2. (20)

II. EXPERIMENTAL RESULTS

PCA method is applied to each pixel in the largest cluster of brightest pixels of the input retinal image. The pixel with the minimum distance E in all the candidate regions and among is located as the center of optic disk. Compared with the location of optic disk as the centroid of the largest cluster of brightest pixels, the proposed algorithm achieves more accurate result. Illustration can be seen in Fig. 6

(a) (b) (c)

(d) (e) (f)

Figure 6. Comparison of the location of optic disk by PCA method with centroid of the largest cluster. 0 indicates the location of optic disk by PCA method and + presents the location by the centroid of the largest cluster of the brightest pixels.

The location of optic disk by centroid of largest cluster in some other images deviates to the bright side of optic disk, which can be shown in Fig. 6. The proposed method improves the precision of the automatic location of optic disk in the color retinal image. This allows the accuracy and robustness of locating the OD to be increased The result from this step is quite successful; the algorithm can locate the OD with 88.76 % accuracy compared with manual OD location from a test set of 89 images. The simulation tests were conducted on DIARETDB1 [18] databases. The fail outcomes resulted from poor image quality or very blurred and unclassifiable OD. Once the vascular structures are removed based on the gray scale morphological closing operation, the boundary detection operation is carried out. To fit active contour onto the optic disc the initial contour must be near to the desired boundary otherwise it can converge to the unwanted regions. In order to automatically position an initial contour, the approximate center of optic disc obtained in the localization method is used. The boundary thus detected is compared with the manually marked optic disc. Fig.7 shows the hand labeled optic disc boundary and automatically detected optic disc boundary overlapped on the ground truth image in different color.

Fig.7 indicate that the overlapping area between ground­truth OD segmentations and those obtained by RSF models is

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(e) (f)

Figure 7. Detected 00 is mapped to the original subimage (a) AutomaticaUy RSF detected boundaries (green colour) overlapped on corresponding hand labeled images. (b) Automatically ACM detected boundaries (green colour) overlapped on corresponding hand labeled images.

higher than those obtained by ACM. All optic disk pixels were set to white, and all non-optic disk pixels were set to black. The new image was saved as a ground truth which will be used for comparison. All the ODs which are automatically detected by our system are then compared with the hand-drawn ground truth. Sensitivity Sn and specificity Sp are used to evaluate the performance of the methods as follows:

(21)

Where Tp, Tn, Fp, and Fn are true pOSitiveS, true nega­tives, false positives, and false negatives, respectively. Total of 79 images were considered from the database. Ten images were not considered as the OD center was not detected properly due to the poor image quality. The overall sensitivity of 90.33%, specificity of 99.77% is achieved and 95.05% average accuracy in localizing the optic disc boundary.

III. CONCLUSION

Two methodologies for automatic OD exploration have been presented in this paper: one to locate the OD based on a PCA and another one to segment its boundary based on RSF. The PCA was used to get a rough location of the OD, and the initial contour was placed closely to the center

of the optic disk. A data fitting energy is defined in terms of a contour and two fitting functions; that approximate the image intensities on the two sides of the contour. This energy is then incorporated into a variational level set formulation, from which a curve evolution equation is derived for energy minimization. We evaluate our method using 89 images of healthy retinas and diseased retinas; we achieved 89% correct detection and 95.05% average accuracy in localizing the optic disc boundary.

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