Automated Segmentation of Optic Disc and Cup in Color Fundus Images

Pre-processing

The input RGB image is resized by factor 0.2 while keeping the aspect ratio as that of original image. The green channel is selected for processing as red channel is more saturated and blue channel has low contrast. The Mathematical morphology in image processing is utilized which is a non-linear methodology that is suitable for analyzing shapes in the image. A closing operation is performed on the resized green channel image using Structuring Element (SE) followed by an opening operation. The closing operation performs dilation followed by erosion while opening operation performs erosion followed by dilation. The formulations for implementing dilation and erosion are as follows in equation 1 and 2. Dilation: C(x,y)= Maximum {A(x-i,y-j) * B(i,j)} (1) Erosion: C(x,y)= Minimum {A(x-i,y-j) * B(i,j)} (2) Where A(x,y) is the input image and C(x,y) is the resulting image obtained after A(x,y) has been processed with a m*n template B(i,j). B is called the structuring element where

0 ≤ i ≤ m-1, 0 ≤ j ≤ n-1 The closing operation with octagonal SE of size 6 pixels is performed in order to fill the vessels in which dilation removes blood vessels and then erosion restores the boundaries. The size of SE is selected such that it keeps actual OD edge and removes all vascular structures on OD region. After performing the closing operation, an opening is performed to remove large picks. The image reconstruction is then performed on an opened image as shown in Figure 3a. The approximate OD center is obtained after thresholding the reconstructed image as shown in Figure 3b and 3c.

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Circular Hough Transform

The hough transform is used for finding any shape which can be represented by a set of parameters. A circle can be transformed into a set of three parameters, representing its center and radius, so that the Hough space becomes three dimensional. A circular shape is described by parametric equation as defined in equation 3.

$$ (\mathrm {x} - \mathrm {p}) 2 + (\mathrm {y} - \mathrm {q}) 2 = \mathrm {z} 2 (3) $$ Where (p,q) is center of circle of radius z that passes through (x,y). The following steps are involved in procedure: 1) An accumulator space is created first which is made up of a cell for each pixel, initially setting all of these values to zero. 2) For every edge point in image (x,y),all cells are incremented, according to the above equation which could be center of circle. These cells are represented by ‘p’ in above equation. 3) All possible values of ‘q’ are found for all possible values of ‘p’ found in previous step. 4) The cells having the highest probability of being the location of the required circle are searched. These are those cells whose value is greater than its neighborhood cells.

An Accumulator space has peaks where circles obtained from each edge point overlap at centers of any circles detected. The maximum accumulator value is then found out which corresponds to radius that matches the OD and corresponding center is detected as OD center. The intermediate steps output is shown in Figure 4 (a-e) for OD localization.

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OD Segmentation using Watershed Transformation

The image is considered as topographic surface where the altitudes are the gray level of the image is considered in the watershed transformation. The region edges correspond to high watersheds and low gradient regions correspond to catchment basins which are homogeneous. The watersheds are defined as the lines separating these catchment basins, which belong to different minima. The regions that the watershed separates are called catchment basins.

The watershed lines represent the boundaries of the objects if each local minimum corresponds to an object of interest under consideration. The watershed may results into many small regions when it infers catchment basins from gradient of the image. To avoid this condition, we used marker controlled watershed transformation in the presented approach. Here two markers are defined- (a) Internal marker, and (b) External marker. The catchment basins are generated by these markers in final segmentation.

In the presented approach, internal marker is selected as a circle having its center and radius is at center and 0.92 times that of radius obtained using circular Hough transform respectively as shown in Figure 5a. While external marker is selected as a circle as shown in Figure 5b with same point as a center as that of internal marker and having radius 1.2 times that of radius obtained using circular Hough transform so that it covers foreground region.

The factor is selected as 1.2 to maintain the distance between two markers. The Gradient of the image is calculated as the input to watershed transformation. We have used gradient magnitude as segmentation function. The Watershed of imposed markers with gradient of image provides the contour of the OD.

The OC segmentation is performed using morphology and watershed transformation. The marker controlled watershed transformation is applied to filtered image to segment OC. As grey level variation is very high in cup area, it is first removed by morphological closing. Then watershed transformation is applied to morphological gradient as shown in Figure 5g of median filtered image by considering locus of OC, k(m,n) that has been calculated as internal marker and square containing OC as external marker centered at (m,n) followed by imposed markers on gradient image produces cup boundary as shown in Figure 5h. The cup to disc ratio (CDR) is also calculated to detect glaucoma.

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Figure 5: Optic disc (OD) and Optic cup (OC) segmentation: (a) internal marker for OD segmentation as circle considering OD center obtained using CHT in previous step as center and radius as 0.92* Q (Q as radius obtained using CHT), (b) external marker for OD segmentation as circle considering CHT processed center and radius as 1.2*Q, (c) marker controlled watershed transformed image which superimposes internal and external markers on gradient (sobel operated gradient) of original image, (d)OD boundary (watershed line), (e) Reconstructed image (reconstruction by dilation) for OC segmentation, (f) median filtered image, (g) morphological gradient of median filtered image, and (h) final segmented result of OD and OC (OC segmentation using marker controlled watershed transformation).