(d) The gradient image with the superposed marker

(b) The biggest particle of the threshed image

(c) The distance function of the particle

(e) The result of the watershed algorithm

(f) The segmentation result

(e) The result of the watershed algorithm

(f) The segmentation result

Figure 7.22: The steps of the algorithm for the detection of the contours.

gray-level saturation Sa

This measure determines the percentage of pixels in the subimage whose gray level is larger than tmax(fr) — a. If this percentage is too high, the channel is saturated and does not contain any exploitable information. We use the red channel, if for a = 30, Sa < 0.5 (this has been found experimentally), if not, the luminance channel is used. We call the used channel fc in the following.

For finding the contours of the optic disk, we shall make use of the watershed transformation applied to the gradient image of a filtered version of the channel fc (see also Fig. 7.22).

3 The gray-level saturation Sa should not be confounded with the color saturation.

First, we attenuate the noise in the image using a Gaussian filter G (type and parameters of the filter are not crucial, we used a 9 x 9 filter with a = 4). Then, the vessels interrupting the circular shape of the optic disk are filled using a morphological closing:

with s1 such that the largest vessels are filled (as explained in the previous section). In order to remove irregularities within the papillary regions that may also produce a high-gradient value, we apply an opening by reconstruction:

s2 = 15 has been found to be a good value for 640 x 480 images. This is a big opening, but thanks to the reconstruction, the contours of p1 are preserved.

Then, the morphological gradient is calculated:

Calculating the watershed transformation of this gradient would lead to a strongly oversegmented result. Once again, we have to find a marker and impose it (see section 7.3). With only one source within the optic disk, the algorithm gives exactly one catchment basin which—if the filtering process has been efficient— coincides exactly with the optic disk. We use the approximated center c as "inner marker." As external marker, we use a circle centered in c with a diameter larger than two times the largest possible diameter of the papilla (factor 2 for the case that the approximation was bad and the approximation of the center c lies on the border of the optic disk).

With this marker, we can now calculate the watershed transformation: Results

The algorithm has been tested on 60 color fundus photographs (640 x 480) taken with a Sony color video 3CCD camera on a Topcon TRC 50 IA

(a) The optic disk in a color (b) Segmentation result image

Figure 7.23: Detection of the optic disk.

retinograph. These images have not been used for the development of the algorithm.

The optic disk has been localized correctly in 57 of these 60 images. In 3 of these 60 images, there were very large accumulations of exudates which inhibited a correct localization of the optic disk. The accuracy of the detection of the contours has been assessed qualitatively by a human grader; there were 48 images, for which the segmentation result was satisfying, with no or few pixels missed or falsely detected (e.g. see Fig. 7.23). In eight images, there were some parts missing due to very poor contrast of the original images, but the result contained still more than 75% of the optic disk. In one image, the result was not satisfying, once again due to low contrast: Indeed the contour was hardly visible, even for a human.

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