## The Algorithm

Our algorithm can be subdivided into two parts: First, we find candidate regions, i.e. regions that possibly contain exudates. In a second step, we determine the Figure 7.33: (a) The luminance channel of a color image of the human retina. (b) The closing of the luminance channel. (c) The local standard variation in a sliding window. (d) Candidate region.

Figure 7.33: (a) The luminance channel of a color image of the human retina. (b) The closing of the luminance channel. (c) The local standard variation in a sliding window. (d) Candidate region.

contours of the exudates. This algorithm has been published and discussed in ; here in we give a sketch of it.

Finding the candidate regions: Regions containing exudates are characterized by a high contrast and a high gray-level. The problem that occurs, if we use the local contrast to determine regions that contain exudates, is that bright regions surrounded by dark vessels may also produce a high local contrast. As shown in the section 7.3, vessels can be removed by means of a morphological closing (see Fig. 7.33(b)):

On this image we calculate the local variation for each pixel x within a window W(x) (see Fig. 7.33(c)) centered in x:

In order to spare computational time, e2 is not calculated for every pixel; it is calculated for a subsampled version of e\. Then e2 is found by interpolation.

Applying a fix threshold on the image e2 at gray level a1, we obtain all regions with a standard variation larger than or equal to ai. However, bright objects larger than the window do produce only a high standard variation on its borders. In order to obtain the whole candidate regions, we fill the holes by reconstructing the image from its borders Bof . We also dilate the candidate region in order to ensure that there are background pixels next to exudates that are included in the candidate regions:

The threshold a1 is chosen favoring sensitivity to specificity: False positives can be identified later. Then, we remove a dilated version of the optic disk and we obtain the candidate regions:

Finding the contours: In order to find the contours of the exudates, we set all the candidate regions to 0 in the original image (see Fig. 7.34(a)): Figure 7.34: (a) The candidate regions set to 0 in the original image. (b) The morphological reconstruction.

Figure 7.34: (a) The candidate regions set to 0 in the original image. (b) The morphological reconstruction.

and then we calculate the morphological reconstruction by dilation of the resulting image under fg (see Fig. 7.34(b)). Exudates are now completely removed from the image, as they are completely comprised in the candidate regions. We can, therefore, calculate the difference to the original image and apply a fix threshold in order to obtain the final segmentation result:

This algorithm has three parameters: The size of the window W and the two thresholds a1 and a2. The choice of the size of W is not crucial, and we have found good results for a window size of 10 x 10. If the window size is very large, small isolated exudates are not detected. From a medical point of view, this is not really problematic. The first threshold a1 determines the minimal variation value within the window that is suspected to be a result of the presence of exudates. If a1 is chosen too low, the number of false positives increases, if it is set too high, sensitivity decreases. The parameter a2 is a contrast parameter: It determines the minimal value a candidate must differ from its surrounding background to be classified as an exudate.

0 0