Kluwer - Handbook of Biomedical Image Analysis Vol

the better the contrast is, the higher the threshold can be chosen. On the other hand, the higher the amount of noise is, the higher the threshold must be chosen.

However, some “fix” information must be incorporated by using lower and

The candidate regions are determined by a double threshold technique (see [6] for details). This technique allows one to apply a lower threshold without accepting a higher number of candidates:

=

This improvement in the determination of the candidate region is important, because the features that are calculated for the candidates depend a lot on this region, as we will see in the following paragraph.

Elimination of the candidates situated on the vessels: Before calculating the features, we can exclude all candidates situated on the vascular tree. As we have seen, a top-hat transformation associated to a morphological closing extracts all dark details that cannot contain the structuring element, i.e., all “holes” and all “ditches,” and as a consequence all microaneurysms and all vessels. Comparing the morphological top-hat transformation with the one associated to the diameter closing of the same size, we can identify the false candidates situated on vessels and hemorrhages: For candidates not situated on vessels, we can

assume that the values of the two top-hat images are approximately the same:

2 3 2 3

( p) (x) ≈ ϑφλ◦ ( p) (x) (7.39)

This is not the case for candidates situated on the vessels. We can write the modified candidate image C A as

C A = #x C A | 2ϑφ(sB) ( p)3 (x) ≤ 2 · 2ϑφλ◦ ( p)3 (x)$ (7.40)

Candidates situated on the optic disk can be easily removed using the segmentation result from section 7.5.2.

Figure 7.31: Two types of false positives that can be identified using the mean value of the prefiltered image on the external gradient of the candidate.

between the mean value on the external gradient of the candidate region

The color: We have already seen in the section 5.2 that the green channel contains the most important information about blood-containing elements in the retina and this is why it is used for the detection of microaneurysms. However, there is also some information in the red, and sometimes in the blue channel. We have studied a lot of color features; the most efficient are the following two:

1.Color Contrast in the Luv color space: In the Luv color space, the euclidean distance can be seen as the “true” distance, i.e. the perceptible distance. We used, therefore, the euclidean distance between the color on the candidate region and the color on its external gradient:

2.Contrast of the principal components of the red and the blue channel: In order to find color information complementary to 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.

contours of the exudates. This algorithm has been published and discussed in [18]; 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

In order to spare computational time, e2 is not calculated for every pixel; it is calculated for a subsampled version of e1. Then e2 is found by interpolation.

Applying a fix threshold on the image e2 at gray level α1, we obtain all regions with a standard variation larger than or equal to α1. 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 Bo f [6]. 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 α1 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.

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 α1 and α2. The choice of the size of W is not crucial, and we have found good results for a window size of 10 × 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 α1 determines the minimal variation value within the window that is suspected to be a result of the presence of exudates. If α1 is chosen too low, the number of false positives increases, if it is set too high, sensitivity decreases. The parameter α2 is a contrast parameter: It determines the minimal value a candidate must differ from its surrounding background to be classified as an exudate.

7.6.2.5 Results

We have tested the algorithm on an image data base of 30 digital images 640 × 480 taken with a Sony color video 3CCD camera on a Topcon TRC 50 IA retinograph. These images have not been used for the development of the algorithm. Fifteen of these images did not contain exudates, and in 13 of these 15 no exudates were found by our algorithm. In two images, few false positives were found (less than 20 pixels).

We asked an ophthalmologist to mark the exudates in the 15 images and compared the results obtained by the algorithm to his. The comparison was done pixel-wise (with 1 pixel tolerance), and as for exudates, the number cannot be determined; it is the surface and the position rather than the number which can be used for diagnostic purposes.

We obtained a mean sensitivity of 92.8% and a predictive value of 92.4%. In Fig. 7.35, an example for the automatic detection of exudates is shown (see also Figs. 7.36 and 7.37).

Figure 7.35: The result of exudates detection.

Figure 7.36: (a) A detail of the green channel of a color image containing exudates. (b) The segmentation result.

Figure 7.37: (a) A detail of the green channel of a color image containing exudates. (b) The segmentation result.