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(a) The distance image of the inverted approximation

(b) The marker image (here superposed to the green channel of the original image)

Figure 7.17: A marker for vessel detection.

(a) The watershed line and the catchment basins

(b) The application of the contrast criterion

(a) The watershed line and the catchment basins

(b) The application of the contrast criterion

Figure 7.18: The watershed line and the result of the application of the contrast criterion.

in the original image may produce a lot of spurious objects in the approximation image. As a consequence, there are more markers than necessary, but the number of minima has been significantly reduced, and the watershed line can now be determined:

Evaluation of the local contrast: The result of the watershed transformation is shown in Fig. 7.18(a). We note that on the one hand nearly all vessels coincide with a branch of the watershed line (WSL), but on the other hand, not all the branches correspond to vessels. Indeed, the high number of false positives (i.e., parts of the WSL that do not correspond to vessels) is a consequence of the fact that the WSL delimits the catchment basins. Hence, if a region is not completely enclosed by vessels, there is necessarily a branch of the WSL that does not correspond to a vessels. The nonideal marker adds even more false positives, for we do not have exactly one marker per entirely or partially enclosed region.

In order to remove these false positives, we have to analyze the WSL. We distinguish

• bifurcation points (BIF): all points of the WSL that have more than two neighbors.

• branches: all connected components of WSL\BIF(WSL). We call Fij the branch being the frontier between the two catchment basins CBj and CBj.

Figure 7.19: Two catchment basins BVi and BVj and the frontier Fit j between them.

In the top-hat image, vessels appear brighter than the background (brighter than the adjacent regions) and changes in gray-level on the vessels are slow. Let us now consider two catchment basins CBi and CB j and the frontier F^ j between them (see also Fig. 7.19). If F^j corresponds to a vessel, the mean gray-level value of the top-hat image on Fi, j must by higher than the mean gray level on the two catchment basins. Let ftp be the top-hat image and #A the number of pixels of the set A. We can then write the first criterion c1:

Evaluating the contrast criterion c1, all the false branches not coinciding with a dark detail extracted by the top-hat are removed. However, the result is not yet satisfying, because there are still false positives that are due to some small, not connected dark details like hemorrhages close to vessels producing also a quite high value for c1. In order to remove these false positives from the segmentation result, we have to take into consideration the local gray-level variation on the branch:

with a a weighting coefficient. With this enhanced contrast criterion, it is quite simple to distinguish between vessels and false positives:

The result V is shown in Fig. 7.18(b). We see that there are still small false positives. In fact, they are so small that the criterion c2 has no meaning. Therefore, we remove all the connected components of V that contain less than X pixels (we chose X = 30):

With this technique, we obtain very satisfying results, if the images do not contain larger exudates that have not been removed by the prefiltering step. Indeed, the spaces between exudates form small channels that are quite similar to vessels. One possibility is to calculate the mean gray level for the branches in the shade corrected image SCnorm and to use it as a complementary information: Only if the mean gray level is lower than a certain threshold, the branch is accepted. In this way, many false positives dues to exudates can be removed. Results

The algorithm has been tested on sixty 640 x 480 fundus photographs 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. We asked an ophthalmologist to mark false detections and missed vessels on the result (a posteriori evaluation). We obtained a sensitivity of 83% and a predictive value of 97% an example is shown in Fig. 7.20.

(a) Original image (containing exu- (b) Segmentation result dates)

Figure 7.20: A result of the vessel detection algorithm.

(a) Original image (containing exu- (b) Segmentation result dates)

Figure 7.20: A result of the vessel detection algorithm.

This kind of evaluation is certainly not the best method, as the expert is influenced by the result of the algorithm. However, vessels are clearly visible and an expert will always be able to mark them; the same holds for false positives. Over and about that, if an expert marks all vessels, it is far from being sure that he will not miss some of them, because this is a boring and time-consuming task.

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