The Detection of the Vascular Tree by Means of the Watershed Transformation

In this section, we present a method for the detection of the vascular tree in color images of the human retina. This algorithm is quite general; only few information specific for retinal images is used. It can therefore be used for the extraction of elongated features in other types of images. Motivation

Detecting the vascular tree is essential for the analysis of fundus images. The structure of the vascular tree gives useful information for other feature or lesion detection algorithms (e.g., optic disk, macula, hemorrhages). Over and above that, it delivers landmarks for image registration. Properties

Vessels are elongated features, much longer than, thick, reddish, and darker than the background. They enter the retina by the optic disk and go all over the retina forming the vascular tree.2 With increasing distance from the optic disk, the vessels become thinner and their contrast decreases. Contrast and color of vessels vary considerably from one image to another. Even in the same image, there may be color differences, as color depends on the vessel type (artery or vein), its diameter (the amount of hemoglobin that is transported), and the illumination of the retinal region where the vessel is situated.

The width of the thickest vessels is almost constant for all images taken with the same angle and the same resolution; we can state that all vascular structures in fundus images are thinner than a parameter X (which depends on resolution and angle of the image).

As we have seen in section 7.2, vessels appear best contrasted in the green channel fg of the color images; our algorithm for vessel detection is exclusively based on the use of this channel. The main difficulties we have to deal with are as follows:

• Often, retinal images are low contrasted and corrupted by noise. As a consequence, vessel contours are not well defined, and not all vessel pixels have a lower gray level than all the background pixels. However, the mean gray level on the vessel is lower than the mean gray level on the background (see also Fig. 7.12(a)).

• The vascular tree may be interrupted by the presence of lesions (as shown in Fig. 7.12(b)) or noise.

• The presence of exudates is a source of false detections, as the spaces between exudates have sometimes properties similar to vessels in terms of luminosity, width, and connectivity (see Fig. 7.13(a)).

2 The vascular tree as it appears in color images, is not a "tree" in the topological sense, as veins and arteries usually cross each other. It is more like a "net" of piecewise linear structures.

(a) Two vessels corrupted by (b) A part of a vessel deconnected from the noise rest of the vascular tree by an exudate

Figure 7.12: Main problems in vessel detection.

• The presence of hemorrhages adds another source of false positives, as they have the same color. If they are connected to the vascular tree, they may be hard to distinguish from the vessels (see Fig. 7.13(b)). State of the Art

There is a large variety of algorithms for vessel detection in retinal images. In most of these algorithms, vessels are modeled like piecewise linear segments with a Gaussian profile. Using linear or morphological filtering, features with this property are enhanced, other features are attenuated. This strategy has been proposed by Chaudhuri in [10] (linear filters) and by Zana in [11] (morphological filters). Drawbacks of these methods are the computational complexity due to directional filtering and some systematic errors on the borders of bright features (like the optic disk or hard exudates).

(a) Hard exudates close to the vascular tree

(b) Hemorrhages close to vessels

Figure 7.13: Main reasons for false detections.

Tracking algorithms are the second important group of vessel detection methods. These algorithms use the connectivity of the vascular tree as a main property. This is, in many images, not acceptable, particularly if lesions are present (see the Fig. 7.13(a)). Hence, this kind of approach must rely on good markers; then, tracking algorithms can, in our opinion, be powerful in detecting the vessel borders, but they are not adapted to detect the vascular structure. The Algorithm

In this section, we present a new method for the detection of vessels in fundus images. The main idea is to detect thin structures in gray-scale images by evaluating the local contrast along watershed lines. This algorithm can also be applied to other problems where thin structures are to be found.

Prefiltering: As we can see in the Fig. 7.13(a), spaces between hard exudates are a systematic source of false positives for vessel detection algorithms. In order to remove small exudates, the prefiltered image p is calculated as follows:

with fg the green channel and y™ the area opening with the parameter X. The result of this prefiltering step is shown in Fig. 7.14(b). One may notice that this filter is not very restrictive, the borders of the different features present in the image are not altered, but the small exudates are removed.

Extraction of dark details: Vessels appear as dark features in the green channel of a color image, their maximal width is known and does not vary with the image (as far as the resolution is the same). As we have seen in section 7.3,

(a) The green channel (b) The prefiltered image

Figure 7.14: The prefiltering step: Small exudates are removed.

(a) The green channel (b) The prefiltered image

Figure 7.14: The prefiltering step: Small exudates are removed.

(a) The top-hat transformation of the (b) An approximation of the vascular prefiltered image tree

Figure 7.15: Top-hat transformation and approximation of the vascular tree.

(a) The top-hat transformation of the (b) An approximation of the vascular prefiltered image tree

Figure 7.15: Top-hat transformation and approximation of the vascular tree.

vessels can be removed from this image by means of the morphological closing with an appropriate size s1 (see also Fig. 7.6(c)). Calculating the difference to the original gives all the dark details that cannot contain the SE:

In the top-hat image tip (shown in Fig. 7.15(a)), vessels appear as bright features, elongated and connected. However, because of contrast differences between retinal images and between different vessels in one image, only a raw approximation of the vascular tree can be found by means of simple threshold techniques, as shown in Fig. 7.15(b). In our example, the vessels are obtained by an area threshold TK, proposed in [12]: The threshold is chosen in such a way that the resulting binary image contains at least K pixels.

Extraction of the crest lines: Considering the image shown in Fig. 7.15(a) as a topographic surface, we can notice that the vessels correspond to the crest lines in this image. An excellent tool for finding the crest lines in a gray-scale image has been presented in section 7.3: the watershed transformation. The strategy is to first find a good marker, then calculate the watershed transformation, and in the final step apply a contrast criterion in order to distinguish real vessels from false detection.

The usual technique to obtain a good segmentation result using the watershed transformation is to use markers (see section 7.3), i.e., the image is flooded only from "important" minima, the others are filled by means of the morphological reconstruction. Here, the markers must be chosen in such a way that the watershed line coincides with the vessels. It is, therefore, very important that

Figure 7.16: An ideal marker image (gray circles).

we mark all the "valleys" that are completely or partially surrounded by the crest lines. Such a marker is shown in the Fig. 7.16.

In order to obtain such a marker, we determine the points having maximal distance from the approximation shown in Fig. 7.15(b). In a first step, we fill the small "holes" of the thresholded image by a surface closing of small size, i.e., we remove all "holes" having less than 5 pixels, and then we invert the result and we determine the local maxima of the distance function:

The distance function is shown in Fig. 7.17(a), its maxima superposed to the original image in Fig. 7.17(b). Of course, the presence of dark noise and features

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