3. Results

In order to test the method presented in this work, a demo has been designed and coded in MATLAB. This program has been run on a workstation equipped with an Intel Pentium B960 CPU at 2.20 GHz and 4GB of RAM processor. The reconstruction time takes into account the time required for image segmentation and fractal interpolation.

#### 3.1. Image segmentation

Figure 8 provides two examples of blood vessel skeletons; they are created from the retinal images shown in Figures 2 and 3. These images have been transformed to binary image using thresholding algorithm (Figure 8a and c). Then, the thinning technique is used to produce a blood vessel skeleton that preserves all geometric and topological features of these vessels (Figure 8b and d).

After performing the skeleton of the retinal vasculature, we use the proposed method for the detection and extraction of the feature points. Figure 9 illustrates an example for the detection of endpoints and bifurcation points. In these examples, the red pixels correspond to the endpoints, and the blue pixels correspond to the bifurcation points.

In addition, Table 1 presents some typical results of endpoints and bifurcation point detection for two test images (image from STARE database and image from

Figure 8.

(a) Result of the binary morphology for image 02\_h.jpg. (b) The resulting skeleton of the image 02\_h.jpg. (c) Result of the binary morphology for image im0139.vk.jpg. (d) The resulting skeleton of the image im0139.vk.jpg.

#### Figure 9.

Minutiae detection (the red pixels show the endpoints, and the blue pixels show the bifurcation points).


#### Table 1.

Detection of endpoints and bifurcation points for image from high-resolution image database (HRF) and image from STARE database.

HRF database). According to the results, we can see that the images from HRF database give a number of endpoints and bifurcation points higher than the images from the other used database; it is due to the image quality and the presence of a higher number of blood vessels in these images.
