To create a representation of the vessel structure at the population level, VBFL requires a large training set of healthy images where fovea position can be clearly identified. Here, we used the REFUGE data set
30 as the training set, referred to as
Dtrain. It contains 840 healthy eye fundus images with a manually annotated fovea location and optic disk position. As a preliminary step, we extracted a vessel information map
vi for each single image
ui. To do so, we used the recent retinal vessel segmentation network SA-UNet,
23 a convolutional neural network designed for biomedical image segmentation. We used the weights provided by the authors, pretrained on the DRIVE data set.
31 REFUGE and DRIVE images were acquired with different fundus cameras, all with a field of view of 45 degrees. The REFUGE data set was collected with both a Zeiss Visucam 500 (resolution 2124 × 2056 pixels) and a Canon CR-2 (resolution 1634 × 1634 pixels). DRIVE images were taken with a Canon CR5 NM (resolution 768 × 584 pixels). To follow SA-UNet requirements, all images were resized to 592 × 592 pixels before they were fed to the network. This method outputs a binary map
v(
x,
y) indicating the presence or not of a vessel at each pixel (
x,
y) of the fundus image, so that
v (
x,
y) = 1 if (
x,
y) belongs to a vessel, and
v (
x,
y) = 0 otherwise. Aggregating these individual vessel maps
vi, we estimated two distribution representations: a vessel density map and a vessel direction map. The vessel density map (
\(\bar V\)) aims at giving, for each position (
x,
y), the likelihood to have a vessel passing through. The whole process is illustrated in
Figure 2 - step 1 and detailed in
Appendix A1. The vessel direction map (
\(\bar D\)) aims at giving, for each pixel (
x,
y), the most likely direction of a vessel between 0 and π. Details of its calculation are provided in the
Appendix A2. The resulting direction
\(\bar D\) map is shown in
Figure 2 (step 1), where, for each pixel (
x,
y), the main direction is represented with a color code, with tensors being represented as ellipses. Note that because small vessels show great variability, they make a relatively small contribution to the vessel maps, as opposed to the larger vessels that exhibit more reproducible structure. For that reason, our approach is essentially guided by the large vessels distribution whereas small vessels show little to no impact.