# Topology-Aware Retinal Artery-Vein Classification via Deep Vascular Connectivity Prediction
## 3 Results and Discussion
### Evaluation Details  
In order to train the auxiliary tasks of the connectivity classification network as classification tasks, we quantized the calculated thickness and orientation values. For the thickness, we made five classes using quantization boundaries of [1; 5; 3; 5; 7]. For the orientation task, every pixel was classified into one of seven classes, including six classes evenly dividing the range of \([-\pi/2,\pi/2)\) and one background class.  
To cope with the increased problem complexity compared to the binary vessel segmentation, which was an original task solved in [7], we changed the number of channels of multi-scale features from 16 to 32 for the thickness/orientation classification. We used two fc layers, one layer before and after the Hadamard product, for the connectivity classification, and the number of units of the first fc layer was set to 256.  
Since the tasks of AV and thickness/orientation classifications are about the type and shape characteristics of vessels, we trained those networks using a pretrained network trained for the vessel segmentation. When training the multi-task network for binary vessel segmentation and AV classification, we used 1, 10, and \(10^{-3}\) for \(\lambda_{segm}\), \(\lambda_{av}\), and the learning rate on the DRIVE set, and 0.01, 1, and \(10^{-2}\) on the IOSTAR set. As for the training of the connectivity classification network, we use a two-step training scheme. We firstly trained the network only using the auxiliary tasks, and then trained the whole network. Thus, we used \(\lambda_{conn}=0\) in the first step. In the second step, we used 100/10 for \(\lambda_{conn}\) and \(10^{-4}/10^{-6}\) for the learning rate on the DRIVE/IOSTAR sets, respectively. \(\lambda_{thick}\) and \(\lambda_{ori}\) were always fixed to 1. We used the learning rate value of \(10^{-6}\) for the optic disc segmentation network. We used an Adam optimizer [21] to train all the networks.  
The types of data augmentation used for training each network are summarized in Table 1. A local contrast enhancement using a high-pass filter was applied to an input image for all the networks in the DRIVE set, while it was applied only for the connectivity classification network in the IOSTAR set. We used a threshold of 0.5 for the connectivity probability for all datasets.  
To evaluate the proposed AV classification method, we adopted the three metrics--sensitivity, specificity, and accuracy--used in [10]. The sensitivity and specificity are defined by:  
\[sensitivity=\frac{tp}{tp+fn},\;specificity=\frac{tn}{tn+fp}, \tag{6}\]  
where \(tp\), \(tn\), \(fp\), and \(fn\) are the true positives, true negatives, false positives, and false negatives, respectively. Here, arteries and veins are regarded as positives and negatives, respectively. The accuracy is defined as the mean of the sensitivity and the specificity.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Network** & **Dataset** & **Horizontal flip** & **Rot.** & **Scale** & **Elastic deform.** & **Crop** & **Brightness** & **Contrast** \\ \hline \multirow{3}{*}{(**a**)} & DRIVE & Y & Y & Y & N & N & N & N \\  & IOSTAR & Y & Y & Y & N & N & N & N \\ \hline \multirow{3}{*}{(**b**)} & DRIVE & Y & Y & N & Y & Y & N & N \\  & IOSTAR & Y & Y & N & N & Y & N & N \\ \hline \multirow{3}{*}{(**c**)} & DRIVE & Y & Y & Y & N & N & N & Y \\  & IOSTAR & Y & Y & N & N & N & N & Y \\ \hline \hline \end{tabular}
\end{table}
Table 1: Data augmentation used for training the networks, each of which is for (**a**) optic disc segmentation, (**b**) binary vessel segmentation and AV classification, and (**c**) vascular connectivity classification. Horizontal flipping, rotation (rot.), scaling, elastic deformation, cropping, random brightness, and contrast adjustment are selectively applied according to the task and the dataset.