# Coronary Centerline Extraction from CCTA Using 3D-UNet
## 4 Experimental Results and Discussion
### Results  
The classical notation of epoch, in which epoch means one pass over the entire training dataset, will no longer apply when working with randomly cut patches. The term epoch is defined here by multiplying the number of volumes in the training set with the largest input volume size divided on each axis with the corresponding patch size, with the result divided by the batch size. As an example, for a patch size 256 \(\times\) 256 \(\times\) 128, a maximum size of an input volume of 512 \(\times\) 512 \(\times\) 388, and a batch size of 2, the number of input patches considered to be an epoch is \(7\times(512/256)\times(512/256)\times(388/128)/2=7\times 2\times 2\times 3/2=42\)This formula was used as a rough approximation of feeding the entire volumes once through the network. Due to this definition, the results are reported for different epochs given various input patch sizes. For the training dataset, the values for one epoch are computed as the average across all the input patches. For the validation dataset, the values for one epoch are computed by assembling the whole volume from the output patches and comparing it with the whole ground truth.  
The overlap and accuracy measures on the validation data are presented in Table 2. Overlap is defined as the percentage of voxels correctly detected as part of the centerline (analogous to recall), with Equation (11). Accuracy is defined as the percentage of voxels segmented as in the ground truth.  
\[accuracy=\frac{TP+TN}{TP+TN+FP+FN} \tag{12}\]  
Since the ground truth is presented as sparse centerlines, meaning that only a subset of the coronary vessel tree is annotated, the results cannot be presented using the F1 score or Jaccard index. The number of \"false positives\" detected by the network will skew the results heavily. Instead, the results are presented in the form of a pair of binary accuracy and overlap (inspired by the results published in [17]). The graphs provided also include the value of the loss function to demonstrate that the learning converges, as depicted in Figure 5 for one of the considered cases. Charts presenting the training and validation evolution for the other configurations can be found in Appendix A.  
Visual validation for the output volumes is provided, as shown in Figure 6. The ground truth centerline is depicted in red. The segmentation (after thinning) is seen in green, making it easier to check that the segmentation follows the centerline. Visual validation for other training configurations can be found in Figure A3.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Patch Size** & **Batch Size** & **Model Reduction** & **Patches with Ground Truth Only** & **Epoch** & **Overlap** & **Accuracy** \\ \hline \(128\times 128\times 96\) & 1 & 1 & true & 231 & 0.934 & 0.921 \\ \(128\times 128\times 128\) & 2 & 2 & true & 260 & 0.895 & 0.940 \\ \(256\times 256\times 128\) & 1 & 2 & true & 232 & 0.917 & 0.943 \\ \(256\times 256\times 128\) & 1 & 2 & false & 392 & 0.944 & 0.911 \\ \(320\times 320\times 64\) & 1 & 4 & false & 1250 & 0.883 & 0.953 \\ \(384\times 384\times 48\) & 1 & 4 & false & 1500 & 0.910 & 0.928 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The overlap and accuracy results for the selected hyperparameters.  
Figure 5: Patch size \(256\times 256\times 128\): (**a**) training only with ground truth patches and (**b**) validation.