## 4 Results
### Results of the Experiments
#### 4.3.2 Optimization of the Algorithm  
After the experiment 3B, we tried to further optimize the results obtained. In order to do that, we developed a novel label propagation technique. The deep expansion model is based on the same network used for segmentation, the main difference regards the input layer, which has been changed in order to accept a concatenation of both the raw volume data and the sparse annotations, rendered as a binary channel. This way, the network is allowed to exploit the information about the sparse 2D annotations to produce a 3D dense canal map, which is expected to be better than just using the raw volume as input. By applying this technique to the secondary dataset, we are able to generate a 3D dense annotation for all the patients that previously had only a sparse annotation, thus having a more informative dataset that can be used as a pretraining for the final task (i.e., segmenting  
Figure 5: Synthetic and schematic description of the division of the CBCT volumes to generate the different datasets used. the IAC by using as input only the raw volume). Moreover, a positional embedding patch was introduced in the algorithm. Since our sub-volumes have been extracted from the original scan following a fixed grid, we exploited positional information derived from the location of the top-left and bottom-right corners of the sub-volume. Exploiting positional information ensures two extremely important benefits:  
1. During training, the CNN is fed with implicit information about areas close to the edges of the scan where the IAN is very unlikely to be present. 2. Information about cut positions helps the network to better shape the output: sub-volumes located close to the mental foramen generally present a much thinner canal than those located in the mandibular foramen. These two adjustments granted more efficacy in the pre-training step and determined a further improvement of the results. The IoU score obtained was 0.64, while the Dice score reached 0.79. To summarize, the training of our network was divided in two phases: Deep Label Propagation, and IAC segmentation. They both used a modified version of UNet3D, where the only difference was the number of input channels. During the Deep Label Propagation, our model took the original 3D volume and the sparse annotation as input, and it was trained to output a 3D segmentation. This process allowed to generate a dense segmentation for all the volumes in our dataset that only have a sparse segmentation. We refer to this data as synthetic (or generated) data. By using exclusively this data (i.e., 3D annotations obtained from 2D ones), we trained the same model to accept only the plain CBCT volume (with no IAC-related information) as input and to output the dense segmentation. As a final step we fine-tuned this latter model with the ground-truth 3D labels. During both phases, we used a patch-based training. For example, sub-patches were extracted from the whole input, fed into the network, and aggregated back together. During the Deep Label Propagation, patches have a size of 120 \(\times\) 120 \(\times\) 120 and a batch size of 2. On the other hand, during the segmentation task, a patch size of 80 \(\times\) 80 \(\times\) 80 and batch size of 6 are employed. In both phases a learning rate of 0.1 with SGD as optimizer have been used for 100 epochs. The learning rate was decreased if no improvements in the evaluation were obtained. The results of the three experiments are summarized in Table 1.