## 5 Discussion  
The inferior alveolar canal has always been a key topic in oral and maxillofacial surgery and several anatomical studies attempted to describe its course [16] accurately. The available literature analyses both the vertical and the horizontal canal path since the three-dimensional relationship with the surrounding structures is crucial in clinical practice [53; 54; 55]. Most of these topographic anatomical studies were performed on cadaver models [41]. However, improved imaging modalities have recently promoted radiological research. The growing diffusion of CBCT in common clinical practice explains the choice of this method for the present work. The experimental model we have applied might appear complex, but the data have been exploited in a different informative way. In fact, each test performed is independent and pursues specific objectives. We have proceeded to discuss the results one by one as reported below. As shown in Figure 4, the first experiment was composed of two different parts. In the first experiment, the CNN was trained in two distinct ways. In the former case, it was trained on a dataset of 68 CBCTs with sparse annotations subject to circular expansion. In the latter case, dense annotations based on the same number of CBCT volumes were used for CNN training. The IoU values obtained were 0.39 (sparse mode) and 0.56 (dense mode), while the Dice score values were 0.52 (sparse mode) and 0.67 (dense mode). Thus, an improvement of the scores of 44% and 29% were found, respectively. The substantial amelioration (IoU 0.39 vs. 0.52, and Dice Score 0.56 vs. 0.67) has to be related to the methodology applied. In fact, while in the experiment, 1A, a bidimensional annotation of the circularly expanded canal, was carried out; in the experiment 1B, a 3D voxel-based annotation system was used. The method with dense annotations ensures the elimination of IAC shape approximation biases, which instead characterizes experiments based on circular expansion. This is anatomically correct because the mandibular canal does not maintain a constant tubular shape and diameter, but it is rather subject to inter- and intra-individual variations along its path [16; 54; 56]. Exactly the same number of CBCT volumes were used in experiments 1A and 1B, and this must also be emphasized; the only differences relied on the type of annotations used. To conclude, the first experiment proves that dense-annotation based dataset is more accurate than the one based on the circular expansion technique only. In the second experiment, the training of the CNN was performed on two circularly expanded datasets. These differed only in the number of CBCT volumes: in the former case, only the secondary dataset was used (256 CBCT volumes), while in the latter test, the secondary dataset was combined with the primary training dataset provided with sparse annotations only (total of 324 CBCT volumes). Despite a substantial rise in the CNN training volumes used in the second scenario (26.6% enhancement), the results were actually pretty similar. In the first case, the IoU and Dice scores were 0.42 and 0.60, while values of 0.45 and 0.62 were obtained by combining the datasets, respectively. Although they represent a good starting point for researchers, the data produced using the circular expansion technique appear to be limited and unsatisfactory according to these results. The third and last experiment was divided in two different parts. In the former stage, the primary and secondary datasets were used together to train CNN resulting in an IoU score of 0.45 and a Dice score of 0.62. These results were not very satisfactory considering that these values are lower than those obtained in the first experiment. Moreover, in the experiment 1B, the overall dataset was smaller because only the primary dataset was used. We hypothesize a performance decrease due to the heterogeneity of the CNN training annotations used in experiment 3A.