# Deep Learning-Based Automatic Segmentation of Mandible and Maxilla in Multi-Center CT Images
## 4 Discussion & Conclusions  
The four neural networks compared in this research exhibited similar performance in the CenterA dataset, which was the domain used for training. Among other neural networks, U-Net and Res-U-Net were considered for the comparison because U-Net is a basic component of HPMR-U-Net, in which showing a difference would represent that HPMR block is effective compared to other basic architectures. Additionally, mU-Net was selected for the comparison as a state-of-the-art neural network for segmentation. We chose comparably simple neural networks because we hypothesized that the data compatibility of the more complex model with larger number of parameters would be worse because of overfitting. CenterA dataset was set as the train dataset because it was MDCT datasets in which easier to make ground truths than CBCT. With training with a dataset easier to constitute, we aimed to show the performance for other institutional MDCTs and CBCTs. PDDCA and TCIA datasets were used for examples of MDCT and CenterB dataset for CBCT. For the external datasets of PDDCA, TCIA, and CenterB, HPMR-U-Net displayed significantly higher performance compared to the U-Net, Res-U-Net, and mU-Net models in both quantitative and qualitative evaluations. All networks produced comparable results for data from the same cohort of the training dataset; however, they exhibited different results for data from out of the training dataset cohort. While the performances of other networks were degraded in the external datasets, HPMR-U-Net produced segmentation of the mandible and maxilla similar to  
Figure 9: Color maps of surface distance from the ground truths to the output segmentations of the best dice coefficient case in the CenterA dataset for the mandible. The pieces of images on the right side are enlargement of mandibular foramen. the ground truths. From these results, HPMR-U-Net infers a high data compatibility for mandible and maxilla features in CT images. The assumed differences in the data cohorts were reflected in the results. For the PDDCA and TCIA datasets, the performance degraded significantly, and the mandible and maxilla were not classified accurately. This is due to their slice thickness being different from that of CenterA dataset, even though they are MDCT. The inter-slice information is important to classify a pixel in a slice as the mandible or maxilla. The results for CenterB dataset were the worst among the external datasets for all models. The segmentation of CenterB dataset is more challenging as it is CBCT, which is not only different from the in-house dataset, but also contains more noise. Additionally, CenterB dataset contains variances in anatomical structure caused by surgeries and noise from surgical plates, orthodontic device, and dental implants (Figure 3). It is remarkable that the score difference between HPMR-U-Net and other models is significant for CenterB. For CBCT, which is a different image protocol than MDCT that was used to train, there was a significant degradation of performance in other models, but minimal degradation in HPMR-U-Net. This demonstrates that HPMR-U-Net is more robust than other models to various data domains that may be different from the training data. We assume that one of the reasons for the better performance of HPMR-U-Net compared to Res-U-Net is the number of parameters. The higher the complexity of the hypothesis space of the deep neural network, the worse is the generalizability, according to the principle of Occam's razor [51]. The number of parameters in HPMR-U-Net is 12,042,179, which is smaller than Res-U-Net with 17,118,019, U-Net with 28,959,299, and mU-Net with 35,230,019. The HPMR block could efficiently decrease the overall number of parameters, which as a result could enhance the generalizability of the model while maintaining its segmentation performance. In future work, an attempt will be made to improve the performance in external datasets for actual clinical applications when the neural network is trained with only one data domain.