# Deep Learning-Based Automatic Segmentation of Mandible and Maxilla in Multi-Center CT Images
## 2 Materials and Methods
### Framework and Network Architectures  
The overall framework and detailed architectures of neural networks are displayed in Figure 4. Preprocessed CT scans are input to the neural network as 2.5D, which outputs one segmentation mask map for each target slice. This process was repeated for all slices in each patient scan. Afterwards, the segmented volume for each patient was post-processed.  
For the neural network, we applied a hierarchical, parallel, and multi-scale residual (HPMR) block [47] to U-Net to enhance the data compatibility of the CNN model. This block was first designed to enhance the performance of a CNN for landmark localization with limited computational resources. The starting point of the architecture is a residual bottleneck block [39] that enables the stable optimization of a deeper model by assisting the propagation of information both forward and backward, improving performance. The other basis for the architecture is the inception block [48], which concatenates features from parallel paths with different receptive field sizes. Compared to the inception residual block, the HPMR block has a smaller number of parameters with the advantage of a parallel path. Compared to the existing research, we combined HPMR block to U-Net and showed its performance on the segmentation task. We used HPMR block for efficient learning to utilize advances of residual bottleneck block and parallel path with the lower number of parameters compared to using inception blocks.  
We compared U-Net with HPMR blocks (HPMR-U-Net) to its base component architecture, U-Net, and U-Net with residual blocks (Res-U-Net) to verify the effects of HPMR blocks. Additionally, modified U-Net (mU-Net) [49] was selected as another state-of-the-art segmentation CNN model for comparison because it requires minimum increase of network parameters. Its residual block is composed of deconvolution and activation operations to pass features to the skip connection of the U-Net adaptively with the object size. mU-Net is designed not only to extract high-level features of large object edges, but also high-level global features of small objects. We hypothesized that the increase in the complexity of model, i.e., the increased number of parameters in the neural network, would hinder the data compatibility of the model. It is well known that overfitting, which impedes the data compatibility of a model, occurs when the number of parameters increases [50].  
Figure 3: Examples of noises caused by surgical plates, orthodontic device, and dental implants in CenterB dataset, which make it more challenging to delineate the CT images.  
Therefore, we chose a simpler neural network with lower number of parameters than other state-of-the-art neural networks for comparison.  
All networks were trained using PyTorch framework in Python under the same conditions for comparison. They were trained with a batch size of 10 for 30 epochs. We employed cross entropy loss as a loss function and Adam optimization with a learning rate of \(10^{-5}\). Training and evaluation were performed on the computer hardware resources of a Nvidia GeForce RTX 3090 with 24 GB memory and 16 of DIMM DDR4 Synchronous 2666 MHz with 32 GiB in a Linux environment.