# A Refined Approach to Segmenting and Quantifying Inter-Fracture Spaces in Facial Bone CT Imaging
## 3 Results
### Preprocessing and Training
#### 3.1.2 Training  
The dataset was initially divided into 80% (1410 cases) for training and validation and 20% (353 cases) for testing. The separate test set was set aside to ensure an unbiased evaluation of the final model performance. The training and validation set was further divided using a five-fold cross-validation method to enhance the model's reliability and minimize bias. In this process, the data were split into five equal subsets, each containing approximately 282 cases. During each iteration of cross-validation, four subsets were used for training, while the remaining one was used for validation. This approach allowed every data point to be used for both training and validation, enhancing the model's generalization capabilities and providing a more reliable performance estimate.  
For the final performance evaluation and extraction of the predicted mask, the model was trained on 1128 cases, with 282 cases used for validation. This final split ensured that the refined ground truth (GT) data could be effectively leveraged to optimize the segmentation performance.  
The training configuration was based on the 3d_fullres set-up, employing a patch size of [40; 224; 192] and utilizing the refined CT-normalized data. The nnU-Net v2 model processes full 3D CT volumes as input rather than relying on bounding boxes or predefined segmentation masks. Instead, it directly learns spatial relationships within a 3D scan through convolutional operations.  
The model architecture is built on the PlainConvUNet structure, consisting of six stages leveraging 3D convolution operations (\"torch.nn.Conv3d\") to capture spatial dependencies across the axial, coronal, and sagittal planes. Each stage of the network contains the following key components:  
* 3D Convolutions: The convolutional layers use kernel sizes of \([1,3,3]\) in the initial layers and \([3,3,3]\) in the deeper layers to extract hierarchical features from the input volumes.
* Downsampling and Upsampling: Strided convolutions for downsampling and transposed convolutions for upsampling enable efficient feature extraction and restoration of the spatial resolution.
* Normalization and Activation: Instance normalization (\"torch.nn.InstanceNorm3d\") is applied after each convolutional layer, followed by LeakyReLU activation to standardize feature distributions and introduce nonlinearity.
* Deep Supervision: nnU-Net v2 utilizes deep supervision by applying auxiliary loss functions at multiple stages to facilitate gradient flow and improve convergence, particularly for small and complex structures.  
Training was performed with a batch size of two, with the batch_dice setting enabled to optimize Dice loss computation across entire batches. Throughout the training process, the model demonstrated progressive improvements in segmentation accuracy, as evidenced by the incremental increase in the exponential moving average (EMA) pseudo-Dice score, which achieved a peak value of 0.1978.  
The output of the model is a binary segmentation mask, where each voxel is classified as either fracture or non-fracture. Post-processing techniques were applied to remove small artifacts and enhance segmentation precision. These results highlight the model's potential to provide accurate and reliable delineation of fracture spaces, which can aid in clinical decision making.  
The detailed performance of the trained model is shown in Table 1.