# Comparison of Image Normalization Methods for Multi-Site Deep Learning
## 2 Methods
### Experiments  
Ground truth tumor segmentations were obtained from a radiologist with five years of experience manually delineating the tumor on T2-weighted pre-therapy MRIs. For treatment response, we used the Dworak regression grade [21]. This system rates the tumor response on a scale of 0 (no regression) to 4 (no remaining tumor cells) and is used on the resected tumor. Sex and age are given in the patient data.  
We trained one network for segmentation and another for classification and regression. We used a modified 2D U-Net [22] with batch normalization and residual connections for segmentation. Although published in 2015, U-Nets are still widely used for medical segmentation tasks [23]. As an architecture for classification and regression, we chose ResNet50 [24], which we used with random initialized weights. We only changed the last layer of ResNet to have the desired number of output neurons. We trained all networks for 100 epochs with 5-fold cross-validation. The three modalities (T2w, ADC and b800) were combined into a three-channel image, and we extracted 32 random patches per image. For segmentation, at least 40% of patches have their center inside the tumor volume. We augmented the patches by rotating them in-plane and uniformly scaling them.  
We trained the network in three different configurations:  
* All. In this configuration, we trained on all images from all centers and evaluated the network performance using cross-validation.
* Except-One. In the next experiment, we trained on all centers except one. We evaluated the performance of the training centers using cross-validation and evaluated the network of each fold on the remaining center.
* Single-Center. In the last configuration, we trained on one center only. Similarly to the Except-One experiment, we evaluated the performance on that center using cross-validation and applied all five networks to the other centers.  
We normalized the three modalities (T2w, ADC, b800) individually. The Perc, M-std and Win methods do not need to be trained, so we only normalized the whole data set once. For HM, Perc-HM and the deep learning method, we trained the methods for each experiment on the patients included in the training and validation set.  
As evaluation metrics, we used the Dice coefficient [25] of the tumor class for segmentation and the area under the receiver operator characteristic curve (AUC) for the prediction of sex and Dworak grade. A zero Dice indicates no overlap with the ground truth, and one indicates a perfect segmentation. For the AUC, a value of 0.5 is equal to pure chance and one means perfect prediction. In the case of several classes, we calculated the AUC by the average of the one-versus-others AUCs. We used the root mean square error (RMSE) for age prediction.  
After training the networks, we evaluated them on previously unseen images from the same center and unseen data from all other centers, using the network from the epoch  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Network** & \multicolumn{4}{c}{**Hyperparameters**} \\ \hline  & **Segmentation** & **Train Only** & **Initial** & **Skip Edges** \\  & **Loss** & **on Image** & **Normalization** & \\ \hline GAN-Def & No & No & Perc & Yes \\ GAN-Seg & Yes & No & Perc & Yes \\ GAN-Img & No & Yes & Perc & Yes \\ GAN-Win & No & No & Win & Yes \\ GAN-No-ed & No & No & Win & No \\ \hline \hline \end{tabular}
\end{table}
Table 1: Hyperparameters for the different GANs used for normalization. The first is the default (GAN-Def). For GAN-Seg, we added segmentation as an additional task to preserve the important details. GAN-Img uses all discriminators on the images and not on the latent space. We trained GAN-Win and GAN-No-ed on images with window normalization with and without propagated edge information.  
with the best performance in the validation set. We used a Student's \(t\) test to determine the significance of the mean differences. We consider a \(p\)-value of less than 0.05 significant.