# A Multi-Channel Uncertainty-Aware Multi-Resolution Network for MR to CT Synthesis
## 3 Results
### Qualitative Evaluation
It can be observed that a significant correlation between uncertainty and error rate exists, suggesting that the model appropriately assigns a higher uncertainty to those regions that are challenging to predict. This correlation is likewise observed when comparing the maps of epistemic and heteroscedastic uncertainty with the corresponding error map, which is demonstrated in Figure 4. In areas around structure borders both epistemic and heteroscedastic uncertainties show large values, as expected. The borders between tissues are not sharp and there is, therefore, some ambiguity in these regions, which is mirrored by  
Figure 2: Ground truth CT and input \(T_{1}-\) and \(T_{2}-\)weighted MR images (first column) followed by predicted pseudo CT images with corresponding Mean Absolute Error (MAE) and Mean Squared Error (MSE) for 3D U-Net, HighRes3 DNet, Deep Boosted Regression, MultiRes without uncertainty and MultiRes\({}_{unc}\) including uncertainty estimation. the corresponding overlapping error in the residuals. In general, a larger amount of data should diminish the epistemic uncertainty by providing the network with a greater number of samples from which the correspondence between MR and CT images can be learned within these areas. The observed blurriness, however, could result in some inconsistency in the synthesis process, which would still be captured by the heteroscedastic uncertainty. We observed a high degree of uncertainty in the vicinity of air pockets. Unlike corporeal structures, it is expected that these pockets are subject to deformation between the MR and CT scanning sessions (and even between \(T1\) and \(T2\) acquisitions), which leads to a lack of correspondence between the acquisitions in these regions. This results in the network attempting to synthesise a morphologically different pocket to what is observed in the MR, resulting in a high degree of uncertainty. Figure 4: Joint histogram of prediction uncertainty and error rate for MultiRes\({}_{unc}\) network: Epistemic (**left**), Heteroscedastic (**right**). Low correlation between uncertainty and error rate is shown in purple and high correlation is shown in yellow. The average error rate at different levels of uncertainty is depicted by the red line. The error rate tends to increase with a higher uncertainty, which shows that the network correlates uncertainty to regions of high error. Figure 3: From left to right: Whole-body CT ground truth, pseudo CT prediction of MultiRes\({}_{unc}\), corresponding residuals, heteroscedastic uncertainty and epistemic uncertainty. Both uncertainties correlate with the residual error map. The additional validation results on the brain database can be seen in Figure 5; the ground truth CT and the pCT predictions generated with a multi-atlas propagation method, 3D U-Net, HighRes3 DNet, DBR, MultiRes and MultiRes\({}_{unc}\) with uncertainty are shown alongside with the subject's MR image as well as the models' corresponding MAE and MSE. It can be seen that similar to the results on the whole-body dataset the biggest error source is bone. This is especially evident in the MSE of the multi-atlas propagation method, 3D U-Net, HighRes3 DNet and DBR, where misclassified bone intensities are squared leading to a large error. However, both MultiRes models reconstruct sharp results and exhibit a lower residual error compared to all baseline methods. Only a small number of voxel intensities are wrongly classified resulting in an overall decreased error. Figure 6 shows a pCT of the brain synthesised with MultiRes\({}_{unc}\) and the correlation between the maps of epistemic and heteroscedastic uncertainty with the corresponding error map. Similarly to the whole-body experiment both epistemic and heteroscedastic uncertainties exhibit the largest values around bone and tissue boundaries, which is expected. The modelled heteroscedastic uncertainty is mainly evident in the cavity of the middle ear, which is a particularly difficult area to model for the network due to the small cartilage tissue structures.