# A Multi-Channel Uncertainty-Aware Multi-Resolution Network for MR to CT Synthesis
## 3 Results
### Qualitative Evaluation  
Figure 2 shows the ground truth CT and the pCT predictions generated with 3D U-Net, HighRes3 DNet, DBR, MultiRes and MultiRes\({}_{unc}\) with uncertainty and the subject's MR image as well as each model's MAE and MSE. The pCT images generated with 3D U-Net, HighRes3 DNet and MultiRes appear sharp and exhibit high bone fidelity. DBR and the uncertainty aware MultiRes\({}_{unc}\) seem blurrier with lower intensities in the bone. This is likely due to the network not being confident in predicting high bone intensities. This observation is confirmed by the MAE and MSE. The error suggests that the highest source of errors for all models stems from bones. 3D U-Net and HighRes3 DNet also struggle to reconstruct lung intensities correctly. The lungs, having a significantly larger cross-sectional area, are visible, but lack internal consistency. Note, that all metrics used in this work are of absolute nature as opposed to relative, thus it is expected that errors in high intensity regions contribute most to the overall error. The MultiRes model exhibits the highest bone fidelity; the individual vertebrae are clearer, with intensities more in line with what would be expected for such tissues, and the femurs have more well-defined borders. It is interesting to note that the MSE of the MultiRes\({}_{unc}\) model is lower than the MSE of its uncertainty unaware counterpart. This shows that the majority of residuals in the pCT generated by MultiRes\({}_{unc}\) are in a lower range than MultiRes without uncertainty and therefore when squared do not contribute as much to the MSE. This is likely because the network is less confident in bone regions, \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Experiments** & **Model Parameters** & **MAE (HU)** & **MSE (HU\({}^{2}\))** \\ \hline
3D U-Net & 14.49M & 92.89 \(\pm\) 13.30 & 37,358.07 \(\pm\) 11,266.56 \\ HighRes3 DNet & 0.81M & 89.05 \(\pm\) 8.77 & 23,346.09 \(\pm\) 3828.22 \\ DBR & 1.62M & 77.58 \(\pm\) 3.20 & 19,026.56 \(\pm\) 2779.69 \\ MultiRes & 2.54M & **72.87 \(\pm\) 2.33** & 18,532.23 \(\pm\) 1538.41 \\ MultiRes\({}_{unc}\) & 2.61M & 73.90 \(\pm\) 6.24 & **16,007.56 \(\pm\) 2164.76** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mean Absolute Error (MAE) and Mean Squared Error (MSE) across all experiments on the whole-body dataset including number of trainable variables. Bolded entries denote best model (_p_-value \(<\) 0.05). \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Experiments** & **Model Parameters** & **MAE (HU)** & **MSE (HU\({}^{2}\))** \\ \hline Multi-Atlas & N/A & 132.15 \(\pm\) 68.89 & 75,364.30.07 \(\pm\) 62,627.20 \\
3D U-Net & 14.49M & 86.18 \(\pm\) 9.95 & 21,624.78 \(\pm\) 6095.86 \\ HighRes3 DNet & 0.81M & 70.52 \(\pm\) 10.80 & 19,876.87 \(\pm\) 5804.39 \\ DBR & 1.62M & 65.21 \(\pm\) 13.01 & 17,308.84 \(\pm\) 6923.93 \\ MultiRes & 2.54M & 57.52 \(\pm\) 17.79 & 9611.25 \(\pm\) 6251.68 \\ MultiRes\({}_{unc}\) & 2.61M & **57.01 \(\pm\) 17.96** & **7291.80 \(\pm\) 2857.76** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: MAE and MSE across all experiments on the brain dataset including number of trainable variables. Bolded entries denote best model (_p_-value \(<\) 0.05). whereas the models that do not compensate for uncertainty are overly confident and predict high bone intensities in the wrong place, resulting in a high error. Figure 3 presents the benefits afforded to MultiRes\({}_{unc}\) for being uncertainty aware. The joint histograms for epistemic uncertainty (left) and heteroscedastic uncertainty (right) are generated by calculating the error rate, taken as the difference between the ground truth CT and pCT averaged across \(N=50\) dropout samples, at different levels of both epistemic and heteroscedastic uncertainty (standard deviations per voxel) and taking the base 10 log. The red line describes the average error rate at each level of uncertainty.