## 4 Results
### Experiment II  
Table 6 shows the registration results. Registration with the baseline NiftyReg improved the Dice coefficient. The benchmark and the proposed multistage network yielded similar Dice coefficients as before registration. Additionally, the benchmark and the proposed multistage network produced a similar level of image folding (\(|J|\leq 0\)). Figure 4: Example results of the registration of two volumes from the second NIDDK dataset. The images show central slices of the coronal plane. The resulting composites for image and segmentation show the fixed data in blue and the moving/moved data in red. The arrow in the composite image indicates the area with misalignment between the fixed and moving image. The deformation field is visualized in RGB channels. \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Proposed Multistage Network**} & \multicolumn{4}{c}{**Benchmark**} \\  & **Affine** & & **Affine-Deformable** & **Affine-Deformable** \\ \cline{2-5}  & **DICE** & \(|J|\leq 0\) & **Dice** & \(|J|\leq 0\) \\ \hline Rigid & 0.0784 & - & & \\ Rigid-Affine & **0.0048** & - & & \\ Rigid-Affine-Deformable & & & 0.3125 & \(<\)**0.00001** & \\ Rigid-Affine-Deformable Finetuned & & & & 0.43675 & \(<\)**0.00001** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: \(p\)-values of the significance tests (paired \(t\)-test or a Wilcoxon signed-rank test, \(p<0.05\)) for the Dice coefficient and Jacobian determinant (\(|J|\)) \(\leq 0\) of the benchmark and proposed multistage network. Metrics with a significant difference (\(p<0.05\)) are indicated in bold. Examples of registration results can be seen in Figure 5. The fixed and moving image already show a reasonably good spatial alignment before registration; only fine structures in the kidney need to be corrected. The registration with the Baseline NiftyReg further improved the overlap of the kidneys. The benchmark and the proposed multistage network yielded similar results as before the registration. The deformation field of the multistage network shows smooth deformations. Table 6 shows the registration results of the neural networks, which were finetuned and evaluated on the augmented external kidney dataset. The benchmark and the proposed multistage network yielded a significantly (\(p<0.05\)) higher Dice coefficient than the baseline and registration with the proposed multistage network, which resulted in a significantly higher Dice coefficient than the benchmark. In addition, for the benchmark and the proposed multistage network, the level of image folding (\(\left|\right|<0\)) is significantly lower than for the baseline. For the benchmark and the proposed multistage network, the \(\left|\right|<0\) is smaller than 0.05. Examples of the registration results can be seen in Figure 6. Before registration, the corresponding images are not well aligned, especially visible at the spleen in the column \"Compos \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Network**} & \multicolumn{2}{c}{**External Kidney Dataset**} & \multicolumn{2}{c}{**External Kidney Dataset**} \\  & **without Augmentation** & **with Augmentation** & **with Augmentation** \\ \cline{2-5}  & **DICE (\%)** & **\(\left|\right|<0\) (\%)** & **DICE (\%)** & \(\left|\right|<0\) (\%)** \\ \hline Before Registration & \(63.9\pm 11.3\) & - & \(45.1\pm 16.9\) & - \\ Baseline NiftyReg & \(67.3\pm 13.9\) & \(0.1\pm 0.2\) & \(59.5\pm 22.5\) & \(0.2\pm 1.0\) \\ Benchmark & \(62.4\pm 13.7\) & \(0.9\pm 0.4\) & \(62.5\pm 15.6\) & \(0.0\pm 0.0\) \\ Proposed Multistage Network & \(61.1\pm 14.0\) & \(1.1\pm 0.6\) & \(64.8\pm 16.2\) & \(0.0\pm 0.0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The Dice coefficient and Jacobian determinant (\(\left|\right|\)) \(\leq 0\) results (mean \(\pm\) SD) of the external kidney dataset without and with augmentation of the baseline, benchmark and proposed multistage network. Dice coefficient: higher value is better (maximum is 100%), \(\left|\right|\leq 0\): lower value is better (minimum is 0%).