## 4 Results
### Experiment I  
Table 4 shows the registration results. The first stage of the multistage network (rigid subnetwork) and the first stage of the benchmark (affine subnetwork) yielded similar Dice coefficients. The rigid-affine subnetwork of the multistage network produced registration results with a significantly (\(p<0.05\)) higher Dice coefficient than the affine subnetwork of the benchmark and a similar Dice coefficient as the baseline NiftyReg. The multistage rigid-affine-deformable network (separately trained subnetworks, row eight in Table 4) and the finetuned variant (row nine in Table 4) yielded similar Dice coefficients as the affine-deformable benchmark networks (separately trained and jointly finetuned, row four and five in Table 4). All stages of the benchmark and the proposed multistage network (Table 4 row three to row nine) yielded registration results with a significantly higher Dice coefficients than before registration (Table 4 row one). The proposed multistage networks computed transformations with a significantly (\(p<0.05\)) lower level of image folding than the benchmark network (\(|J|\leq 0\) in Table 2, row eight and nine vs. row four and five). By jointly finetuning the multistage network, the number of \(|J|\leq 0\) was significantly reduced (row eight vs. row nine in Table 4). The results of the significance tests for the benchmark and proposed multistage network are listed in Table 5.  
Examples of registration results can be seen in Figure 3. Before registration, the abdomen in the T1-weighted (fixed) and T2-weighted (moving) MR images is not well aligned. Registration with the baseline NiftyReg (second row in Figure 3) improved the structural similarity and the overlap of kidney segmentations. The rigid subnetwork (row six in Figure 3) significantly improved the spatial alignment compared to before registration. When adding the affine subnetwork, the overlap of the kidney segmentations is further \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Network** & & **DICE (\%)** & \(|J|\leq 0\) (\%)** \\ \hline \hline Before Registration & & \(67.6\pm 18.1\) & - \\ \hline Baseline NiftyReg & & \(70.9\pm 24.5\) & \(0.2\pm 0.6\) \\ \hline \multirow{3}{*}{Benchmark} & Affine & \(69.1\pm 16.5\) & \(0\pm 0\) \\  & Affine-Deformable & \(76.4\pm 12.4\) & \(0.7\pm 0.8\) \\  & Affine-Deformable Finetuned & \(76.4\pm 12.7\) & \(0.7\pm 0.8\) \\ \hline \multirow{3}{*}{Proposed Multistage Network} & Rigid & \(68.7\pm 17.3\) & \(0\pm 0\) \\  & Rigid-Affine & \(70.9\pm 14.2\) & \(0\pm 0\) \\ \cline{1-1}  & Rigid-Affine-Deformable & \(76.7\pm 11.4\) & \(0.6\pm 0.7\) \\ \cline{1-1}  & Rigid-Affine-Deformable Finetuned & \(76.7\pm 12.5\) & \(0.5\pm 0.7\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The Dice coefficient and Jacobian determinant (\(|J|\leq 0\) results (mean \(\pm\) SD) of the first NIDDK dataset of the baseline and each stage of the benchmark and our proposed multistage network. Dice coefficient: higher value is better (maximum is 100%); \(|J|\leq 0\): lower value is better (minimum is 0%). improved compared to the rigid subnetwork (row six and seven in Figure 3). However, other structures, such as the liver, do not overlap well in the fixed and moved image, as is visible in the composite image. By adding the deformable subnetwork (row eight in Figure 3), the structural similarity of all structures is improved, especially visible in the liver in the composite image. Jointly finetuning the multistage network further increased the overlap of all structures (clearly visible in the liver). Comparing the registration result of the jointly finetuned multistage network (row nine) with the jointly finetuned benchmark (row five) demonstrates improved spatial alignment of all corresponding structures, especially visible in the liver, using the proposed multistage network. The deformations within the organs are smooth (sixth column in Figure 3). The largest deformations are located at the organ boundaries, especially at the liver and spleen.