# Temporal Subtraction Technique for Thoracic MDCT Based on Residual VoxelMorph
## 4 Experiment
### Results and Evaluation
This is because the deformation capability of ResidualVoxelMorph with the proposed method is too high, and the normal structures around the lesion were forcibly deformed and mapped. To solve this problem, devising a deep neural network model that considers new lesions is necessary. \begin{table}
\begin{tabular}{c|c c c|c} \hline \hline  & **Group (A + B)** & **Group (B + C)** & **Group (A + C)** & **Mean** \\ \hline
**ResidualVoxelMorph + Proposed Method** & [16.27, 56.81] & [18.22, 60.18] & [17.84, 59.61] & [17.4, 58.9] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The range of the loss function values for the training sets. \begin{table}
\begin{tabular}{c|c|c|c|c} \hline \hline  & **Group (A + B)** & **Group (B + C)** & **Group (A + C)** & **Mean** \\ \hline
**ResidualVoxelMorph + Proposed Method** & [18.87, 45.97] & [19.33, 47.78] & [19.19, 49.91] & [19.13, 47.9] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The range of the loss function values for the validation sets. In addition, ground truth images were generated by manually leaving only the temporally different lesions, and the root mean square error (RMSE) was calculated using ground truth images and temporal subtraction images to evaluate the performance of the proposed method. The ground truth images were generated manually by using Attractive software (PixSpace, Fukuoka, Japan) to manually create masked regions of only temporally different lesion areas, and then the images output, using the masked image output function, were used as ground truth images. Table 3 lists the RMSEs between the temporal subtraction images generated using ResidualVoxelMorph as deep neural network models of the proposed method, those generated using VoxelMorph as deep neural network models of the proposed method, and those generated by subtracting from deformed images using conventional VoxelMorph [6]. The results showed that the RMSE averages of ResidualVoxelMorph with the proposed method, VoxelMorph with the proposed method, and conventional VoxelMorph were 103.6, 112.6, and 116.8, respectively. Therefore, the average RMSE of the proposed method was 11.3% lower than that of the conventional method. To justify the normality of the difference in RMSE between methods, the Shapiro-Wilk test at a significance level of 0.01 was conducted, and normality was rejected: the comparison of ResidualVoxelMorph with the proposed method vs. VoxelMorph with the proposed method: \(p=0.0039\) (\(p<0.01\)), the comparison of ResidualVoxelMorph with the proposed method vs. the conventional VoxelMorph was \(p=1.1\times 10^{-8}\) (\(p<0.01\)), and the comparison of VoxelMorph with the proposed method vs. the conventional VoxelMorph was \(p=0.0015\) (\(p<0.01\)). Therefore, the Wilcoxon signed rank test with a significance level of 0.01, which was used as a test with significance level of 0.01. Figure 7: Comparison of the results of applying ResidualVoxelMorph with the proposal method, VoxelMorph with the proposal method, and conventional VoxelMorph to the previous and current CT image pair. (**a**) Shows a previous CT image, (**b**) a current CT image, (**c**) a temporal subtraction image from ResidualVoxelMorph with the proposal method, (**d**) a temporal subtraction image from VoxelMorph with the proposal method, and (**e**) a temporal subtraction image from conventional VoxelMorph. Lesions are circled. does not require the normality assumption, indicated that the difference in RMSE between these methods was statistically significant: the comparison of ResidualVoxelMorph with the proposed method vs. VoxelMorph with the proposed method: \(p\) = 2.1 \(\times\) 10\({}^{-15}\) (\(p\) < 0.01), the comparison of ResidualVoxelMorph with the proposed method vs. the conventional VoxelMorph was \(p\) = 4.4 \(\times\) 10\({}^{-13}\) (\(p\) < 0.01), and the comparison of VoxelMorph with the proposed method vs. the conventional VoxelMorph was \(p\) = 5.1 \(\times\) 10\({}^{-5}\) (\(p\) < 0.01).