# Implant Model Generation Method for Mandibular Defect Based on Improved 3D Unet
## 2 Materials and Methods
### The Process of Constructing the Mandible 3D Model Dataset
#### 3.3.2 Statistical Significance Analysis  
We further analyzed whether the improvements of 3D RUnet, 3D DUnet, and the proposed 3D RDUnet were statistically significant for all indicators of the mandible and implants by means of \(t\)-tests. \[t=\frac{\overline{X}_{1}-\overline{X}_{2}}{s_{p}\sqrt{2n}}. \tag{7}\]  
where \(s_{p}=\frac{1}{2}\sqrt{s_{X_{1}}^{2}+s_{X_{2}}^{2}}\) and \(\overline{X}_{1},\overline{X}_{2},s_{X_{1}}^{2},s_{X_{2}}^{2}\) are the mean and the estimated variance with respect to a metric from two trained models. \(n\) is the number of test cases. Table 3 shows the results. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Network**} & \multicolumn{4}{c}{**Mandible Evaluation Index**} & \multicolumn{4}{c}{**Implant Evaluation Index**} \\ \cline{2-9}  & **DCS** & **IoU** & **PPV** & **Recall** & **DCS** & **IoU** & **PPV** & **Recall** \\ \hline
3D Unet & 0.9842 & 0.9690 & 0.9841 & 0.9845 & 0.7113 & 0.5788 & 0.7310 & 0.7315 \\
3D RUnet & 0.9852 & 0.9709 & 0.9855 & 0.9851 & 0.7358 & 0.6042 & 0.7565 & 0.7505 \\
3D DUnet & 0.9841 & 0.9687 & 0.9908 & 0.9776 & 0.6976 & 0.5610 & 0.8118 & 0.6421 \\
3D RDUnet & 0.9873 & 0.9750 & 0.9850 & 0.9897 & 0.8018 & 0.6731 & 0.7782 & 0.8330 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Evaluation index. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Network**} & \multicolumn{4}{c}{**Mandible Evaluation Index**} & \multicolumn{4}{c}{**Implant Evaluation Index**} \\ \cline{2-9}  & **DCS** & **IoU** & **PPV** & **Recall** & **DCS** & **IoU** & **PPV** & **Recall** \\ \hline
3D RUnet-3D Unet & \(3.34\times 10^{-2}\) & \(2.87\times 10^{-2}\) & \(4.57\times 10^{-1}\) & \(1.43\times 10^{-1}\) & \(1.22\times 10^{-2}\) & \(4.28\times 10^{-3}\) & \(4.01\times 10^{-2}\) & \(2.98\times 10^{-2}\) \\
3D DUnet-3D Unet & \(5.03\times 10^{-1}\) & \(5.44\times 10^{-1}\) & \(6.19\times 10^{-3}\) & \(6.55\times 10^{-5}\) & \(3.75\times 10^{-2}\) & \(4.73\times 10^{-2}\) & \(1.42\times 10^{-6}\) & \(3.24\times 10^{-7}\) \\
3D DUnet-3D RUnet & \(9.33\times 10^{-3}\) & \(9.03\times 10^{-3}\) & \(2.58\times 10^{-2}\) & \(6.74\times 10^{-6}\) & \(1.93\times 10^{-4}\) & \(9.56\times 10^{-5}\) & \(3.00\times 10^{-5}\) & \(2.91\times 10^{-5}\) \\
3D RDUnet-3D Unet & \(3.50\times 10^{-4}\) & \(1.76\times 10^{-6}\) & \(3.89\times 10^{-5}\) & \(9.55\times 10^{-5}\) & \(4.92\times 10^{-8}\) & \(2.64\times 10^{-8}\) & \(2.27\times 10^{-4}\) & \(2.85\times 10^{-8}\) \\
3D RDUnet-3D RUnet & \(1.07\times 10^{-4}\) & \(5.13\times 10^{-5}\) & \(9.03\times 10^{-1}\) & \(1.33\times 10^{-3}\) & \(1.06\times 10^{-6}\) & \(9.21\times 10^{-7}\) & \(1.37\times 10^{-2}\) & \(3.15\times 10^{-7}\) \\
3D RDUnet-3D Unet & \(1.49\times 10^{-6}\) & \(8.41\times 10^{-7}\) & \(3.24\times 10^{-2}\) & \(6.35\times 10^{-8}\) & \(6.60\times 10^{-9}\) & \(4.26\times 10^{-9}\) & \(3.65\times 10^{-3}\) & \(3.21\times 10^{-11}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: \(p\) values among the evaluation metrics of the four approaches for statistical significance analysis. We adopt \(P_{T}\) = 0.05 as the threshold to categorize whether the difference is significant. Comparing the results of 3 DUNet with 3 DRUnet, in the mandibular evaluation index, DCS and IoU were significantly improved (\(0.01<p<0.05\)), while PPV and Recall were not significantly improved (\(p>0.05\)). In the implant evaluation index, IoU was extremely significantly improved (\(p<0.01\)), and other indicators were significantly improved (\(0.01<p<0.05\)). Comparing the results of 3 DDUnet with 3 DUNet, in the mandibular evaluation index, DCS and IoU lifting were not significant (\(p>0.05\)), and PPV and IoU lifting were significant (\(0.01<p<0.05\)). In the implant evaluation index, DCS and IoU lifting were significant (\(0.01<p<0.05\)), and PPV and Recall lifting were extremely significant (\(p<0.01\)).