## 3 Results
### Accuracy Validation of the Maxillofacial Reconstruction 3D Model
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Item** & **Min Dist. (mm)** & **Max Dist. (mm)** & **Avg Dist. (mm)** & **Sigma** & **Max Error** \\ \hline Comparison Group 1 & 0 & 2.12302 & 0.00194347 & 0.0463828 & 0.474721 \\ Comparison Group 2 & 0 & 0.961699 & 0.000793175 & 0.0276074 & 0.480849 \\ Comparison Group 3 & 0 & 1.54807 & 0.0021574 & 0.107401 & 0.485219 \\ Comparison Group 4 & 0 & 0.984759 & 0.000181556 & 0.01337 & 0.49238 \\ Comparison Group 5 & 0 & 2.08695 & 0.00691822 & 0.0849521 & 0.466656 \\ Comparison Group 6 & 0 & 1.75678 & 0.0015742 & 0.084108 & 0.501194 \\ Comparison Group 7 & 0 & 1.17924 & 0.000235022 & 0.0166461 & 0.589619 \\ Comparison Group 8 & 0 & 2.14656 & 0.0488051 & 0.220108 & 0.479986 \\ Comparison Group 9 & 0 & 1.85413 & 0.0045168 & 0.187401 & 0.485412 \\ Comparison Group 10 & 0 & 2.37459 & 0.0506271 & 0.238065 & 0.530976 \\ \hline Average & 0 & 1.7015798 & 0.011775204 & 0.10260414 & 0.4987012 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Surface distance calculation results by comparison group. Figure 11: _Cont._  
The heatmap is displayed in a blue-green-yellow-red gradient based on each comparison group's Max dist. and Min dist. values. Areas with the smallest distance differences are closer to blue, while areas with larger distance differences are closer to red. In the heatmaps for Comparison Groups 1, 2, and 5, blue areas are prominent, indicating that there are many areas where the target model and the test model align precisely. However, red areas appear in the resected regions of the maxillofacial models, indicating differences in the resection locations between the test model and the target model. The numerical differences in these areas approximate the Max dist. values for each comparison group, suggesting that slight adjustments in the simulator during resection could bring the resection locations closer to those of the target model. In the heatmaps for Comparison Groups 4, 7, and 8, there is a small difference in resection locations between the target model and the test model, but a slight overall shape difference can be observed. This discrepancy appears to be due to the mesh used in the simulator model having fewer elements than the mesh in the CAD software, resulting in shape differences. Adjusting the number of mesh elements in the simulator model should bring it closer to the target model. In particular, Comparison Group 8 shows a significant difference in the number of mesh elements in the mandibular condyle area, which is displayed as red areas. These red areas could potentially be minimized through additional mesh post-processing. Overall, the overlay results for all comparison groups mostly show blue or green areas, indicating that the target model and test model have similar shapes. Resolving the localized discrepancy areas could make the test model nearly identical to the target model. Figure 11: Heatmap results for the six comparison groups: (**a**) Comparison Group 1; (**b**) Comparison Group 2; (**c**) Comparison Group 4; (**d**) Comparison Group 5; (**e**) Comparison Group 7; and (**f**) Comparison Group 8. With some improvements and adjustments applied to the simulation, it is expected that an adequately accurate maxillofacial reconstruction model can be generated.