# Dual-Dimensional Gaussian Splatting Integrating 2D and 3D Gaussians for Surface Reconstruction
## 4 Experiments and Discussion
### Evaluation and Analysis  
In Table 1, we compare the Chamfer Distance and training time for the DTU dataset. Among all compared methods, our method DDGS achieves the lowest average Chamfer Distance, indicating the highest reconstruction accuracy overall. In particular, DDGS significantly improves surface reconstruction quality over the base model, 2 DGS, across all scenes in the DTU dataset. This improvement, however, comes with a slight increase in average training time. Figure 2 shows the spatial distribution of 2D and 3D Gaussians, reflecting DDGS's adaptive assignment based on surface geometry. Table 2 compares the F1 score and training time on the TnT dataset. DDGS achieves the highest average F1 score among all methods and demonstrates particularly high accuracy on the Truck scene. Similar to the DTU results, DDGS consistently requires more training time than 2 DGS. Figure 3 shows qualitative improvements in surface reconstruction quality with DDGS. Table 3 presents a comparison of PSNR, SSIM, LPIPS, and training time on the Mip-NeRF 360 dataset, which does not provide surface ground truth. Although DDGS enhances surface quality, its rendering performance is lower than that of 3 DGS. This trade-off is expected because our method is specifically designed to enhance surface reconstruction and mesh extraction, where mesh-quality metrics such as Chamfer Distance and F1 score are more relevant than image-quality metrics used in image rendering, such as PSNR, SSIM, and LPIPS. While DDGS sacrifices some rendering fidelity, it significantly improves geometric accuracy, which is the primary goal of this work. Nevertheless, DDGS maintains rendering performance comparable to 2 DGS, indicating a substantial improvement in geom \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{10}{c}{**DTU Scene ID**} & \multicolumn{10}{c}{**Mean**} \\  & **24** & **37** & **40** & **55** & **63** & **65** & **69** & **83** & **97** & **105** & **106** & **110** & **114** & **118** & **122** & **CD** \(\downarrow\) & **Time** \(\downarrow\) \\ \hline
3 DGS & 2.54 & 1.35 & 2.03 & 1.77 & 3.07 & 2.61 & 1.79 & 2.20 & 2.15 & 1.87 & 2.05 & 2.38 & 1.89 & 1.65 & 1.72 & 2.07 & **6 min** \\ SuGaR & 1.79 & 1.05 & 1.04 & 0.69 & 1.86 & 1.59 & 1.27 & 1.80 & 1.86 & 1.31 & 1.01 & 1.83 & 1.37 & 1.04 & 0.83 & 1.36 & 39 min \\
2 DGS & _0.50_ & **0.81** & **0.34** & _0.43_ & _0.94_ & _0.85_ & _0.82_ & _1.28_ & _1.21_ & _0.64_ & _0.69_ & _1.37_ & _0.42_ & _0.67_ & _0.48_ & _0.76_ & _11 min_ \\ Ours & **0.47** & **0.81** & **0.34** & **0.41** & **0.91** & **0.84** & **0.76** & **1.20** & **1.10** & **0.63** & **0.65** & **1.10** & **0.40** & **0.57** & **0.42** & **0.71** & 15 min \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Quantitative comparison of Chamfer Distance (mm) and training time on the DTU dataset [35]. Lower Chamfer Distance \(\downarrow\) and training time \(\downarrow\) indicate better performance. **Bold** indicates the best performance, and _italic_ indicates the second-best. etry while preserving reasonable visual quality. Figure 4 shows qualitative improvements in surface reconstruction. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Methods** & \multicolumn{5}{c}{**TnT Scene ID**} & \multicolumn{5}{c}{**Mean**} \\  & **Barn** & **Caterpillar** & **Courthouse** & **Ignatius** & **Meetingroom** & **Truck** & **F1-Score**\(\uparrow\) & **Time**\(\downarrow\) \\ \hline
3 DGS & 0.16 & 0.13 & 0.08 & 0.20 & 0.12 & 0.21 & 0.15 & **14 min** \\ SuGaR & 0.06 & 0.07 & 0.03 & 0.17 & 0.09 & 0.21 & 0.11 & 50 min \\
2 DGS & **0.39** & **0.24** & **0.16** & _0.50_ & **0.20** & _0.45_ & _0.32_ & _16 min_ \\ Ours & _0.38_ & _0.23_ & **0.16** & **0.51** & **0.20** & **0.54** & **0.34** & 23 min \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Quantitative comparison of F1 score and training time on the Tanks and Temples dataset [36]. Higher F1 score \(\uparrow\) and lower training time \(\downarrow\) indicate better performance.