# Dual-Dimensional Gaussian Splatting Integrating 2D and 3D Gaussians for Surface Reconstruction
## 4 Experiments and Discussion
### Evaluation and Analysis
**Bold** indicates the best performance, and _italic_ indicates the second-best. Figure 2: Qualitative comparison on the DTU dataset [35]. The first row visualizes the distribution of 2D and 3D Gaussians: 3D Gaussians are shown in orange, and 2D Gaussians in blue. For DDGS, 2D Gaussians are primarily used on flat surfaces, while 3D Gaussians are applied to complex volumetric structures. The second and third rows show surface reconstruction results across different methods. This enhancement in surface reconstruction can be attributed to DDGS's adaptive assignment of Gaussian dimensionality based on local surface geometry. Specifically, DDGS assigns 2D Gaussians to flat surfaces and 3D Gaussians to geometrically complex or volumetric regions. This adaptive strategy enables more effective modeling of diverse surface structures within a scene. As shown in Figure 2, 3 DGS captures geometrically complex surfaces relatively well but fails to accurately reconstruct large, flat regions. In contrast, 2 DGS effectively models flat surfaces but tends to over-smooth complex structures. DDGS instead adaptively selects between 2D and 3D Gaussians based on local geometry, resulting in more detailed and accurate surface reconstruction across varying surface types. Moreover, we conduct quantitative analyses to evaluate the effectiveness of the proposed regularization terms. The evaluation is based on the average Chamfer Distance computed over 15 scenes from the DTU dataset. In Table 4, we compare our full model, which incorporates all regularization terms, with ablated versions where each term is removed  
Figure 3: Qualitative comparison on the Tanks and Temples dataset [36]. DDGS demonstrates more precise and detailed surface reconstruction than other methods. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{3}{c}{**Outdoor Scene (Mean)**} & \multicolumn{3}{c}{**Indoor Scene (Mean)**} \\  & **PSNR \(\uparrow\)** & **SSIM \(\uparrow\)** & **LPIPS \(\downarrow\)** & **Time \(\downarrow\)** & **PSNR \(\uparrow\)** & **SSIM \(\uparrow\)** & **LPIPS \(\downarrow\)** & **Time \(\downarrow\)** \\ \hline
3 DGS & **24.60** & **0.726** & **0.240** & **29 min** & **30.91** & **0.923** & **0.188** & **23 min** \\ SuGaR & 22.94 & 0.647 & 0.312 & 66 min & 29.46 & 0.906 & 0.208 & 58 min \\
2 DGS & 24.16 & 0.702 & 0.288 & _33 min_ & _30.03_ & _0.909_ & 0.214 & _35 min_ \\ Ours & _24.24_ & _0.713_ & _0.267_ & 40 min & 29.44 & 0.908 & _0.205_ & 46 min \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quantitative comparison on the Mip-NeRF 360 dataset [37]. Higher PSNR \(\uparrow\) and SSIM \(\uparrow\), and lower LPIPS \(\downarrow\) and training time \(\downarrow\) indicate better performance. **Bold** indicates the best performance, and _italic_ indicates the second-best. individually. Removing any of the regularization terms--including the gradient-aware normal consistency weight \(\omega_{grad}\), the first-order gradient loss \(\lambda_{g1}\), or the second-order gradient loss \(\lambda_{g2}\)--consistently results in degraded surface reconstruction quality. Among these, removing \(\lambda_{g2}\) leads to the largest performance drop, indicating the importance of curvature-level alignment. These results demonstrate the complementary contributions of each regularization term in our design. We empirically found that when the smallest scaling factor is more than ten times smaller than the second smallest one, the Gaussian should be transformed into a 2D representation. To validate the robustness of this threshold, we conducted an ablation study  
Figure 4: Qualitative comparison on the Mip-NeRF 360 dataset [37]. Compared to other methods, DDGS achieves more accurate and detailed surface reconstruction. by varying the ratio from 5 to 30, as shown in Table 5. Using Chamfer Distance on the DTU dataset as the evaluation metric, we observed the best performance at a ratio threshold of 10, with only negligible variations up to 30.