# Dual-Dimensional Gaussian Splatting Integrating 2D and 3D Gaussians for Surface Reconstruction
## 5 Conclusions  
In this paper, we introduced DDGS, a hybrid approach for accurate surface reconstruction that leverages both 2D and 3D Gaussians. By combining the strengths of 2D and 3D representations, DDGS adapts the Gaussian dimensionality based on spatial scale, enabling \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**Image Rendering Speed \(\uparrow\) (fps)**} & \multicolumn{2}{c}{**Mean Mesh Extraction Time \(\downarrow\) (s)**} \\  & **DTU** & **TnT** & **Mip-NeRF 360** & **DTU** & **TnT** & **Mip-NeRF 360** \\ \hline
3 DGS & **261.27** & **163.14** & **97.55** & **1.36** & 376.24 & 58.59 \\ SuGaR & 78.74 & 82.02 & 72.79 & 98.11 & 295.15 & 471.96 \\
2 DGS & _140.30_ & _112.33_ & 50.29 & 1.52 & **158.60** & **42.70** \\ Ours & 102.91 & 82.43 & 43.92 & 1.49 & 178.62 & 43.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Quantitative comparison of image rendering speed and mesh extraction time on the DTU [35], Tanks and Temples [36], and Mip-NeRF 360 [37] datasets. Higher speed \(\uparrow\) and lower time \(\downarrow\) indicate better performance. **Bold** indicates the best performance, and _italic_ indicates the second-best. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Ablation Setting**} & \multirow{2}{*}{\(\omega_{grad}\)} & \multirow{2}{*}{\(\lambda_{g1}\)} & \multirow{2}{*}{\(\lambda_{g2}\)} & **Mean** \\  & & & & **CD**\(\downarrow\) \\ \hline w/o gradient-aware normal consistency weight & & ✓ & ✓ & 0.7239 \\ w/o first-order gradient loss & ✓ & & ✓ & 0.7216 \\ w/o second-order gradient loss & ✓ & ✓ & & 0.7457 \\ \hline Full model & ✓ & ✓ & ✓ & **0.7074** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Quantitative comparison of Chamfer Distance (mm) for the ablation study of the regularization terms on the DTU dataset [35]. We report the average Chamfer Distance across 15 scenes. Lower Chamfer Distance \(\downarrow\) indicates better performance. **Bold** indicates the best performance, and _italic_ indicates the second-best. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Ratio Threshold** & **5** & **10** & **15** & **20** & **25** & **30** \\ \hline
**Mean Chamfer Distance \(\downarrow\)** & 0.7248 & **0.7074** & 0.7159 & 0.7170 & 0.7144 & _0.7123_ \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Quantitative comparison of Chamfer Distance (mm) for the ablation study on the ratio threshold for transforming 3D Gaussians into 2D on the DTU dataset [35]. We report the average Chamfer Distance \(\downarrow\) indicates better performance. **Bold** indicates the best performance, and _italic_ indicates the second-best. more flexible and precise modeling of complex surfaces. We further proposed gradient-based regularization terms to mitigate over-smoothing and enhance surface alignment. DDGS achieves superior surface reconstruction accuracy across both flat and volumetric regions, as demonstrated by experimental results on the DTU and TnT datasets, where it outperforms prior methods such as 3 DGS, SuGaR, and 2 DGS in terms of Chamfer Distance and F1 score. Nevertheless, DDGS still struggles to accurately reconstruct challenging regions such as semi-transparent surfaces and specular highlights, often resulting in incomplete geometry or visible holes in the reconstructed mesh. This limitation mainly stems from the difficulty of Gaussian Splatting in modeling high-frequency, view-dependent reflections. Addressing these issues remains an important direction for future work, potentially through the integration of shading functions to better capture reflective effects. Conceptualization, J.P.; methodology, J.P.; software, J.P.; validation, J.P. and Y.B. ; formal analysis, J.P. and Y.B. ; writing--original draft preparation, J.P.; writing--review and editing, J.P., J.-W.S., and Y.B. ; visualization, J.P.; supervision, Y.B. ; project administration, Y.B. All authors have read and agreed to the published version of the manuscript.