\section{Experiments}

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\paragraph{Implementation details.}
We implement our method by extending NexusGS~\citep{zheng2025nexusgs}, training for 30k iterations on a single NVIDIA RTX 3090 GPU. Our representation maintains full compatibility with the standard 3DGS~\citep{kerbl2023gaussiansplatting}. We conduct a comprehensive evaluation on the LLFF~\citep{llff} and Mip-NeRF360~\citep{barron2022mipnerf360} benchmarks, reporting performance across a range of input view counts. Further details are provided in the appendix.
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\input{tables/main/comparison_llff}
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\paragraph{Results on the LLFF dataset.}
Table~\ref{tab:comparison_llff} presents quantitative comparisons under sparse-view settings. NeRF-based methods \citep{jain2021dietnerf,niemeyer2022regnerf,yang2023freenerf,wang2023sparsenerf} perform poorly with only 3 views, yielding blurry reconstructions. While the seminal 3DGS \citep{kerbl2023gaussiansplatting} achieves strong results with dense inputs, it also degrades significantly under extreme sparsity (19.86 dB PSNR at 3 views), revealing susceptibility to sparse supervision. Compared to recent 3DGS variants~\citep{li2024dngaussian,zhu2024fsgs,cheng2024scgaussian,zheng2025nexusgs}, our method achieves the best or second-best results across all regimes. With only 3 views, it attains 21.52 dB PSNR and 0.161 LPIPS, outperforming NexusGS by +0.5 dB and $-$0.017 LPIPS, while maintaining state-of-the-art performance at 6 and 9 views, respectively. Qualitative results in Figure~\ref{fig:com_llffv3} show that NeRF-based methods produce blurry edges. Although 3DGS and FSGS improve sharpness, they suffer from floaters and fragmented geometry. SCGaussian better preserves structure but introduces noise, and NexusGS improves stability yet still fails under extreme sparsity. In contrast, our approach reconstructs sharp stone edges in fortress, preserves fine structures in horns, and accurately captures contours in complex scenes such as leaves and orchids.

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\input{figs/main/com_llffv3}
\input{tables/main/comparison_360}
\input{figs/main/com_360v24}

\paragraph{Results on the Mip-NeRF360 dataset.}  
We further evaluate our method on the Mip-NeRF360 dataset, with quantitative results summarized in Table~\ref{tab:comparison_360}. NeRF-based methods perform well with dense inputs, but degrade significantly under sparse settings, with the vanilla 3DGS dropping to 19.73 dB when only 3 views are provided. Compared to the 3DGS baselines, including DNGaussian~\citep{li2024dngaussian}, FSGS~\citep{zhu2024fsgs}, SCGaussian~\citep{cheng2024scgaussian}, and NexusGS~\citep{zheng2025nexusgs}, our method achieves the best or second-best performance across all settings. Specifically, it reaches 20.81 dB PSNR and 0.198 LPIPS under the 3-view condition, surpassing NexusGS by +0.4 dB in PSNR and $-$0.012 LPIPS, while maintaining state-of-the-art results with 6 and 9 views. Qualitative comparisons are shown in Figure~\ref{fig:com_360v24}. NeRF-based methods suffer from blur and loss of detail;  3DGS~\citep{kerbl2023gaussiansplatting} and FSGS\citep{zhu2024fsgs} improve sharpness but often introduce floaters and undesired thin structures. SCGaussian better preserves geometry but introduces texture noise, and NexusGS~\citep{zheng2025nexusgs} enhances stability yet still fails to recover fine details. In contrast, our approach reconstructs clean building edges in the garden scene, maintains thin structures such as poles and wires in the room, and produces sharp contours in the  counter scene, resulting in more coherent and realistic textures.

\paragraph{Ablation studies.}  
Figure~\ref{fig:com_ablation} shows ablation results with components added progressively. The entropy-based opacity loss $\mathcal{L}_{\mathrm{opacity}}$ raises PSNR/SSIM/LPIPS from 21.03/0.737/0.178 to 21.12/0.744/0.173, reducing floaters and allowing more pruning. Adding the topology-aware graph regularizer brings scores to 21.33/0.753/0.165 by stabilizing geometry and repairing thin structures. The GNN-based appearance module further improves shading coherence, reaching 21.41/0.758/0.163 without inference cost. With the full model, we achieve the best results: 21.52 PSNR, 0.760 SSIM, and 0.161 LPIPS, preserving sharp contours and rare details. Visually, each component progressively enhances edge sharpness and texture quality. The final model remains compatible with the standard 3DGS rasterizer, maintaining real-time rendering while delivering superior reconstruction.


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\input{figs/main/com_ablation}

