\section{Related Work}

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%\paragraph{Novel View Synthesis.}
%NVS has gained widespread attention in the fields of 3D vision and computer graphics due to its ability to generate realistic renderings of 3D objects and scenes from multiple viewpoints while enabling effective 3D modeling. NeRF~\citep{mildenhall2020nerf} introduces an implicit volumetric rendering approach that achieves high fidelity but suffers from heavy optimization and dense-view dependence. Subsequent extensions improve scalability: Mip-NeRF~\citep{barron2021mipnerf} and Mip-NeRF 360~\citep{barron2022mipnerf360} address anti-aliasing and unbounded scenes, while Zip-NeRF~\citep{barron2023zipnerf} incorporates grid-based sampling. To accelerate training, explicit encodings such as PlenOctrees~\citep{yu2021plenoctrees}, Plenoxels~\citep{fridovichkeil2022plenoxels}, and Instant-NGP~\citep{mueller2022instantngp} replace MLP inference. Methods like pixelNeRF~\citep{yu2021pixelnerf} and DietNeRF~\citep{jain2021dietnerf} pursue improved generalization. More recently, 3D Gaussian Splatting (3DGS)~\citep{kerbl2023gaussiansplatting} enables real-time photorealistic rendering and inspires variants for avatars and relighting. Overall, the field evolves from implicit radiance fields~\citep{mildenhall2020nerf,barron2021mipnerf,barron2022mipnerf360} to efficient explicit encodings~\citep{yu2021plenoctrees,fridovichkeil2022plenoxels,mueller2022instantngp} and real-time splatting~\citep{kerbl2023gaussiansplatting}, laying the foundation for topology-, appearance-, and semantics-aware extensions such as TAS-GS.
\paragraph{Novel View Synthesis.}  
NVS has become a key area in 3D vision and graphics for generating realistic renderings from multiple viewpoints. NeRF~\citep{mildenhall2020nerf} introduced implicit volumetric rendering, achieving high fidelity but relying on dense-view optimization. Later extensions improved scalability: Mip-NeRF~\citep{barron2021mipnerf} and Mip-NeRF 360~\citep{barron2022mipnerf360} tackled anti-aliasing and unbounded scenes, while Zip-NeRF~\citep{barron2023zipnerf} introduced grid-based sampling. To accelerate training, explicit encodings like PlenOctrees~\citep{yu2021plenoctrees}, Plenoxels~\citep{fridovichkeil2022plenoxels}, and Instant-NGP~\citep{mueller2022instantngp} replaced MLPs. Methods like pixelNeRF~\citep{yu2021pixelnerf} and DietNeRF~\citep{jain2021dietnerf} focused on better generalization. Recent work, including 3DGS~\citep{kerbl2023gaussiansplatting}, enables real-time photorealistic rendering, inspiring variants for avatars and relighting. The field has evolved from implicit radiance fields~\citep{mildenhall2020nerf,barron2021mipnerf,barron2022mipnerf360} to efficient explicit encodings~\citep{yu2021plenoctrees,fridovichkeil2022plenoxels,mueller2022instantngp}, and real-time splatting~\citep{kerbl2023gaussiansplatting}, laying the groundwork for topology-, appearance-, and semantics-aware methods like TAS-GS.


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%\paragraph{Sparse-View Reconstruction.}
%Sparse-view 3D reconstruction remains a fundamentally ill-posed problem due to its severe geometric ambiguity and under-constrained nature. To mitigate this, the field increasingly relies on strong priors and regularization: methods like DS-NeRF~\citep{deng2021dsnerf} introduce depth supervision, IBRNet~\citep{wang2021ibrnet} interpolates pixel-aligned features across views, and GeoNeRF~\citep{johari2022geonerf} explicitly exploits epipolar geometry. Further stability is achieved through regularizers employed in RegNeRF~\citep{niemeyer2022regnerf}, FreeNeRF~\citep{yang2023freenerf}, and SparseNeRF~\citep{wang2023sparsenerf}, while semantic cues and generalizable representations provide higher-level guidance, as seen in DietNeRF~\citep{jain2021dietnerf}. In a nutshell, these advances demonstrate that robust sparse-view reconstruction necessitates a holistic integration of geometric, regularization, and semantic constraints—a principle that motivates our unified framework, TAS-GS, to effectively combine topology-, appearance-, and semantics-aware learning.
\paragraph{Sparse-View Reconstruction.}  
Sparse-view 3D reconstruction is ill-posed due to severe geometric ambiguity and under-constrained nature. To address this, recent methods leverage strong priors and regularization: DS-NeRF~\citep{deng2021dsnerf} introduces depth supervision, IBRNet~\citep{wang2021ibrnet} interpolates pixel-aligned features, and GeoNeRF~\citep{johari2022geonerf} exploits epipolar geometry. Regularizers in RegNeRF~\citep{niemeyer2022regnerf}, FreeNeRF~\citep{yang2023freenerf}, and SparseNeRF~\citep{wang2023sparsenerf} improve stability, while methods like DietNeRF~\citep{jain2021dietnerf} incorporate semantic cues for higher-level guidance. These advances highlight the need for integrating geometric, regularization, and semantic constraints—principles that inform our unified framework, TAS-GS, combining topology-, appearance-, and semantics-aware learning.


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%\paragraph{Sparse-View 3D Gaussian Splatting.}
%Despite its real-time rendering capability, 3D Gaussian Splatting (3DGS)~\citep{kerbl2023gaussiansplatting} often suffers from floaters and geometric distortions under sparse-view conditions. To address these issues, recent methods incorporate structural priors: FSGS~\citep{zhu2024fsgs} introduces unpooling and virtual-view consistency, SCGaussian~\citep{cheng2024scgaussian} enforces multi-view ray consistency, and NexusGS~\citep{zheng2025nexusgs} injects epipolar geometry constraints. Other approaches adopt explicit regularization strategies, such as DropGaussian~\citep{park2025dropgaussian}, CoR-GS~\citep{zhang2024corgs}, and DNGaussian~\citep{li2024dngaussian}. Meanwhile, generalizable splatting models like FreeSplat~\citep{wang2024freesplat} and MVSplat~\citep{chen2024mvsplat} leverage cross-scene training for improved generalization. Overall, these advances balance rendering efficiency with robust prior-based, regularized, and generalizable optimization. Building on this direction, TAS-GS further enhances sparse-view reconstruction by jointly incorporating topological, appearance, and semantic constraints within a unified framework.
\paragraph{Sparse-View 3D Gaussian Splatting.}  
Despite real-time rendering, 3DGS~\citep{kerbl2023gaussiansplatting} suffers from floaters and geometric distortions under sparse views. Recent methods address these issues with structural priors: FSGS~\citep{zhu2024fsgs} introduces unpooling and virtual-view consistency, SCGaussian~\citep{cheng2024scgaussian} enforces multi-view ray consistency, and NexusGS~\citep{zheng2025nexusgs} incorporates epipolar geometry constraints. Regularization strategies like DropGaussian~\citep{park2025dropgaussian}, CoR-GS~\citep{zhang2024corgs}, and DNGaussian~\citep{li2024dngaussian} further improve stability. Generalizable models like FreeSplat~\citep{wang2024freesplat} and MVSplat~\citep{chen2024mvsplat} enhance cross-scene training. TAS-GS builds on these advances by integrating topological, appearance, and semantic constraints for improved sparse-view reconstruction.
