As a flexible representation, NeRF has been first adopted for 3D representation. With density-based volumetric rendering, it however suffers both intensive computational overhead and inaccurate mesh extraction. Using a signed distance field and Marching Tetrahedra, DMTet allows for precise mesh extraction and real-time rendering but is limited in handling large topological changes in meshes, leading to optimization challenges. Alternatively, 3D Gaussian Splatting (3DGS) is favored in both training and rendering efficiency while falling short in mesh extraction. In this work, we introduce a novel 3D representation, Tetrahedron Splatting (TeT-Splatting), that supports easy convergence during optimization, precise mesh extraction, and real-time rendering simultaneously.

Recent advancements in visualizing deep neural networks provide insights into their structures and mesh extraction from Continuous Piecewise Affine (CPWA) functions. Meanwhile, developments in neural surface representation learning incorporate non-linear positional encoding, addressing issues like spectral bias; however, this poses challenges in applying mesh extraction techniques based on CPWA functions.

Li Zhang (lizhangfd@fudan.edu.cn) is the corresponding author. To further increase efficiency, we include a pre-filtering process to remove nearly transparent tetrahedra, reducing the number of tetrahedra necessary for splatting.

As a flexible representation, NeRF has been first adopted for 3D representation. With density-based volumetric rendering, it however suffers both intensive computational overhead and inaccurate mesh extraction. Using a signed distance field and Marching Tetrahedra, DMTet allows for precise mesh extraction and real-time rendering but is limited in handling large topological changes in meshes, leading to optimization challenges. Alternatively, 3D Gaussian Splatting (3DGS) is favored in both training and rendering efficiency while falling short in mesh extraction. In this work, we introduce a novel 3D representation, Tetrahedron Splatting (TeT-Splatting), that supports easy convergence during optimization, precise mesh extraction, and real-time rendering simultaneously.

Recent advancements in visualizing deep neural networks provide insights into their structures and mesh extraction from Continuous Piecewise Affine (CPWA) functions. Meanwhile, developments in neural surface representation learning incorporate non-linear positional encoding, addressing issues like spectral bias; however, this poses challenges in applying mesh extraction techniques based on CPWA functions. Moreover, we introduce a method for approximating intersecting points among three hypersurfaces contributing to broader applications.

Large-scale 3D reconstruction is critical in the field of robotics, and the potential of 3D Gaussian Splatting (3DGS) for achieving accurate object-level reconstruction has been demonstrated. However, ensuring geometric accuracy in outdoor and unbounded scenes remains a significant challenge. This study introduces LI-GS, a reconstruction system that incorporates LiDAR and Gaussian Splatting to enhance geometric accuracy in large-scale scenes. 2D Gaussain surfels are employed as the map representation to enhance surface alignment. Additionally, a novel modeling method is proposed to convert LiDAR point clouds to plane-constrained multimodal Gaussian Mixture Models (GMMs). The GMMs are utilized during both initialization and optimization stages to ensure sufficient and continuous supervision over the entire scene while mitigating the risk of over-fitting. Furthermore, GMMs are employed in mesh extraction to eliminate artifacts and improve the overall geometric quality. Experiments demonstrate that our method outperforms state-of-the-art methods in large-scale 3D reconstruction, achieving higher accuracy compared to both LiDAR-based methods and Gaussian-based methods with improvements of 52.6% and 68.7%, respectively.