Related papers: Laplace-Beltrami Operator for Gaussian Splatting
3D Gaussian Splatting (3DGS) has recently emerged as a fast, high-quality method for novel view synthesis (NVS). However, its use of low-degree spherical harmonics limits its ability to capture spatially varying color and view-dependent…
Recently, 3D Gaussian Splatting (3DGS) has emerged as a significant advancement in 3D scene reconstruction, attracting considerable attention due to its ability to recover high-fidelity details while maintaining low complexity. Despite the…
Generating synthetic images is a useful method for cheaply obtaining labeled data for training computer vision models. However, obtaining accurate 3D models of relevant objects is necessary, and the resulting images often have a gap in…
3D Gaussian Splatting is a recognized method for 3D scene representation, known for its high rendering quality and speed. However, its substantial data requirements present challenges for practical applications. In this paper, we introduce…
3D Gaussian Splatting is a novel method for 3D view synthesis, which can gain an implicit neural learning rendering result than the traditional neural rendering technology but keep the more high-definition fast rendering speed. But it is…
3D Gaussian Splatting (3DGS) excels at producing highly detailed 3D reconstructions, but these scenes often require specialised renderers for effective visualisation. In contrast, point clouds are a widely used 3D representation and are…
3D Gaussian splatting (3DGS) is a popular radiance field method, with many application-specific extensions. Most variants rely on the same core algorithm: depth-sorting of Gaussian splats then rasterizing in primitive order. This ensures…
3D Gaussian Splatting (3DGS) achieves remarkable results in the field of surface reconstruction. However, when Gaussian normal vectors are aligned within the single-view projection plane, while the geometry appears reasonable in the current…
We propose a variational functional and fast algorithms to reconstruct implicit surface from point cloud data with a curvature constraint. The minimizing functional balances the distance function from the point cloud and the mean curvature…
Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace--Beltrami operator on rather general curved surfaces. Our algorithm, which is based…
Recently, 3D Gaussian Splatting has dominated novel-view synthesis with its real-time rendering speed and state-of-the-art rendering quality. However, during the rendering process, the use of the Jacobian of the affine approximation of the…
LiDARs provide accurate geometric measurements, making them valuable for ego-motion estimation and reconstruction tasks. Although its success, managing an accurate and lightweight representation of the environment still poses challenges.…
Gaussian Splatting has emerged as a prominent model for constructing 3D representations from images across diverse domains. However, the efficiency of the 3D Gaussian Splatting rendering pipeline relies on several simplifications. Notably,…
This work presents uniform preconditioners for the discrete Laplace--Beltrami operator on hypersurfaces. In particular, within the framework of fast auxiliary space preconditioning (FASP), we develop efficient and user-friendly multilevel…
The underwater 3D scene reconstruction is a challenging, yet interesting problem with applications ranging from naval robots to VR experiences. The problem was successfully tackled by fully volumetric NeRF-based methods which can model both…
Standard Gaussian splatting methods rely on heuristic densification and pruning to adaptively allocate primitives during training, and the resulting Gaussian count strongly influences both reconstruction quality and runtime. This makes…
3D Gaussian Splatting is emerging as a state-of-the-art technique in novel view synthesis, recognized for its impressive balance between visual quality, speed, and rendering efficiency. However, reliance on third-degree spherical harmonics…
Recent approaches representing 3D objects and scenes using Gaussian splats show increased rendering speed across a variety of platforms and devices. While rendering such representations is indeed extremely efficient, storing and…
We introduce a new local meshfree method for the approximation of the Laplace-Beltrami operator on a smooth surface of co-dimension one embedded in $\R^3$. A key element of this method is that it does not need an explicit expression of the…
Recent advances in 3D Gaussian Splatting have enabled impressive photorealistic novel view synthesis. However, to transition from a pure rendering engine to a reliable spatial map for autonomous agents and safety-critical applications,…