Related papers: Laplace-Beltrami Operator for Gaussian Splatting
This paper is dedicated to the development of numerical analysis for high-order methods solving partial differential equations on scattered point clouds. We build a novel geometric error analysis framework by estimating the error in the…
3D Gaussian splatting models, as a novel explicit 3D representation, have been applied in many domains recently, such as explicit geometric editing and geometry generation. Progress has been rapid. However, due to their mixed scales and…
This paper introduces a novel method for the efficient and accurate computation of the volume of a domain whose boundary is given by an orientable hypersurface which is implicitly given as the iso-contour of a sufficiently smooth level-set…
Differentiable 3D Gaussian splatting has emerged as an efficient and flexible rendering technique for representing complex scenes from a collection of 2D views and enabling high-quality real-time novel-view synthesis. However, its reliance…
With the emergence of Gaussian Splats, recent efforts have focused on large-scale scene geometric reconstruction. However, most of these efforts either concentrate on memory reduction or spatial space division, neglecting information in the…
The convergence problem of the Laplace-Beltrami operators plays an essential role in the convergence analysis of the numerical simulations of some important geometric partial differential equations which involve the operator. In this note…
Gaussian Splatting (GS) has proven to be highly effective in novel view synthesis, achieving high-quality and real-time rendering. However, its potential for reconstructing detailed 3D shapes has not been fully explored. Existing methods…
This paper presents a novel system designed for 3D mapping and visual relocalization using 3D Gaussian Splatting. Our proposed method uses LiDAR and camera data to create accurate and visually plausible representations of the environment.…
Point cloud is a critical 3D representation with many emerging applications. Because of the point sparsity and irregularity, high-quality rendering of point clouds is challenging and often requires complex computations to recover the…
Unoriented surface reconstructions based on the Gauss formula have attracted much attention due to their elegant mathematical formulation and excellent performance. However, the isotropic characteristics of the formulation limit their…
Gaussian processes are an effective model class for learning unknown functions, particularly in settings where accurately representing predictive uncertainty is of key importance. Motivated by applications in the physical sciences, the…
We consider numerical approximations of spectral fractional Laplace-Beltrami problems on closed surfaces. The proposed numerical algorithms rely on their Balakrishnan integral representation and consist of a sinc quadrature coupled with…
The emergence of 3D Gaussian Splatting (3DGS) has greatly accelerated the rendering speed of novel view synthesis. Unlike neural implicit representations like Neural Radiance Fields (NeRF) that represent a 3D scene with position and…
3D Gaussian Splatting has garnered extensive attention and application in real-time neural rendering. Concurrently, concerns have been raised about the limitations of this technology in aspects such as point cloud storage, performance, and…
3D Gaussian Splatting represents a breakthrough in the field of novel view synthesis. It establishes Gaussians as core rendering primitives for highly accurate real-world environment reconstruction. Recent advances have drastically…
TL;DR: Gaussian Splatting is a widely adopted approach for 3D scene representation, offering efficient, high-quality reconstruction and rendering. A key reason for its success is the simplicity of representing scenes with sets of Gaussians,…
Gaussian curvature is an important geometric property of surfaces, which has been used broadly in mathematical modeling. Due to the full nonlinearity of the Gaussian curvature, efficient numerical methods for models based on it are uncommon…
Existing neural implicit surface reconstruction methods have achieved impressive performance in multi-view 3D reconstruction by leveraging explicit geometry priors such as depth maps or point clouds as regularization. However, the…
The Laplace-Beltrami operator on (the surface of) a triaxial ellipsoid admits a sequence of real eigenvalues diverging to plus infinity. By introducing ellipsoidal coordinates, this eigenvalue problem for a partial differential operator is…
In recent years, parametric representations of point clouds have been widely applied in tasks such as memory-efficient mapping and multi-robot collaboration. Highly adaptive models, like spline surfaces or quadrics, are computationally…