Related papers: Laplace-Beltrami Operator for Gaussian Splatting
Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the…
Recently, 3D Gaussian Splatting (3DGS) has emerged as an efficient approach for accurately representing scenes. However, despite its superior novel view synthesis capabilities, extracting the geometry of the scene directly from the Gaussian…
Surface reconstruction has been widely studied in computer vision and graphics. However, existing surface reconstruction works struggle to recover accurate scene geometry when the input views are extremely sparse. To address this issue, we…
In this work, we introduce the 3D Gaussian Point Encoder, an explicit per-point embedding built on mixtures of learned 3D Gaussians. This explicit geometric representation for 3D recognition tasks is a departure from widely used implicit…
3D urban scene reconstruction and modelling is a crucial research area in remote sensing with numerous applications in academia, commerce, industry, and administration. Recent advancements in view synthesis models have facilitated…
Using the embedded gradient vector field method (see P. Birtea, D. Comanescu, Hessian operators on constraint manifolds, J. Nonlinear Science 25, 2015), we present a general formula for the Laplace-Beltrami operator defined on a constraint…
The accurate reconstruction of dynamic street scenes is critical for applications in autonomous driving, augmented reality, and virtual reality. Traditional methods relying on dense point clouds and triangular meshes struggle with moving…
In this study, we explore the challenge of efficiently representing scenes with a constrained number of Gaussians. Our analysis shifts from traditional graphics and 2D computer vision to the perspective of point clouds, highlighting the…
Graph Laplacian based algorithms for data lying on a manifold have been proven effective for tasks such as dimensionality reduction, clustering, and denoising. In this work, we consider data sets whose data points lie on a manifold that is…
Recent advancements in photo-realistic novel view synthesis have been significantly driven by Gaussian Splatting (3DGS). Nevertheless, the explicit nature of 3DGS data entails considerable storage requirements, highlighting a pressing need…
Current learning-based methods predict NeRF or 3D Gaussians from point clouds to achieve photo-realistic rendering but still depend on categorical priors, dense point clouds, or additional refinements. Hence, we introduce a novel point…
Recent advances in 3D Gaussian Splatting (3DGS) have demonstrated remarkable capabilities in real-time and photorealistic novel view synthesis. However, traditional 3DGS representations often struggle with large-scale scene management and…
Traditional 3D garment creation requires extensive manual operations, resulting in time and labor costs. Recently, 3D Gaussian Splatting has achieved breakthrough progress in 3D scene reconstruction and rendering, attracting widespread…
We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or surface. First we give an algorithm for estimation of the…
In this paper, we present a novel geometry-aware RGB-D Gaussian Splatting SLAM system, named G2S-ICP SLAM. The proposed method performs high-fidelity 3D reconstruction and robust camera pose tracking in real-time by representing each scene…
3D Gaussians have recently emerged as a highly efficient representation for 3D reconstruction and rendering. Despite its high rendering quality and speed at high resolutions, they both deteriorate drastically when rendered at lower…
Gaussian Splatting has emerged as a leading method for novel view synthesis, offering superior training efficiency and real-time inference compared to NeRF approaches, while still delivering high-quality reconstructions. Beyond view…
High-quality scene reconstruction and novel view synthesis based on Gaussian Splatting (3DGS) typically require steady, high-quality photographs, often impractical to capture with handheld cameras. We present a method that adapts to camera…
We derive error estimates for the piecewise linear finite element approximation of the Laplace--Beltrami operator on a bounded, orientable, $C^3$, surface without boundary on general shape regular meshes. As an application, we consider a…
Neural implicit representations, including Neural Distance Fields and Neural Radiance Fields, have demonstrated significant capabilities for reconstructing surfaces with complicated geometry and topology, and generating novel views of a…