Related papers: Laplace-Beltrami Operator for Gaussian Splatting
The 3D Gaussian splatting method has drawn a lot of attention, thanks to its high performance in training and high quality of the rendered image. However, it uses anisotropic Gaussian kernels to represent the scene. Although such…
Recently, 3D Gaussian Splatting (3DGS) has enabled photorealistic view synthesis at high inference speeds. However, its splatting-based rendering model makes several approximations to the rendering equation, reducing physical accuracy. We…
We propose a new and simple discretization, named the Modified Virtual Grid Difference (MVGD), for numerical approximation of the Laplace-Beltrami (LB) operator on manifolds sampled by point clouds. The key observation is that both the…
3D Gaussian splatting (3D-GS) is a new rendering approach that outperforms the neural radiance field (NeRF) in terms of both speed and image quality. 3D-GS represents 3D scenes by utilizing millions of 3D Gaussians and projects these…
We present a fast and efficient volumetric capture and reconstruction system that processes either RGB-D or RGB-only input to generate 3D representations in the form of point clouds and Gaussian splats. For Gaussian splat reconstructions,…
3D Gaussian Splatting (3DGS) enables photorealistic rendering but suffers from artefacts due to sparse Structure-from-Motion (SfM) initialisation. To address this limitation, we propose GP-GS, a Gaussian Process (GP) based densification…
Rendering novel view images in dynamic scenes is a crucial yet challenging task. Current methods mainly utilize NeRF-based methods to represent the static scene and an additional time-variant MLP to model scene deformations, resulting in…
The Laplace-Beltrami problem $\Delta_\Gamma \psi = f$ has several applications in mathematical physics, differential geometry, machine learning, and topology. In this work, we present novel second-kind integral equations for its solution…
Recently, Gaussian splatting has demonstrated significant success in novel view synthesis. Current methods often regress Gaussians with pixel or point cloud correspondence, linking each Gaussian with a pixel or a 3D point. This leads to the…
While Gaussian Splatting (GS) demonstrates efficient and high-quality scene rendering and small area surface extraction ability, it falls short in handling large-scale aerial image surface extraction tasks. To overcome this, we present…
Rendering high-fidelity images from sparse point clouds is still challenging. Existing learning-based approaches suffer from either hole artifacts, missing details, or expensive computations. In this paper, we propose a novel framework to…
The advent of 3D Gaussian Splatting (3DGS) has recently brought about a revolution in the field of neural rendering, facilitating high-quality renderings at real-time speed. However, 3DGS heavily depends on the initialized point cloud…
Recently, 3D Gaussian Splatting (3DGS) has become one of the mainstream methodologies for novel view synthesis (NVS) due to its high quality and fast rendering speed. However, as a point-based scene representation, 3DGS potentially…
Many shape analysis methods treat the geometry of an object as a metric space that can be captured by the Laplace-Beltrami operator. In this paper, we propose to adapt the classical Hamiltonian operator from quantum mechanics to the field…
Recent work has shown that 3D Gaussian-based SLAM enables high-quality reconstruction, accurate pose estimation, and real-time rendering of scenes. However, these approaches are built on a tremendous number of redundant 3D Gaussian…
Gaussian Splatting (GS) has demonstrated impressive quality and efficiency in novel view synthesis. However, shape extraction from Gaussian primitives remains an open problem. Due to inadequate geometry parameterization and approximation,…
Recently, 3D Gaussian splatting has gained attention for its capability to generate high-fidelity rendering results. At the same time, most applications such as games, animation, and AR/VR use mesh-based representations to represent and…
3D Gaussian Splatting has achieved impressive performance in novel view synthesis with real-time rendering capabilities. However, reconstructing high-quality surfaces with fine details using 3D Gaussians remains a challenging task. In this…
3D Gaussian Splatting (3DGS) is a recent approach for scene rendering. Although primarily designed for view synthesis, its potential for scene understanding tasks remains underexplored. In this work, we conduct a comparative evaluation of…
3D Gaussian Splatting (3DGS) has demonstrated its advantages in achieving fast and high-quality rendering. As point clouds serve as a widely-used and easily accessible form of 3D representation, bridging the gap between point clouds and…