On the Error Analysis of 3D Gaussian Splatting and an Optimal Projection Strategy

• URL: http://arxiv.org/abs/2402.00752v4
• Date: Mon, 26 Aug 2024 16:27:42 GMT
• Title: On the Error Analysis of 3D Gaussian Splatting and an Optimal Projection Strategy
• Authors: Letian Huang, Jiayang Bai, Jie Guo, Yuanqi Li, Yanwen Guo,
• Abstract summary: 3D Gaussian Splatting has garnered extensive attention and application in real-time neural rendering. However, there has been a notable lack of attention to the fundamental problem of projection errors introduced by the local affine approximation. This paper addresses the projection error function of 3D Gaussian Splatting, commencing with the residual error from the first-order Taylor expansion of the projection function.
• Score: 15.62029018680868
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 robustness in sparse viewpoints, leading to various improvements. However, there has been a notable lack of attention to the fundamental problem of projection errors introduced by the local affine approximation inherent in the splatting itself, and the consequential impact of these errors on the quality of photo-realistic rendering. This paper addresses the projection error function of 3D Gaussian Splatting, commencing with the residual error from the first-order Taylor expansion of the projection function. The analysis establishes a correlation between the error and the Gaussian mean position. Subsequently, leveraging function optimization theory, this paper analyzes the function's minima to provide an optimal projection strategy for Gaussian Splatting referred to Optimal Gaussian Splatting, which can accommodate a variety of camera models. Experimental validation further confirms that this projection methodology reduces artifacts, resulting in a more convincingly realistic rendering.

Related papers

• RobustSplat++: Decoupling Densification, Dynamics, and Illumination for In-the-Wild 3DGS [85.90134051583368]
  3D Gaussian Splatting (3DGS) has gained significant attention for its real-time, photo-realistic rendering in novel-view synthesis and 3D modeling.<n>Existing methods struggle with accurately modeling in-the-wild scenes affected by transient objects and illuminations.<n>We propose RobustSplat++, a robust solution based on several critical designs.
  arXiv  Detail & Related papers  (2025-12-04T14:05:09Z)
• RobustSplat: Decoupling Densification and Dynamics for Transient-Free 3DGS [79.15416002879239]
  3D Gaussian Splatting has gained significant attention for its real-time, photo-realistic rendering in novel-view synthesis and 3D modeling.<n>Existing methods struggle with accurately modeling scenes affected by transient objects, leading to artifacts in the rendered images.<n>We propose RobustSplat, a robust solution based on two critical designs.
  arXiv  Detail & Related papers  (2025-06-03T11:13:48Z)
• Micro-splatting: Maximizing Isotropic Constraints for Refined Optimization in 3D Gaussian Splatting [0.3749861135832072]
  This work implements an adaptive densification strategy that dynamically refines regions with high image gradients. It results in a denser and more detailed gaussian means where needed, without sacrificing rendering efficiency.
  arXiv  Detail & Related papers  (2025-04-08T07:15:58Z)
• S2Gaussian: Sparse-View Super-Resolution 3D Gaussian Splatting [47.75073170368562]
  We propose a novel Sparse-view Super-resolution 3D Gaussian Splatting framework, dubbed S2Gaussian, that can reconstruct structure-accurate and detail-faithful 3D scenes with only sparse and low-resolution views. Experiments demonstrate superior results and in particular establishing new state-of-the-art performances with more consistent geometry and finer details.
  arXiv  Detail & Related papers  (2025-03-06T10:58:26Z)
• GSplatLoc: Ultra-Precise Camera Localization via 3D Gaussian Splatting [0.0]
  We present GSplatLoc, a camera localization method that leverages the differentiable rendering capabilities of 3D Gaussian splatting for ultra-precise pose estimation. GSplatLoc sets a new benchmark for localization in dense mapping, with important implications for applications requiring accurate real-time localization, such as robotics and augmented reality.
  arXiv  Detail & Related papers  (2024-12-28T07:14:14Z)
• Pushing Rendering Boundaries: Hard Gaussian Splatting [72.28941128988292]
  3D Gaussian Splatting (3DGS) has demonstrated impressive Novel View Synthesis (NVS) results in a real-time rendering manner. We propose Hard Gaussian Splatting, dubbed HGS, which considers multi-view significant positional gradients and rendering errors to grow hard Gaussians. Our method achieves state-of-the-art rendering quality while maintaining real-time efficiency.
  arXiv  Detail & Related papers  (2024-12-06T07:42:47Z)
• Projecting Gaussian Ellipsoids While Avoiding Affine Projection Approximation [1.4792750204228]
  3D Gaussian Splatting has dominated novel-view synthesis with its real-time rendering speed and state-of-the-art rendering quality. We introduce an ellipsoid-based projection method to calculate the projection of Gaussian ellipsoid onto the image plane, which is the primitive of 3D Gaussian Splatting. Experiments over multiple widely adopted benchmark datasets show that our ellipsoid-based projection method can enhance the rendering quality of 3D Gaussian Splatting and its extensions.
  arXiv  Detail & Related papers  (2024-11-12T06:29:48Z)
• No Pose, No Problem: Surprisingly Simple 3D Gaussian Splats from Sparse Unposed Images [100.80376573969045]
  NoPoSplat is a feed-forward model capable of reconstructing 3D scenes parameterized by 3D Gaussians from multi-view images. Our model achieves real-time 3D Gaussian reconstruction during inference. This work makes significant advances in pose-free generalizable 3D reconstruction and demonstrates its applicability to real-world scenarios.
  arXiv  Detail & Related papers  (2024-10-31T17:58:22Z)
• PF3plat: Pose-Free Feed-Forward 3D Gaussian Splatting [54.7468067660037]
  PF3plat sets a new state-of-the-art across all benchmarks, supported by comprehensive ablation studies validating our design choices. Our framework capitalizes on fast speed, scalability, and high-quality 3D reconstruction and view synthesis capabilities of 3DGS.
  arXiv  Detail & Related papers  (2024-10-29T15:28:15Z)
• Visual SLAM with 3D Gaussian Primitives and Depth Priors Enabling Novel View Synthesis [11.236094544193605]
  Conventional geometry-based SLAM systems lack dense 3D reconstruction capabilities. We propose a real-time RGB-D SLAM system that incorporates a novel view synthesis technique, 3D Gaussian Splatting.
  arXiv  Detail & Related papers  (2024-08-10T21:23:08Z)
• AbsGS: Recovering Fine Details for 3D Gaussian Splatting [10.458776364195796]
  3D Gaussian Splatting (3D-GS) technique couples 3D primitives with differentiable Gaussianization to achieve high-quality novel view results. However, 3D-GS frequently suffers from over-reconstruction issue in intricate scenes containing high-frequency details, leading to blurry rendered images. We present a comprehensive analysis of the cause of aforementioned artifacts, namely gradient collision. Our strategy efficiently identifies large Gaussians in over-reconstructed regions, and recovers fine details by splitting.
  arXiv  Detail & Related papers  (2024-04-16T11:44:12Z)
• GPS-Gaussian: Generalizable Pixel-wise 3D Gaussian Splatting for Real-time Human Novel View Synthesis [70.24111297192057]
  We present a new approach, termed GPS-Gaussian, for synthesizing novel views of a character in a real-time manner. The proposed method enables 2K-resolution rendering under a sparse-view camera setting.
  arXiv  Detail & Related papers  (2023-12-04T18:59:55Z)
• Scaffold-GS: Structured 3D Gaussians for View-Adaptive Rendering [71.44349029439944]
  Recent 3D Gaussian Splatting method has achieved the state-of-the-art rendering quality and speed. We introduce Scaffold-GS, which uses anchor points to distribute local 3D Gaussians. We show that our method effectively reduces redundant Gaussians while delivering high-quality rendering.
  arXiv  Detail & Related papers  (2023-11-30T17:58:57Z)
• GaussianShader: 3D Gaussian Splatting with Shading Functions for Reflective Surfaces [45.15827491185572]
  We present a novel method that applies a simplified shading function on 3D Gaussians to enhance the neural rendering in scenes with reflective surfaces. Experiments show that GaussianShader strikes a commendable balance between efficiency and visual quality.
  arXiv  Detail & Related papers  (2023-11-29T17:22:26Z)
• GS-SLAM: Dense Visual SLAM with 3D Gaussian Splatting [51.96353586773191]
  We introduce textbfGS-SLAM that first utilizes 3D Gaussian representation in the Simultaneous Localization and Mapping system. Our method utilizes a real-time differentiable splatting rendering pipeline that offers significant speedup to map optimization and RGB-D rendering. Our method achieves competitive performance compared with existing state-of-the-art real-time methods on the Replica, TUM-RGBD datasets.
  arXiv  Detail & Related papers  (2023-11-20T12:08:23Z)
• Differentiable Rendering with Perturbed Optimizers [85.66675707599782]
  Reasoning about 3D scenes from their 2D image projections is one of the core problems in computer vision. Our work highlights the link between some well-known differentiable formulations and randomly smoothed renderings. We apply our method to 3D scene reconstruction and demonstrate its advantages on the tasks of 6D pose estimation and 3D mesh reconstruction.
  arXiv  Detail & Related papers  (2021-10-18T08:56:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.