直接在高斯点云上计算拉普拉斯-贝尔特拉米算子，提升几何处理精度。
Laplace-Beltrami Operator for Gaussian Splatting
- 基于马哈拉诺比斯距离，直接在高斯点云上定义拉普拉斯算子。
- 相比传统点云方法，在高斯中心点云上精度显著提升。
- 可实时评估优化过程中的重建质量，适合3D重建与渲染应用。
随着3D高斯溅射在渲染与三维重建等领域的广泛应用，对其直接进行几何处理的需求日益增长。尽管可将高斯中心视为点云或进行网格化以使用现有算法，但可能忽略数据中的信息或带来不必要的计算开销。此外，高斯溅射常包含大量不影响渲染质量的离群点，需正确处理以避免几何处理中产生噪声。本文提出一种基于马哈拉诺比斯距离的拉普拉斯-贝尔特拉米算子计算方法，直接作用于高斯溅射表示。实验表明，该方法在高斯中心编码的点云上表现优于传统点云拉普拉斯算子，并可用于优化过程中评估输出质量。
原文摘要 · Abstract (English)
With the rising popularity of 3D Gaussian splatting and the expanse of applications from rendering to 3D reconstruction, there comes also a need for geometry processing applications directly on this new representation. While considering the centers of Gaussians as a point cloud or meshing them is an option that allows to apply existing algorithms, this might ignore information present in the data or be unnecessarily expensive. Additionally, Gaussian splatting tends to contain a large number of outliers which do not affect the rendering quality but need to be handled correctly in order not to produce noisy results in geometry processing applications. In this work, we propose a formulation to compute the Laplace-Beltrami operator, a widely used tool in geometry processing, directly on Gaussian splatting using the Mahalanobis distance. While conceptually similar to a point cloud Laplacian, our experiments show superior accuracy on the point clouds encoded in the Gaussian splatting centers and, additionally, the operator can be used to evaluate the quality of the output during optimization.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。