发表机构
Universidade de São Paulo; Stanford University; UFRPE; IMPA（圣保罗大学; 斯坦福大学; 伯南布哥联邦农村大学; 纯数学与应用数学国家研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
PCAsplat是基于可微局部PCA正则化的高斯溅射框架，可减少漂浮物，提升表面近似效果，支持下游几何处理任务，在相关基准任务中表现具竞争力。
AI 中文摘要
高斯溅射已成为一种灵活的、用于从已校准图像进行3D重建的表示方法。然而，现有方法主要基于光栅化损失进行优化，该损失仅在溅射物对采样相机光线有贡献时才对其进行监督。因此，被遮挡或对采样视图贡献极小的高斯会收到微弱或没有几何梯度，可能会偏离底层表面，产生不期望的漂浮物。我们提出PCAsplat，一种基于可微局部主成分分析（PCA）的、用于高斯溅射的几何感知正则化框架。我们的PCA正则化器直接作用于高斯中心的邻域，因此可以更新对当前训练视图无贡献的高斯。我们对PCA特征值进行正则化，以鼓励高斯移动到底层表面并具有各向同性的切平面覆盖；同时，我们将每个高斯的法线与PCA估计的邻域法线对齐，以确保方向一致。在DTU、Tanks and Temples和NeRF Synthetic上的实验表明，PCAsplat生成的溅射物能更好地近似参考表面的样本，同时大幅减少不期望的漂浮物。这些与表面对齐的溅射物可用于下游几何处理任务，包括点云分割和直接泊松重建。此外，PCAsplat在常规的新视图合成和网格提取任务中仍具有竞争力。代码将被发布。
英文摘要
Gaussian splatting has emerged as a flexible representation for 3D reconstruction from posed images. However, existing methods are optimized primarily using rasterization-based losses, which supervise a splat only when it contributes to sampled camera rays. Gaussians that are occluded or contribute little to the sampled view therefore receive weak or no geometric gradients and may drift away from the underlying surface, producing undesired floaters. We introduce PCAsplat, a geometry-aware regularization framework for Gaussian splatting based on differentiable local principal component analysis (PCA). Our PCA regularizer acts directly on neighborhoods of Gaussian centers and can therefore update Gaussians that do not contribute to the current training view. We regularize the PCA eigenvalues to encourage Gaussians to move to the underlying surface with isotropic tangent-plane coverage. We also align each Gaussian normal with the PCA-estimated neighborhood normal to enforce consistent orientation. Experiments on DTU, Tanks and Temples, and NeRF Synthetic show that the splats produced by PCAsplat better approximate samples of the reference surface while substantially reducing undesired floaters. These surface-aligned splats enable downstream geometry-processing tasks, including point cloud segmentation, and direct Poisson reconstruction. Additionally, PCAsplat remains competitive under conventional novel view synthesis and mesh extraction tasks. Code will be released.
