面向 3D 高斯泼溅的即插即用 PDE 优化：迈向高质量渲染与重建
Plug-and-Play PDE Optimization for 3D Gaussian Splatting: Toward High-Quality Rendering and Reconstruction
把 3DGS 的优化过程建模为带粘性项的 PDE，并用物质点法（MPM）做数值求解，为高斯优化提供全局与局部约束；这套即插即用的优化器可直接嵌入现有 3DGS 管线，缓解复杂场景下的模糊与漂浮物问题。
原文依据 we present a plug-and-play PDE-based optimization method that overcomes the optimization constraints of 3DGS-based approaches
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论3D 高斯泼溅（3DGS）通过引入 3D 高斯基元来表示场景，以快速渲染实现高质量新视角合成，从而革新了辐射场重建。然而，当应用于复杂场景时，3DGS 会出现模糊与漂浮物，其原因在于重建出了冗余且歧义的几何结构。我们将该问题归因于高斯优化的不稳定性。为克服这一局限，我们提出一种基于偏微分方程（PDE）的即插即用优化方法，突破了基于 3DGS 的方法在新视角合成与表面重建等各类任务中的优化约束。首先，我们从理论上推导出 3DGS 的优化过程可建模为一个 PDE，并引入粘性项以保证优化的稳定性。其次，我们采用物质点法（MPM）获得该 PDE 的稳定数值解，从而同时增强全局与局部约束。此外，我们引入有效的高斯稠密化策略与粒子约束，以确保细粒度细节。大量定性与定量实验证实，我们的方法达到了最优的渲染与重建质量。
英文原文摘要 1241 字符
3D Gaussian Splatting (3DGS) has revolutionized radiance field reconstruction by achieving high-quality novel view synthesis with fast rendering speed, introducing 3D Gaussian primitives to represent the scene. However, 3DGS encounters blurring and floaters when applied to complex scenes, caused by the reconstruction of redundant and ambiguous geometric structures. We attribute this issue to the unstable optimization of the Gaussians. To address this limitation, we present a plug-and-play PDE-based optimization method that overcomes the optimization constraints of 3DGS-based approaches in various tasks, such as novel view synthesis and surface reconstruction. Firstly, we theoretically derive that the 3DGS optimization procedure can be modeled as a PDE, and introduce a viscous term to ensure stable optimization. Secondly, we use the Material Point Method (MPM) to obtain a stable numerical solution of the PDE, which enhances both global and local constraints. Additionally, an effective Gaussian densification strategy and particle constraints are introduced to ensure fine-grained details. Extensive qualitative and quantitative experiments confirm that our method achieves state-of-the-art rendering and reconstruction quality.