Exact-GS：用于三维 X 射线重建的数学严谨且精确的三维高斯泼溅
Exact-GS: Mathematically Rigorous and Accurate 3D Gaussian Splatting for 3D X-ray Reconstruction
提出无需仿射近似的闭式高斯泼溅公式，可直接替换现有 3DGS 渲染器中的投影近似，消除伪影并保持 CUDA 光栅化速度，适用于任何需要精确投影的泼溅式渲染任务。
原文依据 We introduce a novel closed-form splatting solution for this problem with mathematically rigorous derivation.
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论我们提出 Exact-GS，一种新颖的数学严谨且精确的三维高斯泼溅模型，旨在执行三维 X 射线计算机断层扫描（CT）重建和新视角合成。近期，三维高斯泼溅在三维表示方面取得了可观进展。然而，由于投影变换的仿射近似，先前基于三维高斯泼溅的方法不可避免地遭受伪影和投影不一致问题。为解决此问题，一些基于光线追踪的方法沿光线跨高斯进行积分。但这些方法在前向和反向传播中计算效率低下。我们为此问题引入一种新颖的闭式泼溅解决方案，并给出数学严谨的推导。我们的模型首次在基于泼溅的公式下，无需任何近似即达到与基于光线追踪的方法完全相同的精确渲染质量，同时支持快速的基于 CUDA 的硬件光栅化。此外，我们提出一种精确的高斯-瓦片相交算法，实现更快速高效的渲染。我们通过不同合成和真实世界数据集上的重建与新视角合成展示了性能提升。代码公开于：https://github.com/brucee1323/Exact-GS。
英文原文摘要 1280 字符
We propose Exact-GS, a novel mathematically rigorous and accurate 3D Gaussian Splatting model designed to perform 3D X-ray computed tomography (CT) reconstruction and novel view synthesis. Recently, 3D Gaussian Splatting achieved considerable progress at 3D representation. Unfortunately, due to the affine approximation of the projective transformation, previous 3DGS-based methods inevitably suffer from artifacts and projection inconsistencies. To address this problem, some ray tracing based methods perform integration along the ray across Gaussians. However, these methods are computationally inefficient on the forward and backward pass. We introduce a novel closed-form splatting solution for this problem with mathematically rigorous derivation. Our model is the first to achieve the same exact rendering quality as ray tracing based methods without any approximation under a splatting-based formulation, enabling fast CUDA-based hardware rasterization. Additionally, we present a precise Gaussian-tile intersection algorithm, enabling faster and efficient rendering. We demonstrate the performance gains by reconstruction and novel view synthesis through different synthetic and real-world datasets. Code is publicly available at: https://github.com/brucee1323/Exact-GS.