3D Gaussian splatting (3DGS) has shown promising results in image rendering
and surface reconstruction. However, its potential in volumetric reconstruction
tasks, such as X-ray computed tomography, remains under-explored. This paper
introduces R2-Gaussian, the first 3DGS-based framework for sparse-view
tomographic reconstruction. By carefully deriving X-ray rasterization
functions, we discover a previously unknown integration bias in the standard
3DGS formulation, which hampers accurate volume retrieval. To address this
issue, we propose a novel rectification technique via refactoring the
projection from 3D to 2D Gaussians. Our new method presents three key
innovations: (1) introducing tailored Gaussian kernels, (2) extending
rasterization to X-ray imaging, and (3) developing a CUDA-based differentiable
voxelizer. Extensive experiments demonstrate that our method outperforms
state-of-the-art approaches by 0.93 dB in PSNR and 0.014 in SSIM. Crucially, it
delivers high-quality results in 3 minutes, which is 12x faster than NeRF-based
methods and on par with traditional algorithms. The superior performance and
rapid convergence of our method highlight its practical value.

本文介绍了第一个基于 3D 高斯喷洒（3DGS）的稀疏视图层析重建框架 R2-Gaussian，通过从 3D 到 2D 高斯的重投影，引入了定制高斯核、扩展到 X 射线成像以及基于 CUDA 的可微体素化器等三个关键创新，通过大量实验证明，我们的方法在 PSNR 和 SSIM 方面优于最先进的方法 0.93 dB 和 0.014，关键是能够在 3 分钟内产生高质量结果，比 NeRF 方法快 12 倍，并与传统算法持平，凸显出其实用价值。

R$^2$- 高斯：纠正放射高斯喷射用于层析重建

R$^2$-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic  Reconstruction

We introduce a new machine learning approach for image segmentation that uses
a neural network to model the conditional energy of a segmentation given an
image. Our approach, combinatorial energy learning for image segmentation
(CELIS) places a particular emphasis on modeling the inherent combinatorial
nature of dense image segmentation problems. We propose efficient algorithms
for learning deep neural networks to model the energy function, and for local
optimization of this energy in the space of supervoxel agglomerations. We
extensively evaluate our method on a publicly available 3-D microscopy dataset
with 25 billion voxels of ground truth data. On an 11 billion voxel test set,
we find that our method improves volumetric reconstruction accuracy by more
than 20% as compared to two state-of-the-art baseline methods: graph-based
segmentation of the output of a 3-D convolutional neural network trained to
predict boundaries, as well as a random forest classifier trained to
agglomerate supervoxels that were generated by a 3-D convolutional neural
network.

本文提出了一种基于神经网络的图像分割方法（CELIS），其能够处理密集图像分割问题并有效地进行 3D 数据的体积重建，该方法在公共可获得的 3D 显微镜数据上的测试结果表明，相较于基于图形分割的方法和随机森林聚合方法提高了高达 20% 的体积重建准确度。