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

TL;DR

This paper introduces R$^2$-Gaussian, a novel 3D Gaussian splatting framework tailored for sparse-view tomographic reconstruction, addressing integration bias issues and achieving faster, more accurate volumetric imaging.

Contribution

The paper presents the first 3D Gaussian splatting-based framework for X-ray tomography, including a rectification method for projection bias and a CUDA-based differentiable voxelizer.

Findings

Outperforms state-of-the-art in accuracy and efficiency

Achieves high-quality reconstructions in 4 minutes

Runs 12 times faster than NeRF-based methods

Abstract

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 R$^2$-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. Experiments on synthetic and real-world datasets demonstrate that our method outperforms state-of-the-art approaches in accuracy and efficiency. Crucially, it delivers high-quality results in 4 minutes, which is 12$\times$ faster than NeRF-based methods and on par with traditional algorithms. Code and models are available on the project page https://github.com/Ruyi-Zha/r2_gaussian.