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

Ruyi Zha, Tao Jun Lin, Yuanhao Cai, Jiwen Cao, Yanhao Zhang, Hongdong Li

Keywords: 3D Gaussian Splatting, 3D Reconstruction, CT Reconstruction, Tomographic Reconstruction

TL;DR: We discover an inherent problem in 3DGS and develop a novel 3DGS-based framework for tomographic reconstruction.

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 \emph{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.

Primary Area: Machine vision

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Submission Number: 3935