R\(^2\)-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction

• Published in: arXiv.org
• Main Authors: Zha, Ruyi, Lin, Tao Jun, Cai, Yuanhao, Cao, Jiwen, Zhang, Yanhao, Li, Hongdong
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 31.05.2024
• Subjects: Algorithms; Computed tomography; Image reconstruction; X ray imagery
• ISSN: 2331-8422

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.