Research map / 3D vision / Gaussian splatting
R$^2$-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction
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Introduces R²-Gaussian, the first 3DGS-based framework for sparse-view CT reconstruction, rectifying an integration bias in standard 3DGS via radiative Gaussian kernels, X-ray rasterization, and a CUDA differentiable voxelizer.
Problem
Sparse-view tomographic (X-ray CT) reconstruction is ill-posed and existing methods are either low quality (analytical), out-of-distribution fragile (supervised), or slow (NeRF-based, >30 minutes). Standard 3DGS cannot directly recover consistent 3D density volumes.
Approach
Derives X-ray rasterization by integrating 3D Gaussian kernels along rays, identifies an covariance-dependent integration bias in 3DGS's 3D-to-2D projection, and fixes it by assigning actual 3D density to radiative Gaussian kernels (no view-dependent color), with a differentiable CUDA voxelizer for volume extraction and TV regularization.
Key results
- On synthetic 75-view data, Ours (30k iter) reaches 38.88 dB PSNR / 0.959 SSIM vs SAX-NeRF 38.07 dB / 0.950 at 13h5m, and 10k iterations takes about 2m38s.
- Rectifying integration bias improves 3D PSNR by 17.77 dB over the X-3DGS variant (full model 37.98 dB vs X-3DGS at 50-view 21.24 dB).
- Ablations: FDK initialization adds 0.9 dB PSNR; full model improves over baseline by 1.51 dB at 50-view, with training under 9 minutes.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| rectify the integration bias in 3D-to-2D Gaussian projection (ablation) | X-3DGS · Synthetic dataset, 75/50/25-view | 3D PSNR: +17.77 dB PSNR | Helped |
| add FDK initialization (ablation) | R²-Gaussian baseline · Synthetic 50-view | PSNR: 36.47 -> 37.37 | Helped |
| add adaptive control (ablation) | R²-Gaussian baseline · Synthetic 50-view | PSNR: 36.47 -> 37.33 | Helped |
| add TV regularization (ablation) | R²-Gaussian baseline · Synthetic 50-view | SSIM: 0.934 -> 0.943 | Helped |
| use 5k rather than 50k initialized Gaussians (ablation) | R²-Gaussian · Synthetic 50-view | PSNR: 37.98 -> 37.44 | Hurt |
| use 10k rather than 50k initialized Gaussians (ablation) | R²-Gaussian · Synthetic 50-view | PSNR: 37.98 -> 37.56 | Hurt |
| use 100k rather than 50k initialized Gaussians (ablation) | R²-Gaussian · Synthetic 50-view | PSNR: 37.98 -> 38.03 | Helped |
| use 200k rather than 50k initialized Gaussians (ablation) | R²-Gaussian · Synthetic 50-view | PSNR: 37.98 -> 37.82 | Hurt |
| set TV loss weight to 0.01 rather than 0.05 (ablation) | R²-Gaussian · Synthetic 50-view | PSNR: 37.98 -> 37.88 | Hurt |
| increase TV loss weight to 0.1 or 0.15 (ablation) | R²-Gaussian · Synthetic 50-view | PSNR: 37.98 -> 37.73; 37.98 -> 37.40 | Hurt |
| vary TV volume size from D=32 (ablation) | R²-Gaussian · Synthetic 50-view | PSNR: 37.98 -> 37.74 (D=8); 37.98 -> 37.94 (D=16); 37.98 -> 37.90 (D=48); 37.98 -> 37.82 (D=64) | Mixed |
| use R²-Gaussian instead of SAX-NeRF | R²-Gaussian · Synthetic 75/50-view | PSNR: 38.07 -> 38.88; 36.86 -> 37.98 | Helped |
Surprising findings
- Standard 3DGS's integration bias has negligible effect on 2D rendering yet severely corrupts 3D density retrieval (X-3DGS 3D PSNR 23.40 vs 38.86 dB at 75 views).
- Under limited-angle CT, the method has slightly lower PSNR than NAF, attributed to 3DGS's local optimization hurting extrapolation.
Experimental setup
Datasets: LIDC-IDRI Pancreas-CT X-Plant SciVis FIPS
Benchmarks: synthetic CT dataset (15 volumes) FIPS real-world projections limited-angle CT
Metrics: PSNR SSIM training time
Baselines: FDK SART ASD-POCS IntraTomo NAF SAX-NeRF X-3DGS
Builds on: 3D Gaussian splatting FDK TIGRE NAF X-Gaussian
Closest papers by meaning
- Volumetrically Consistent 3D Gaussian Rasterization (CVPR 2025 · similarity 0.92)
- Sparse2DGS: Geometry-Prioritized Gaussian Splatting for Surface Reconstruction from Sparse Views (CVPR 2025 · similarity 0.90)
- DDGS-CT: Direction-Disentangled Gaussian Splatting for Realistic Volume Rendering (NeurIPS 2024 · similarity 0.89)
- Metropolis-Hastings Sampling for 3D Gaussian Reconstruction (NeurIPS 2025 · similarity 0.89)
- 3D Convex Splatting: Radiance Field Rendering with 3D Smooth Convexes (CVPR 2025 · similarity 0.89)
- GaussianPro: 3D Gaussian Splatting with Progressive Propagation (ICML 2024 · similarity 0.89)
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