Research map / 3D vision / Gaussian splatting
SOGS: Second-Order Anchor for Advanced 3D Gaussian Splatting
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Proposes SOGS, an anchor-based 3D Gaussian splatting method that uses covariance-based second-order anchor features and a selective gradient loss to reduce anchor feature dimension and model size while improving novel view synthesis quality.
Problem
Anchor-based 3D Gaussian splatting (Scaffold-GS) faces a trade-off among anchor feature size, model size, and rendering quality: smaller anchor features shrink the model but degrade Gaussian attribute prediction and cause artifacts.
Approach
Compute a covariance/correlation matrix across anchor feature dimensions over all anchors, take top-M eigenvectors as global co-variation patterns, and combine them with each anchor's feature to augment features without increasing stored anchor size; add a selective gradient loss that weights Sobel gradient-map discrepancies by their error to focus training on hard-to-render textures and edges.
Key results
- On Mip-NeRF360, SOGS with 16-dim anchors reaches PSNR 27.85 and LPIPS 0.221 vs Scaffold-GS (32-dim) 27.50 and 0.252.
- On BungeeNeRF, SOGS (16-dim) improves PSNR from 26.62 to 27.06 and LPIPS from 0.241 to 0.171 over Scaffold-GS (32-dim).
- Ablation on BungeeNeRF: second-order anchor raises PSNR 26.62 to 27.25; adding selective gradient loss further raises it to 27.39.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SOGS instead of Scaffold-GS | Scaffold-GS · Mip-NeRF360 | PSNR: 27.50 -> 27.85 | Helped |
| Use SOGS instead of Scaffold-GS | Scaffold-GS · Tanks&Temples | PSNR: 23.96 -> 24.14 | Helped |
| Use SOGS instead of Scaffold-GS | Scaffold-GS · Deep Blending | PSNR: 30.21 -> 30.29 | Helped |
| Use SOGS instead of Scaffold-GS | Scaffold-GS · BungeeNeRF | PSNR: 26.62 -> 27.06 | Helped |
| Add second-order anchors (ablation) | Scaffold-GS on BungeeNeRF · BungeeNeRF | PSNR: 26.62 -> 27.25 | Helped |
| Add second-order anchors (ablation) | Scaffold-GS on BungeeNeRF · BungeeNeRF | SSIM: 0.865 -> 0.879 | Helped |
| Add second-order anchors (ablation) | Scaffold-GS on BungeeNeRF · BungeeNeRF | LPIPS: 0.241 -> 0.208 | Helped |
| Add selective gradient loss to second-order anchors (ablation) | Scaffold-GS on BungeeNeRF · BungeeNeRF | PSNR: 27.25 -> 27.39 | Helped |
| Add selective gradient loss to second-order anchors (ablation) | Scaffold-GS on BungeeNeRF · BungeeNeRF | SSIM: 0.879 -> 0.887 | Helped |
| Add selective gradient loss to second-order anchors (ablation) | Scaffold-GS on BungeeNeRF · BungeeNeRF | LPIPS: 0.208 -> 0.161 | Helped |
Surprising findings
- SOGS with 12-dim anchors outperforms Scaffold-GS with 32-dim anchors on the reported benchmarks.
Limitations
- Time complexity increases slightly due to the second-order anchor computations
- Comparisons omit HAC and ContextGS because they target storage compression rather than model size
Experimental setup
Datasets: Mip-NeRF360 Tanks&Temples Deep Blending BungeeNeRF
Benchmarks: Mip-NeRF360 Tanks&Temples Deep Blending BungeeNeRF
Metrics: PSNR SSIM LPIPS anchor size
Baselines: 3D-GS Scaffold-GS HAC ContextGS
Builds on: 3D Gaussian Splatting Scaffold-GS Sobel operator
Closest papers by meaning
- ContextGS : Compact 3D Gaussian Splatting with Anchor Level Context Model (NeurIPS 2024 · similarity 0.90)
- FlexGS: Train Once, Deploy Everywhere with Many-in-One Flexible 3D Gaussian Splatting (CVPR 2025 · similarity 0.90)
- Speedy-Splat: Fast 3D Gaussian Splatting with Sparse Pixels and Sparse Primitives (CVPR 2025 · similarity 0.89)
- IBGS: Image-Based Gaussian Splatting (NeurIPS 2025 · similarity 0.89)
- GaussianPro: 3D Gaussian Splatting with Progressive Propagation (ICML 2024 · similarity 0.89)
- 3D-HGS: 3D Half-Gaussian Splatting (CVPR 2025 · similarity 0.89)
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