Research map / 3D vision / Gaussian splatting
BG-Triangle: Bezier Gaussian Triangle for 3D Vectorization and Rendering
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Proposes BG-Triangle, a hybrid of Bézier triangle vector primitives and pixel-aligned Gaussians with discontinuity-aware alpha blending and adaptive split/prune, enabling sharp-edged, compact 3D differentiable rendering from coarse point cloud initialization.
Problem
Differentiable rendering with smooth probabilistic proxies (volumes, 3D Gaussians) blurs sharp object boundaries, especially in close-up views, and requires many primitives.
Approach
Use Bézier triangle surfaces as explicit shape primitives whose tessellation yields coordinate/index maps; generate pixel-aligned Gaussian sub-primitives on the fly from them, and softly suppress Gaussian contributions outside each primitive via a boundary-based blending coefficient, so boundaries stay sharp while rendering remains differentiable.
Key results
- On NeRF Synthetic with ~343.5K parameters, BG-Triangle reaches 29.16 PSNR, 0.937 SSIM, 0.050 LPIPS, versus 3DGS at 27.18 PSNR and 0.103 LPIPS at 383.5K parameters.
- In close-up views (test distance 40%), BG-Triangle achieves 21.19 PSNR and 0.306 LPIPS, outperforming 3DGS (20.66, 0.333) and other compact baselines.
- Full-primitive 3DGS still scores higher on PSNR/SSIM (33.79 vs. BG-Triangle's compact results), which the authors acknowledge; BG-Triangle is slightly worse than 3DGS on classic metrics at full scale.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use BG-Triangle instead of 3DGS | BG-Triangle · NeRF Synthetic | PSNR: 27.18 -> 29.16 | Helped |
| use BG-Triangle instead of 3DGS | BG-Triangle · Tanks & Temple | PSNR: 27.56 -> 27.23 | Hurt |
| use BG-Triangle instead of 3DGS | BG-Triangle · NeRF Synthetic close-up | PSNR: 20.66 -> 21.19 | Helped |
| increase attribute-map effective pixel count from 1 to the default setting (ablation) | BG-Triangle · NeRF Synthetic | PSNR: 28.31 -> 29.16 | Helped |
| increase attribute-map effective pixel count from the default setting to 10 (ablation) | BG-Triangle · NeRF Synthetic | PSNR: 29.16 -> 29.67 | Helped |
| add spherical harmonics coefficients (ablation) | BG-Triangle · NeRF Synthetic | PSNR: 27.54 -> 29.16 | Helped |
| add discontinuity-aware blending coefficients (ablation) | BG-Triangle · NeRF Synthetic | PSNR: 28.98 -> 29.16 | Helped |
Surprising findings
- Without the discontinuity-aware blending (w/o B), PSNR is close to the full method, but artifacts appear under zoom-in, indicating Gaussian overfitting to training views.
- The method is slightly worse than 3DGS on PSNR and SSIM at full scale, which the authors attribute to classic metrics not capturing edges and boundaries.
Limitations
- Slightly worse than 3DGS on PSNR and SSIM at full scale.
- Tile-based blending and CUDA rasterization during training are not very efficient, increasing backward time.
- Trades off structural alignment: under close-up views it may misalign structure in favor of sharp boundaries.
Experimental setup
Datasets: NeRF Synthetic Masked Tanks & Temples Synthetic cube and ball toy datasets
Benchmarks: NeRF Synthetic Tanks & Temples (masked)
Metrics: PSNR SSIM LPIPS #Parameters
Baselines: 3DGS Mip-Splatting Mini-Splatting Scaffold-GS
Builds on: 3D Gaussian Splatting Bézier triangle surfaces Mip-Splatting DiffVG
Closest papers by meaning
- Normal-GS: 3D Gaussian Splatting with Normal-Involved Rendering (NeurIPS 2024 · similarity 0.87)
- Evolving High-Quality Rendering and Reconstruction in a Unified Framework with Contribution-Adaptive Regularization (CVPR 2025 · similarity 0.87)
- Bézier Splatting for Fast and Differentiable Vector Graphics Rendering (NeurIPS 2025 · similarity 0.87)
- GSDF: 3DGS Meets SDF for Improved Neural Rendering and Reconstruction (NeurIPS 2024 · similarity 0.87)
- Gaussian Herding across Pens: An Optimal Transport Perspective on Global Gaussian Reduction for 3DGS (NeurIPS 2025 · similarity 0.87)
- Optimized Minimal 3D Gaussian Splatting (NeurIPS 2025 · similarity 0.87)
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