Research map / 3D vision / NeRF and radiance fields
GL-NeRF: Gauss-Laguerre Quadrature Enables Training-Free NeRF Acceleration
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Proposes GL-NeRF, a training-free replacement for NeRF's volume-rendering quadrature that uses Gauss-Laguerre quadrature after a change of variables, cutting color-MLP calls to about 4-32 points per ray with a modest quality drop.
Problem
Volume rendering in NeRF requires many MLP evaluations per ray because the integral is approximated by dense uniform sampling, which makes rendering slow and memory-hungry.
Approach
A change of variables x(t)=∫σ turns the volume rendering integral into a pure exponentially weighted integral of color, so Gauss-Laguerre quadrature can compute it with a few deterministic points chosen where accumulated density equals Laguerre roots; no new networks or data structures are added.
Key results
- On LLFF with TensoRF, GL-NeRF uses 4 MLP calls versus 118.51 for the original sampling, with PSNR 25.63 vs 26.51.
- On NeRF-Synthetic with TensoRF, GL-NeRF uses 4 MLP calls versus 31.08, with PSNR 30.99 vs 32.39.
- On WebGL Lego rendering, GL-NeRF reaches 22.34 FPS versus 5.84 for TensoRF at PSNR 33.09 vs 33.28.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace dense TensoRF rendering samples with GL-NeRF using 4 color MLP calls | TensoRF · LLFF | Avg. MLPs: 118.51 -> 4 | Helped |
| Replace dense TensoRF rendering samples with GL-NeRF using 4 color MLP calls | TensoRF · NeRF-Synthetic | Avg. MLPs: 31.08 -> 4 | Helped |
| Replace vanilla sampling with GL-NeRF using 32 points | Vanilla NeRF · LLFF | PSNR: 27.62 -> 27.21 | Hurt |
| Replace vanilla sampling with GL-NeRF using 32 points | Vanilla NeRF · NeRF-Synthetic | PSNR: 30.63 -> 29.18 | Hurt |
| Apply GL-NeRF rendering | TensoRF · Lego | FPS: 5.84 -> 22.34 | Helped |
| Apply GL-NeRF rendering | InstantNGP · Blender | PSNR: 32.05 -> 30.35 | Hurt |
| Increase the number of sampled points from 1 to 8 per ray (ablation) | GL-NeRF on TensoRF · LLFF | PSNR: 23.49 -> 26.10 | Helped |
| Increase the number of sampled points from 1 to 8 per ray (ablation) | GL-NeRF on TensoRF · LLFF | SSIM: 0.752 -> 0.812 | Helped |
| Increase the number of sampled points from 1 to 8 per ray (ablation) | GL-NeRF on TensoRF · LLFF | LPIPS: 0.166 -> 0.142 | Helped |
Surprising findings
- Using only 4-8 Gauss-Laguerre points per ray gives quality close to the original 100+ point sampling of TensoRF.
- Applying GL-NeRF to vanilla NeRF at test time gives 1.2-2x faster rendering while keeping metrics near the original.
Limitations
- Rendering quality drops noticeably compared to the original sampling, e.g. LPIPS rises on NeRF-Synthetic (0.032 to 0.048 for TensoRF).
- Speedup depends on cheap density estimation; vanilla NeRF still needs a heavy density network, limiting real-time speed.
- The polynomial approximation of the color function is only validated empirically with a relative error up to about 6.5%.
Experimental setup
Datasets: NeRF-Synthetic LLFF
Benchmarks: NeRF-Synthetic LLFF
Metrics: PSNR SSIM LPIPS average MLP calls render time FPS
Baselines: NeRF TensoRF Instant-NGP MC-NeRF
Builds on: NeRF TensoRF Instant-NGP Gauss quadrature
Closest papers by meaning
- NeRFix: fixing subtle mistakes in the quadrature of the NeRF volumetric integral (NeurIPS 2026 · similarity 0.92)
- Rad-NeRF: Ray-decoupled Training of Neural Radiance Field (NeurIPS 2024 · similarity 0.89)
- L0-Sampler: An L0 Model Guided Volume Sampling for NeRF (CVPR 2024 · similarity 0.88)
- Ced-NeRF: A Compact and Efficient Method for Dynamic Neural Radiance Fields (AAAI 2024 · similarity 0.87)
- A General Implicit Framework for Fast NeRF Composition and Rendering (AAAI 2024 · similarity 0.87)
- CF-NeRF: Camera Parameter Free Neural Radiance Fields with Incremental Learning (AAAI 2024 · similarity 0.87)
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