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BANF: Band-Limited Neural Fields for Levels of Detail Reconstruction
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Shows that training a neural field by fitting its linear-interpolated grid samples yields an implicit low-pass filter, and uses cascaded residual training to decompose neural fields into frequency bands for anti-aliased level-of-detail reconstruction.
Problem
Neural fields lack a direct filtering mechanism, so frequency decomposition and anti-aliased level-of-detail reconstruction (e.g. marching cubes on regular grids) are hard to achieve without heuristics or specialized architectures.
Approach
Fitting a neural field whose output is the linear (or sinc) interpolation of its values on a regular lattice acts as a low-pass filter during optimization; a cascaded, Laplacian-pyramid-like training over levels then yields band-pass components that sum to the full signal, with no architecture change.
Key results
- On Synthetic NeRF at 1/8x scale, BANF averages 11.4 Chamfer distance vs 17.3 for NeuS (x10^-2, lower better).
- On MobileBrick at 1/4x scale, BANF averages 7.39 Chamfer distance vs 15.5 for NeuS (x10^-3).
- On SDF fitting for Asian Dragon at 32 resolution, BANF achieves Chamfer-L2 1.23 vs 1.97 for iNGP (x10^-2).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply BANF frequency decomposition during NeUS training | NeUS · Synthetic NeRF Dataset, 1/8x | Chamfer Distance (×10−2): 17.3 -> 11.4 | Helped |
| Apply BANF frequency decomposition during NeUS training | NeUS · Synthetic NeRF Dataset, 1x | Chamfer Distance (×10−2): 7.45 -> 7.45 | No clear effect |
| Apply BANF frequency decomposition during NeUS training | NeUS · MobileBrick, 1/4x | Chamfer Distance (×10−3): 15.5 -> 7.39 | Helped |
| Apply BANF frequency decomposition during NeUS training | NeUS · Asian Dragon, 32 | Chamfer-L2 distance (×102): 1.97 -> 1.23 | Helped |
| Apply BANF frequency decomposition during iNGP training | iNGP · Thai Statue, 128 | Chamfer-L2 distance (×102): 0.38 -> 0.40 | Hurt |
| Use BANF with different field representations (ablation) | BANF · Stanford shapes, resolutions 32, 64, and 128 | Chamfer-L2 distance (×10−2): HashGrid: 1.35, 0.82, 0.54; Dense: 1.38, 0.83, 0.55; MLP: 1.37, 0.79, 0.58 | No clear effect |
Surprising findings
- Bilinear/linear interpolation in feature space is itself a filter, but it acts on the feature space rather than the output co-domain, which the authors note as an interesting distinction.
- Coarse-scale quality gains are largest where Nyquist is violated; at full resolution BANF and iNGP perform similarly.
Limitations
- Focused on uniformly sampled signals; does not handle contracted/unbounded representations used in NeRF.
- Highly memory-intensive at higher grid resolutions in current implementation.
- Linear interpolation is only an approximate low-pass filter (sinc^2 spectrum).
Experimental setup
Datasets: DIV2K Stanford Asian Dragon Thai Statue Synthetic NeRF MobileBrick Kodak
Benchmarks: DIV2K Synthetic NeRF MobileBrick Stanford SDF meshes
Metrics: Chamfer distance PSNR
Baselines: iNGP BACON NeuS
Builds on: iNGP NeuS BACON Multiplicative Filter Networks Laplacian pyramids
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