BANF: Band-limited Neural Fields for Levels of Detail Reconstruction

TL;DR

BANF tackles aliasing in neural fields by enabling band-limited representations through a simple training-time modification that uses a band-limited interpolation on a regular grid and cascaded optimization to build a multi-band decomposition across $[0,\omega]$, $[\omega_1,\omega_2]$, etc. This approach is architecture-agnostic and robust across 2D and 3D tasks, enabling anti-aliased level-of-detail reconstructions and high-quality mesh extraction without requiring prefiltered ground-truth signals. Empirical results across 2D image fitting, 3D SDF reconstruction, and 3D-from-2D inverse rendering show that BANF improves coarse-scale reconstructions and Nyquist-adherent sampling compared to strong baselines like BACON, iNGP, and NeUS, while preserving fine-scale details. The method offers a practical, broadly applicable tool for frequency-aware neural-field pipelines with potential impact on rendering, simulation, and 3D reconstruction workflows.

Abstract

Largely due to their implicit nature, neural fields lack a direct mechanism for filtering, as Fourier analysis from discrete signal processing is not directly applicable to these representations. Effective filtering of neural fields is critical to enable level-of-detail processing in downstream applications, and support operations that involve sampling the field on regular grids (e.g. marching cubes). Existing methods that attempt to decompose neural fields in the frequency domain either resort to heuristics or require extensive modifications to the neural field architecture. We show that via a simple modification, one can obtain neural fields that are low-pass filtered, and in turn show how this can be exploited to obtain a frequency decomposition of the entire signal. We demonstrate the validity of our technique by investigating level-of-detail reconstruction, and showing how coarser representations can be computed effectively.

Figures (11)

• Figure 1: We introduce BANF, a method for band-limited frequency decomposition in neural fields. Our minimal yet impactful enhancements to the training process achieves anti-aliased coarse-to-fine signal reconstruction, seamlessly integrating with commonly used mesh extraction techniques MarchingCubes, significantly surpassing prior methods in quality. The reconstruction artifacts due to view-dependent effects (i.e. vase bowl not being smooth) are due to the reconstruction baseline we employ, and is orthogonal to our method.
• Figure 2: Filtering by optimization -- We compare two approaches to generate a low-pass version of a neural field's signal. Left shows training a neural field to a 1D signal, and sampling the result a-posteriori on a regular lattice. On the right, our approach trains the neural field in a way that is "sampling aware", as the field is expressed as the (linear) interpolation of sampled field values. In other words, our method executes low-pass filtering during optimization. At the bottom we visualize the signal's spectra, where the baseline's reconstruction is clearly affected by aliasing, while our reconstruction is clearly low-pass filtered.
• Figure 3: Cascaded training -- We visualize our neural field decomposition where each level produces a signal with frequency band $[\boldsymbol{\omega}_{i}, \boldsymbol{\omega}_{i+1}]$. The decomposition is generated by a cascaded optimization akin to the generation of Laplacian pyramids in signal processing. Analogously, as the decomposition is quasi-orthogonal, we can generate the signal at any level through superposition. Image taken from the Kodak dataset kodak.
• Figure 4: A standard neural field (left). Our band-limited neural field (right), which samples the outputs of a neural field $f_w$ on a regular grid and interpolates to output a band-limited signal $\sigma_w(x)$. This enables direct control of the frequency bandwidth $\omega$ of the signal $\sigma_\omega(x)$.
• Figure 5: Interpolation Kernels -- By changing the interpolation kernel we can control the frequency cut in the Fourier domain.