Bacon: Band-limited Coordinate Networks for Multiscale Scene Representation

Coordinate-based networks have emerged as a powerful tool for 3D representation and scene reconstruction. These networks are trained to map continuous input coordinates to the value of a signal at each point. Still, current architectures are black boxes: their spectral characteristics cannot be easily analyzed, and their behavior at unsupervised points is difficult to predict. Moreover, these networks are typically trained to represent a signal at a single scale, so naive downsampling or upsampling results in artifacts. We introduce band-limited coordinate networks (BACON), a network architecture with an analytical Fourier spectrum. Bacon has constrained behavior at unsupervised points, can be designed based on the spectral characteristics of the represented signal, and can represent signals at multiple scales without per-scale supervision. We demonstrate Bacon for multiscale neural representation of images, radiance fields, and 3D scenes using signed distance functions and show that it outperforms conventional single-scale coordinate networks in terms of interpretability and quality.