# BACON: Band-limited Coordinate Networks for Multiscale Scene Representation

arXiv: https://arxiv.org/abs/2112.04645 · HTML: https://mlsanity.com/paper/2112.04645/

## Key facts

- Cited by 143 papers in the map (data through 14 Oct 2026).
- Builds on 62 of its 92 references that are in the map.
- First posted on arXiv 9 Dec 2021.

## Builds on (most cited first, 30 of 62)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [pi-GAN: Periodic Implicit Generative Adversarial Networks for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2012.00926/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)

## Built on by (most cited first, 30 of 143)

- [Generative Novel View Synthesis with 3D-Aware Diffusion Models](https://mlsanity.com/paper/2304.02602/) (2023)
- [BungeeNeRF: Progressive Neural Radiance Field for Extreme Multi-scale Scene Rendering](https://mlsanity.com/paper/2112.05504/) (2021)
- [SPIn-NeRF: Multiview Segmentation and Perceptual Inpainting with Neural Radiance Fields](https://mlsanity.com/paper/2211.12254/) (2022)
- [Tri-MipRF: Tri-Mip Representation for Efficient Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2307.11335/) (2023)
- [NeuSG: Neural Implicit Surface Reconstruction with 3D Gaussian Splatting Guidance](https://mlsanity.com/paper/2312.00846/) (2023)
- [StreetSurf: Extending Multi-view Implicit Surface Reconstruction to Street Views](https://mlsanity.com/paper/2306.04988/) (2023)
- [F2-NeRF: Fast Neural Radiance Field Training with Free Camera Trajectories](https://mlsanity.com/paper/2303.15951/) (2023)
- [Variable Bitrate Neural Fields](https://mlsanity.com/paper/2206.07707/) (2022)
- [Operator Learning with Neural Fields: Tackling PDEs on General Geometries](https://mlsanity.com/paper/2306.07266/) (2023)
- [AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions](https://mlsanity.com/paper/2212.07564/) (2022)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions](https://mlsanity.com/paper/2309.15426/) (2023)
- [SparsePose: Sparse-View Camera Pose Regression and Refinement](https://mlsanity.com/paper/2211.16991/) (2022)
- [NIRVANA: Neural Implicit Representations of Videos with Adaptive Networks and Autoregressive Patch-wise Modeling](https://mlsanity.com/paper/2212.14593/) (2022)
- [Watch Your Steps: Local Image and Scene Editing by Text Instructions](https://mlsanity.com/paper/2308.08947/) (2023)
- [VCR-GauS: View Consistent Depth-Normal Regularizer for Gaussian Surface Reconstruction](https://mlsanity.com/paper/2406.05774/) (2024)
- [Neural Signed Distance Function Inference through Splatting 3D Gaussians Pulled on Zero-Level Set](https://mlsanity.com/paper/2410.14189/) (2024)
- [CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimization](https://mlsanity.com/paper/2210.02757/) (2022)
- [CG3D: Compositional Generation for Text-to-3D via Gaussian Splatting](https://mlsanity.com/paper/2311.17907/) (2023)
- [Reference-guided Controllable Inpainting of Neural Radiance Fields](https://mlsanity.com/paper/2304.09677/) (2023)
- [Hi-LASSIE: High-Fidelity Articulated Shape and Skeleton Discovery from Sparse Image Ensemble](https://mlsanity.com/paper/2212.11042/) (2022)
- [LODE: Locally Conditioned Eikonal Implicit Scene Completion from Sparse LiDAR](https://mlsanity.com/paper/2302.14052/) (2023)
- [DreamSparse: Escaping from Plato's Cave with 2D Frozen Diffusion Model Given Sparse Views](https://mlsanity.com/paper/2306.03414/) (2023)
- [Active Neural Mapping](https://mlsanity.com/paper/2308.16246/) (2023)
- [GenSDF: Two-Stage Learning of Generalizable Signed Distance Functions](https://mlsanity.com/paper/2206.02780/) (2022)
- [DINER: Disorder-Invariant Implicit Neural Representation](https://mlsanity.com/paper/2211.07871/) (2022)
- [Neural Fourier Filter Bank](https://mlsanity.com/paper/2212.01735/) (2022)
- [Disorder-invariant Implicit Neural Representation](https://mlsanity.com/paper/2304.00837/) (2023)
- [ResFields: Residual Neural Fields for Spatiotemporal Signals](https://mlsanity.com/paper/2309.03160/) (2023)
- [Residual Multiplicative Filter Networks for Multiscale Reconstruction](https://mlsanity.com/paper/2206.00746/) (2022)

## Abstract (arXiv)

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.