Official PyTorch implementation of BACON.
BACON: Band-limited Coordinate Networks for Multiscale Scene Representation
David B. Lindell*, Dave Van Veen, Jeong Joon Park, Gordon Wetzstein
Stanford University

To setup a conda environment use these commands

conda env create -f environment.yml
conda activate bacon

# download all datasets
python download_datasets.py

Now you can train networks to fit a 1D function, images, signed distance fields, or neural radiance fields with the following commands.

cd experiments
python train_1d.py --config ./config/1d/bacon_freq1.ini  # train 1D function
python train_img.py --config ./config/img/bacon.ini  # train image
python train_sdf.py --config ./config/sdf/bacon_armadillo.ini  # train SDF
python train_radiance_field.py --config ./config/nerf/bacon_lr.ini  # train NeRF

To visualize outputs in Tensorboard, run the following.

tensorboard --logdir=../logs --port=6006

Band-limited coordinate networks have an analytical Fourier spectrum and interpretible behavior. We demonstrate using these networks for fitting simple 1D signals, images, 3D shapes via signed distance functions and neural radiance fields.

Datasets can be downloaded using the download_datasets.py script. This script

• downloads the synthetic Blender dataset from the original NeRF paper,
• generates a multiscale version of the Blender dataset,
• downloads 3D models originating from the Stanford 3D Scanning Repository, which we have adjusted to make watertight, and
• downloads an example image from the Kodak dataset.

We provide scripts for training and configuration files to reproduce the results in the paper.

To run the 1D examples, use the experiments/train_1d.py script with any of the config files in experiments/config/1d. These scripts allow training models with BACON, Fourier Features, or SIREN. For example, to train a BACON model you can run

python train_1d.py --config ./config/1d/bacon_freq1.ini

To change the bandwidth of BACON, adjust the maximum frequency with the --max_freq flag. This sets network-equivalent sampling rate used to represent the signal. For example, if the signal you wish to represent has a maximum frequency of 5 cycles per unit interval, this value should be set to at least the Nyquist rate of 2 samples per cycle or 10 samples per unit interval. By default, the frequencies represented by BACON are quantized to intervals of 2*pi; thus, the network is periodic over an interval from -0.5 to 0.5. That is, the output of the network will repeat for input coordinates that exceed an absolute value of 0.5.

Image fitting can be performed using the config files in experiments/config/img and the train_img.py script. We support training BACON, Fourier Features, SIREN, and networks with the positional encoding from Mip-NeRF.

Config files for SDF fitting are in experiments/config/sdf and can be used with the train_sdf.py script. Be sure to download the example datasets before running this script.

We also provide a rendering script to extract meshes from the trained models. The render_sdf.py program extracts a mesh using marching cubes and, optionally, our proposed multiscale adaptive SDF evaluation procedure.

Use the config files in experiments/config/nerf with the train_radiance_field.py script to train neural radiance fields. Note that training the full resolution model can takes a while (a few days) so it may be easier to train a low-resolution model to get started. We provide a low-resolution config file in experiments/config/nerf/bacon_lr.ini.

To render output images from a trained model, use the render_nerf.py script. Note that the Blender synthetic datasets should be downloaded and the multiscale dataset generated before running this script.

Finally, we also show a visualization of our initialization scheme in experiments/plot_activation_distributions.py. As shown in the paper, our initialization scheme prevents the distribution of activations from becoming vanishingly small, even for deep networks.

For convenience, we include pretrained models for the SDF fitting and NeRF reconstruction tasks in the pretrained_models directory. The outputs of these models can be rendered directly using the experiments/render_sdf.py and experiments/render_nerf.py scripts.

@article{lindell2021bacon,
author = {Lindell, David B. and Van Veen, Dave and Park, Jeong Joon and Wetzstein, Gordon},
title = {BACON: Band-limited coordinate networks for multiscale scene representation},
journal = {arXiv preprint arXiv:2112.04645},
year={2021}
}

This project was supported in part by a PECASE by the ARO and NSF award 1839974.