Sobolev Training for Implicit Neural Representations with Approximated Image Derivatives

The experimental code of "Sobolev Training for Implicit Neural Representations with Approximated Image Derivatives" in ECCV 2022.

Abstract

Recently, Implicit Neural Representations (INRs) parameterized by neural networks have emerged as a powerful and promising tool to represent different kinds of signals due to its continuous, differentiable properties, showing superiorities to classical discretized representations. However, the training of neural networks for INRs only utilizes input-output pairs, and the derivatives of the target output with respect to the input, which can be accessed in some cases, are usually ignored. In this paper, we propose a training paradigm for INRs whose target output is image pixels, to encode image derivatives in addition to image values in the neural network. Specifically, we use finite differences to approximate image derivatives. We show how the training paradigm can be leveraged to solve typical INRs problems, i.e., image regression and inverse rendering, and demonstrate this training paradigm can improve the data-efficiency and generalization capabilities of INRs.

Setup

Environment

• Clone this repo

  git clone https://github.com/megvii-research/Sobolev_INRs.git
  cd Sobolev_INRs

• Install dependencies

  Python 3 dependencies (click to expand)

  * PyTorch >= 1.10 * torchvision * ConfigArgParse * einops * imageio * kornia * matplotlib * numpy * opencv_python * Pillow * scipy * tqdm

  To setup a conda environment:

  conda create -n st_inrs python=3.7
  conda activate st_inrs
  pip install -r requirements.txt

  Data

• Create a directory with command:

  mkdir data

• Download data:
  • Download Set5 for image regression task.
  • Download LLFF data from NeRF authors' drive for inverse rendering task.
  • Download gt_bach.wav and gt_counting.wav from SIREN authors' drive for audio regression task. Put two WAV files to folder Audio.
• Create soft links:

  ln -s [path to nerf_llff_data] ./data
  ln -s [path to Set5] ./data
  ln -s [path to Audio] ./data

Reproducing Experiments

Image Regression

cd Experiments/image_regression
python main.py --config [config txt file]

For example, training with value and derivative supervision on Baby with a sine-based model:

python main.py --config configs/baby/val_der/sine.txt

Inverse Rendering

cd Experiments/inverse_rendering
python train.py --config [config txt file]

For example, train with value and derivative supervision on Fern with a ReLU-based MLP:

python train.py --config configs/fern/val_der/relu.txt

After training for 400K iterations, you can find novel view results in logs/fern/val_der/relu/testset_400000, you can evaluate results with following command and score.txt will be generated in logs/fern/val_der/relu/testset_400000/score.txt:

python eval.py --config configs/fern/val_der/relu.txt

Audio Regression

cd Experiments/audio_regression
python main.py --config [config txt file]

For example, training with value supervision and on Bach with a sine-based model:

python main.py --config configs/bach/val_sine.txt

Citation

If you find our work useful in your research, please cite:

@inproceedings{yuan2022sobolev,
  title={Sobolev Training for Implicit Neural Representations with Approximated Image Derivatives},
  author={Wentao Yuan and Qingtian Zhu and Xiangyue Liu and Yikang Ding and Haotian Zhang and Chi Zhang},
  year={2022},
  booktitle={ECCV},

Acknowledgements

Some codes of image regression task and audio regression task are borrowed from SIREN. The implementation of inverse rendering task are based on NeRF-PyTorch, which is a PyTorch implementation of original NeRF. Thanks to these authors for releasing the code.