Geometric Mesh CNN

The code in this repository is an implementation of the Gauge Equivariant Mesh CNN introduced in the paper Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphsDownload PDF by Pim de Haan, Maurice Weiler, Taco Cohen and Max Welling, presented at ICLR 2021.

We would like to thank Ruben Wiersma as his implementation of Harmonic Surface Networks served as an inspiration for some parts of the code. Furthermore, we would like to thank Julian Suk for beta-testing the code.

Installation & dependencies

Make sure the following dependencies are installed:

• Python (tested on 3.8)
• Pytorch (tested on 1.8)
• Pytorch Geometric (tested on 1.6.3)
• Conda

Then to install, clone this repository and install the gem_cnn package by executing in this directory:

pip install .

Docker

Alternatively, if you have a GPU with CUDA 11.1 and have set up docker, then you can easily run the experiment at experiments/shapes.py in the following way:.

To build the image run in this directory:

docker build . -t gem_cnn_demo

Then to run:

docker run -it --rm --runtime=nvidia gem_cnn_demo python experiments/shapes.py

In order to run the FAUST experiments via Docker, we recommend mounting the local data folder inside the docker container by running:

docker run -it --rm --runtime=nvidia -v $(pwd)/data:/workspace/data gem_cnn_demo python experiments/faust_direct.py

Then run once, and follow instructions on how to download the dataset. Then run again to train the FAUST model.

Usage

The code implements a graph convolution with Pytorch Geometric.

Example experiments

In the folder experiments, the following examples are given:

• experiments/shapes.py a simple toy experiment to classify geometric shapes.
• experiments/faust_direct.py an implementation of a network similar the network used in our paper on the FAUST dataset. It does message passing directly over the edges of the mesh and does not use pooling. The used input features are the non-equivariant XYZ coordinates.
• experiments/faust_pool.py is an alternative implementation for FAUST. It uses convolution over larger distances than direct neighbours, pooling and the equivariant matrix features.

All example experiments use Pytorch-Ignite, but the GEM-CNN code does not depend on this.

Reference

If you find our work useful, please cite

@inproceedings{dehaan2021,  
  title={Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs},  
  author={Pim de Haan and Maurice Weiler and Taco Cohen and Max Welling}
  booktitle={International Conference on Learning Representations},  
  year={2021},  
  url={https://openreview.net/forum?id=Jnspzp-oIZE}  
}

Export

This software may be subject to U.S. and international export, re-export, or transfer (“export”) laws. Diversion contrary to U.S. and international law is strictly prohibited.