DeltaConv

[Paper] [Project page]

Code for the SIGGRAPH 2022 paper "DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds" by Ruben Wiersma, Ahmad Nasikun, Elmar Eisemann, and Klaus Hildebrandt.

Anisotropic convolution is a central building block of CNNs but challenging to transfer to surfaces. DeltaConv learns combinations and compositions of operators from vector calculus, which are a natural fit for curved surfaces. The result is a simple and robust anisotropic convolution operator for point clouds with state-of-the-art results.

Top: unlike images, surfaces have no global coordinate system. Bottom: DeltaConv learns both scalar and vector features using geometric operators.

Contents

• Installation
• Replicating the experiments
• Tests
• Citation

Installation

1. Clone this repository:

git clone https://github.com/rubenwiersma/deltaconv.git

2. Create a conda environment from the environment.yml:

conda env create -n deltaconv -f environment.yml

Done!

Manual installation

If you wish to install DeltaConv in your own environment, proceed as follows.

1. Make sure that you have installed:

   • Numpy - pip install numpy
   • PyTorch - see instructions
   • PyG - conda install pyg -c pyg

2. Install DeltaConv:

pip install deltaconv

Building DeltaConv for yourself

1. Make sure you clone the repository with submodules:

git clone --recurse-submodules https://github.com/rubenwiersma/deltaconv.git

If you have already cloned the repository without submodules, you can fix it with git submodule update --init --recursive.

2. Install from folder:

cd [root_folder]
pip install

Replicating the experiments

See the README.md in replication_scripts for instructions on replicating the experiments and using the pre-trained weights (available in experiments/pretrained_weights).

In short, you can run bash scripts to replicate our experiments. For example, evaluating pre-trained weights on ShapeNet:

cd [root_folder]
conda activate deltaconv
bash replication_scripts/pretrained/shapenet.sh

You can also directly run the python files in experiments:

python experiments/train_shapenet.py

Use the -h or --help flag to find out which arguments can be passed to the training script:

python experiments/train_shapenet.py -h

You can keep track of the training process with tensorboard:

tensorboard logdir=experiments/runs/shapenet_all

Anisotropic Diffusion

The code that was used to generate Figure 2 from the paper and Figure 2 and 3 from the supplement is a notebook in the folder experiments/anisotropic_diffusion.

Data

The training scripts assume that you have a data folder in experiments. ModelNet40 and ShapeNet download the datasets from a public repository. Instructions to download the data for human body shape segmentation, SHREC, and ScanObjectNN are given in the training scripts.

Tests

In the paper, we make statements about a number of properties of DeltaConv that are either a result of prior work or due to the implementation. We created a test suite to ensure that these properties hold for the implementation, along with unit tests for each module. For example:

• Section 3.6, 3.7: Vector MLPs are equivariant to norm-preserving transformations, or coordinate-independent (rotations, reflections)
  • test/nn/test_mlp.py
  • test/nn/test_nonlin.py
• Section 3.7: DeltaConv is coordinate-independent, a forward pass on a shape with one choice of bases leads to the same output and weight updates when run with different bases
  • test/nn/test_deltaconv.py
• Introduction, section 3.2: The operators are robust to noise and outliers.
  • test/geometry/test_grad_div.py
• Supplement, section 1: Vectors can be mapped between points with equation (15).
  • test/geometry/test_grad_div.py

Citations

Please cite our paper if this code contributes to an academic publication:

@Article{Wiersma2022DeltaConv,
  author    = {Ruben Wiersma, Ahmad Nasikun, Elmar Eisemann, Klaus Hildebrandt},
  journal   = {Transactions on Graphics},
  title     = {DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds},
  year      = {2022},
  month     = jul,
  number    = {4},
  volume    = {41},
  doi       = {10.1145/3528223.3530166},
  publisher = {ACM},
}

The farthest point sampling code relies on Geometry Central:

@misc{geometrycentral,
  title = {geometry-central},
  author = {Nicholas Sharp and Keenan Crane and others},
  note = {www.geometry-central.net},
  year = {2019}
}

And we make use of PyG (and underlying packages) to load point clouds, compute sparse matrix products, and compute nearest neighbors:

@inproceedings{Fey/Lenssen/2019,
  title={Fast Graph Representation Learning with {PyTorch Geometric}},
  author={Fey, Matthias and Lenssen, Jan E.},
  booktitle={ICLR Workshop on Representation Learning on Graphs and Manifolds},
  year={2019},
}