LieTorch: Tangent Space Backpropagation

Introduction

The LieTorch library generalizes PyTorch to 3D transformation groups. Just as torch.Tensor is a multi-dimensional matrix of scalar elements, lietorch.SE3 is a multi-dimensional matrix of SE3 elements. We support common tensor manipulations such as indexing, reshaping, and broadcasting. Group operations can be composed into computation graphs and backpropagation is automatically peformed in the tangent space of each element. For more details, please see our paper:

Tangent Space Backpropagation for 3D Transformation Groups
Zachary Teed and Jia Deng, CVPR 2021

@inproceedings{teed2021tangent,
  title={Tangent Space Backpropagation for 3D Transformation Groups},
  author={Teed, Zachary and Deng, Jia},
  booktitle={Conference on Computer Vision and Pattern Recognition},
  year={2021},
}

Installation

Requirements:

• Cuda >= 10.1 (with nvcc compiler)
• PyTorch >= 1.6

We recommend installing within a virtual enviornment. Make sure you clone using the --recursive flag. If you are using Anaconda, the following command can be used to install all dependencies

git clone --recursive https://github.com/princeton-vl/lietorch.git
cd lietorch

conda create -n lie_env
conda activate lie_env
conda install scipy pyyaml pytorch torchvision torchaudio cudatoolkit=10.2 -c pytorch

To run the examples, you will need OpenCV and Open3D. Depending on your operating system, OpenCV and Open3D can either be installed with pip or may need to be built from source

pip install opencv-python open3d

Installing:

Clone the repo using the --recursive flag and install using setup.py (may take up to 10 minutes)

git clone --recursive https://github.com/princeton-vl/lietorch.git
python setup.py install
./run_tests.sh

Overview

LieTorch currently supports the 3D transformation groups.

Each group supports the following operations:

Simple Example:

Compute the angles between all pairs of rotation matrices

import torch
from lietorch import SO3

phi = torch.randn(8000, 3, device='cuda', requires_grad=True)
R = SO3.exp(phi)

# relative rotation matrix, SO3 ^ {100 x 100}
dR = R[:,None].inv() * R[None,:]

# 100x100 matrix of angles
ang = dR.log().norm(dim=-1)

# backpropogation in tangent space
loss = ang.sum()
loss.backward()

Examples

We provide real use cases in the examples directory

1. Pose Graph Optimization
2. Deep SE3/Sim3 Registrtion
3. RGB-D SLAM / VO

Acknowledgements

Many of the Lie Group implementations are adapted from Sophus.