RoMa: A lightweight library to deal with 3D rotations in PyTorch.

RoMa (which stands for Rotation Manipulation) provides differentiable mappings between 3D rotation representations, mappings from Euclidean to rotation space, and various utilities related to rotations.

It is implemented in PyTorch and aims to be an easy-to-use and reasonably efficient toolbox for Machine Learning and gradient-based optimization.

Documentation

Latest documentation is available here: https://naver.github.io/roma/.

Below are some examples of use of RoMa:

import torch
import roma

# Arbitrary numbers of batch dimensions are supported, for convenience.
batch_shape = (2, 3)

# Conversion between rotation representations
rotvec = torch.randn(batch_shape + (3,))
q = roma.rotvec_to_unitquat(rotvec)
R = roma.unitquat_to_rotmat(q)
Rbis = roma.rotvec_to_rotmat(rotvec)
euler_angles = roma.unitquat_to_euler('xyz', q, degrees=True)

# Regression of a rotation from an arbitrary input:
# Special Procrustes orthonormalization of a 3x3 matrix
R1 = roma.special_procrustes(torch.randn(batch_shape + (3, 3)))
# Conversion from a 6D representation
R2 = roma.special_gramschmidt(torch.randn(batch_shape + (3, 2)))
# From the 10 coefficients of a 4x4 symmetric matrix
q = roma.symmatrixvec_to_unitquat(torch.randn(batch_shape + (10,)))

# Metrics on the rotation space
R1, R2 = roma.random_rotmat(size=5), roma.random_rotmat(size=5)
theta = roma.utils.rotmat_geodesic_distance(R1, R2)
cos_theta = roma.utils.rotmat_cosine_angle(R1.transpose(-2, -1) @ R2)

# Operations on quaternions
q_identity = roma.quat_product(roma.quat_conjugation(q), q)

# Spherical interpolation between rotation vectors (shortest path)
rotvec0, rotvec1 = torch.randn(batch_shape + (3,)), torch.randn(batch_shape + (3,))
rotvec_interpolated = roma.rotvec_slerp(rotvec0, rotvec1, steps)

# Rigid transformation T composed of a rotation part R and a translation part t
t = torch.randn(batch_shape + (3,))
T = roma.Rigid(R, t)
# Composing and inverting transformations
identity = T @ T.inverse()
# Casting the result to a batch of 4x4 homogeneous matrices
M = identity.to_homogeneous()

Installation

The easiest way to install RoMa is to use pip:

pip install roma

Alternatively one can install the latest version of RoMa directly from the source repository:

pip install git+https://github.com/naver/roma

With old pytorch versions (torch<1.8), we recommend installing torch-batch-svd to achieve a significant speed-up with special_procrustes on CUDA GPUs. You can check that this module is properly loaded using the function roma.utils.is_torch_batch_svd_available(). With recent pytorch installations (torch>=1.8), torch-batch-svd is no longer needed or used.

License

RoMa, Copyright (c) 2020 NAVER Corp., is licensed under the 3-Clause BSD License (see license).

Bits of code were adapted from SciPy. Documentation is generated, distributed and displayed with the support of Sphinx and other materials (see notice).

References

For a more in-depth discussion regarding differentiable mappings on the rotation space, please refer to:

• Romain Brégier, Deep Regression on Manifolds: a 3D Rotation Case Study. in 2021 International Conference on 3D Vision (3DV), 2021.

Please cite this work in your publications:

@inproceedings{bregier2021deepregression,
	title={Deep Regression on Manifolds: a {3D} Rotation Case Study},
	author={Br{\'e}gier, Romain},
	journal={2021 International Conference on 3D Vision (3DV)},
	year={2021}
}