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https://github.com/eigenvivek/pytorchse3
Numerically stable implementation of batched SE(3) exponential and logarithmic maps
https://github.com/eigenvivek/pytorchse3
se3
Last synced: about 2 months ago
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Numerically stable implementation of batched SE(3) exponential and logarithmic maps
- Host: GitHub
- URL: https://github.com/eigenvivek/pytorchse3
- Owner: eigenvivek
- License: mit
- Created: 2023-12-05T16:12:15.000Z (about 1 year ago)
- Default Branch: main
- Last Pushed: 2023-12-07T18:49:25.000Z (about 1 year ago)
- Last Synced: 2024-04-08T20:13:02.716Z (9 months ago)
- Topics: se3
- Language: Python
- Homepage: https://vivekg.dev/pytorchse3/
- Size: 337 KB
- Stars: 2
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
pytorchse3
================
**⚠️ PyTorch3D v0.7.6 [improved the numerical stability](https://github.com/facebookresearch/pytorch3d/commit/292acc71a33bf389225ef02af237dd82a8319f59) of their `so3_log_map`/`so3_exp_map`, addressing the main issues fixed by this package. Therefore, you should install PyTorch3D instead for SO(3)/SE(3) transformations.**
## Install
``` sh
pip install pytorchse3
```
## How to use
``` python
import torch
from pytorchse3.se3 import se3_exp_map, se3_log_map
```
Here are two transformation matrices for which `PyTorch3D` recovers the
wrong log map (see [this
issue](https://github.com/facebookresearch/pytorch3d/issues/1609?notification_referrer_id=NT_kwDOAcYOvLM3MzY1NTAxMTY0OjI5NzU3MTE2#issuecomment-1839450529)).
``` python
T = torch.Tensor(
[
[
[-0.7384057045, 0.3333132863, -0.5862244964, 0.0000000000],
[0.3520625532, -0.5508944392, -0.7566816807, 0.0000000000],
[-0.5751599669, -0.7651259303, 0.2894364297, 0.0000000000],
[-0.1840534210, -0.1836946011, 0.9952554703, 1.0000000000],
],
[
[-0.7400283217, 0.5210028887, -0.4253400862, 0.0000000000],
[0.5329059958, 0.0683888718, -0.8434065580, 0.0000000000],
[-0.4103286564, -0.8508108258, -0.3282552958, 0.0000000000],
[-0.1197679043, 0.1799146235, 0.5538908839, 1.0000000000],
],
],
).transpose(-1, -2)
```
`pytorchse3` computes the correct log map.
``` python
log_T_vee = se3_log_map(T)
log_T_vee
```
tensor([[ 1.1319, 1.4831, -2.5131, -0.8503, -0.1170, 0.7346],
[ 1.1288, 2.2886, -1.8147, -0.8812, 0.0367, -0.1004]])
Exponentiating the log map recovers the original transformation matrix
with 1e-4 absolute error.
``` python
eq_T = se3_exp_map(log_T_vee)
assert torch.allclose(T, eq_T, atol=1e-4)
```
``` python
T - eq_T
```
tensor([[[-9.2983e-06, -2.3842e-07, 1.1504e-05, 2.9802e-08],
[-5.1558e-06, 8.5235e-06, -8.6427e-06, -2.9802e-08],
[ 8.6427e-06, -6.4373e-06, 4.4703e-07, 0.0000e+00],
[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00]],
[[ 8.0466e-06, 1.6212e-05, 6.0201e-06, -3.7253e-08],
[ 4.5896e-06, 8.6352e-06, 3.3975e-06, 2.9802e-08],
[-8.5831e-06, 1.0610e-05, -1.6809e-05, 0.0000e+00],
[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00]]])
## References
- `pytorchse3` implements log/exp maps defined in Section 2 and 3 of
[Ethan Eade’s tutorial](https://ethaneade.com/lie.pdf)
- Our numerically stable
[`so3_log_map`](https://vivekg.dev/pytorchse3/so3.html#so3_log_map) is
a PyTorch port of
[`pytransform3d`](https://github.com/dfki-ric/pytransform3d/blob/c45e817c4a7960108afe9f5259542c8376c0e89a/pytransform3d/rotations/_conversions.py#L1719-L1787)
- Taylor expansions for some coefficients in
[`se3_log_map`](https://vivekg.dev/pytorchse3/se3.html#se3_log_map)
are taken from
[`H2-Mapping`](https://github.com/SYSU-STAR/H2-Mapping/blob/11b8ab15f3302ccb2b4b3d2b30f76d86dcfcde2c/mapping/src/se3pose.py#L89-L118)