Numerically stable implementations of batched SE(3) exp and log maps
Project description
pytorchse3
Install
pip install pytorchse3
How to use
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).
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)
T
tensor([[[-0.7384, 0.3521, -0.5752, -0.1841],
[ 0.3333, -0.5509, -0.7651, -0.1837],
[-0.5862, -0.7567, 0.2894, 0.9953],
[ 0.0000, 0.0000, 0.0000, 1.0000]],
[[-0.7400, 0.5329, -0.4103, -0.1198],
[ 0.5210, 0.0684, -0.8508, 0.1799],
[-0.4253, -0.8434, -0.3283, 0.5539],
[ 0.0000, 0.0000, 0.0000, 1.0000]]])
pytorchse3
computes the correct log map.
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.
eq_T = se3_exp_map(log_T_vee)
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]]])
assert torch.allclose(
T,
eq_T,
atol=1e-4,
)
References
pytorchse3
implements log/exp maps defined in Section 2 and 3 of Ethan Eade’s tutorial- Our numerically stable
so3_log_map
is a PyTorch port ofpytransform3d
- Taylor expansions for some coefficients in
se3_log_map
are taken fromH2-Mapping
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