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Description:

pytorchse3 0.0.3

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)

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)
assert torch.allclose(T, eq_T, atol=1e-4)

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
Our numerically stable
so3_log_map is
a PyTorch port of
pytransform3d
Taylor expansions for some coefficients in
se3_log_map
are taken from
H2-Mapping