mirror of
https://github.com/facebookresearch/pytorch3d.git
synced 2025-08-02 03:42:50 +08:00
34a0df0630
Summary: Fixes the case where the rotation angle is exactly 0/PI. Added a test for `so3_log_map(identity_matrix)`. Reviewed By: nikhilaravi Differential Revision: D21477078 fbshipit-source-id: adff804da97f6f0d4f50aa1f6904a34832cb8bfe
220 lines
8.1 KiB
Python
220 lines
8.1 KiB
Python
# Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.
|
|
|
|
|
|
import math
|
|
import unittest
|
|
|
|
import numpy as np
|
|
import torch
|
|
from common_testing import TestCaseMixin
|
|
from pytorch3d.transforms.so3 import (
|
|
hat,
|
|
so3_exponential_map,
|
|
so3_log_map,
|
|
so3_relative_angle,
|
|
)
|
|
|
|
|
|
class TestSO3(TestCaseMixin, unittest.TestCase):
|
|
def setUp(self) -> None:
|
|
super().setUp()
|
|
torch.manual_seed(42)
|
|
np.random.seed(42)
|
|
|
|
@staticmethod
|
|
def init_log_rot(batch_size: int = 10):
|
|
"""
|
|
Initialize a list of `batch_size` 3-dimensional vectors representing
|
|
randomly generated logarithms of rotation matrices.
|
|
"""
|
|
device = torch.device("cuda:0")
|
|
log_rot = torch.randn((batch_size, 3), dtype=torch.float32, device=device)
|
|
return log_rot
|
|
|
|
@staticmethod
|
|
def init_rot(batch_size: int = 10):
|
|
"""
|
|
Randomly generate a batch of `batch_size` 3x3 rotation matrices.
|
|
"""
|
|
device = torch.device("cuda:0")
|
|
|
|
# TODO(dnovotny): replace with random_rotation from random_rotation.py
|
|
rot = []
|
|
for _ in range(batch_size):
|
|
r = torch.qr(torch.randn((3, 3), device=device))[0]
|
|
f = torch.randint(2, (3,), device=device, dtype=torch.float32)
|
|
if f.sum() % 2 == 0:
|
|
f = 1 - f
|
|
rot.append(r * (2 * f - 1).float())
|
|
rot = torch.stack(rot)
|
|
|
|
return rot
|
|
|
|
def test_determinant(self):
|
|
"""
|
|
Tests whether the determinants of 3x3 rotation matrices produced
|
|
by `so3_exponential_map` are (almost) equal to 1.
|
|
"""
|
|
log_rot = TestSO3.init_log_rot(batch_size=30)
|
|
Rs = so3_exponential_map(log_rot)
|
|
dets = torch.det(Rs)
|
|
self.assertClose(dets, torch.ones_like(dets), atol=1e-4)
|
|
|
|
def test_cross(self):
|
|
"""
|
|
For a pair of randomly generated 3-dimensional vectors `a` and `b`,
|
|
tests whether a matrix product of `hat(a)` and `b` equals the result
|
|
of a cross product between `a` and `b`.
|
|
"""
|
|
device = torch.device("cuda:0")
|
|
a, b = torch.randn((2, 100, 3), dtype=torch.float32, device=device)
|
|
hat_a = hat(a)
|
|
cross = torch.bmm(hat_a, b[:, :, None])[:, :, 0]
|
|
torch_cross = torch.cross(a, b, dim=1)
|
|
self.assertClose(torch_cross, cross, atol=1e-4)
|
|
|
|
def test_bad_so3_input_value_err(self):
|
|
"""
|
|
Tests whether `so3_exponential_map` and `so3_log_map` correctly return
|
|
a ValueError if called with an argument of incorrect shape or, in case
|
|
of `so3_exponential_map`, unexpected trace.
|
|
"""
|
|
device = torch.device("cuda:0")
|
|
log_rot = torch.randn(size=[5, 4], device=device)
|
|
with self.assertRaises(ValueError) as err:
|
|
so3_exponential_map(log_rot)
|
|
self.assertTrue("Input tensor shape has to be Nx3." in str(err.exception))
|
|
|
|
rot = torch.randn(size=[5, 3, 5], device=device)
|
|
with self.assertRaises(ValueError) as err:
|
|
so3_log_map(rot)
|
|
self.assertTrue("Input has to be a batch of 3x3 Tensors." in str(err.exception))
|
|
|
|
# trace of rot definitely bigger than 3 or smaller than -1
|
|
rot = torch.cat(
|
|
(
|
|
torch.rand(size=[5, 3, 3], device=device) + 4.0,
|
|
torch.rand(size=[5, 3, 3], device=device) - 3.0,
|
|
)
|
|
)
|
|
with self.assertRaises(ValueError) as err:
|
|
so3_log_map(rot)
|
|
self.assertTrue(
|
|
"A matrix has trace outside valid range [-1-eps,3+eps]."
|
|
in str(err.exception)
|
|
)
|
|
|
|
def test_so3_exp_singularity(self, batch_size: int = 100):
|
|
"""
|
|
Tests whether the `so3_exponential_map` is robust to the input vectors
|
|
the norms of which are close to the numerically unstable region
|
|
(vectors with low l2-norms).
|
|
"""
|
|
# generate random log-rotations with a tiny angle
|
|
log_rot = TestSO3.init_log_rot(batch_size=batch_size)
|
|
log_rot_small = log_rot * 1e-6
|
|
R = so3_exponential_map(log_rot_small)
|
|
# tests whether all outputs are finite
|
|
R_sum = float(R.sum())
|
|
self.assertEqual(R_sum, R_sum)
|
|
|
|
def test_so3_log_singularity(self, batch_size: int = 100):
|
|
"""
|
|
Tests whether the `so3_log_map` is robust to the input matrices
|
|
who's rotation angles are close to the numerically unstable region
|
|
(i.e. matrices with low rotation angles).
|
|
"""
|
|
# generate random rotations with a tiny angle
|
|
device = torch.device("cuda:0")
|
|
identity = torch.eye(3, device=device)
|
|
rot180 = identity * torch.tensor([[1.0, -1.0, -1.0]], device=device)
|
|
r = [identity, rot180]
|
|
r.extend(
|
|
[
|
|
torch.qr(identity + torch.randn_like(identity) * 1e-4)[0]
|
|
for _ in range(batch_size - 2)
|
|
]
|
|
)
|
|
r = torch.stack(r)
|
|
# the log of the rotation matrix r
|
|
r_log = so3_log_map(r)
|
|
# tests whether all outputs are finite
|
|
r_sum = float(r_log.sum())
|
|
self.assertEqual(r_sum, r_sum)
|
|
|
|
def test_so3_log_to_exp_to_log_to_exp(self, batch_size: int = 100):
|
|
"""
|
|
Check that
|
|
`so3_exponential_map(so3_log_map(so3_exponential_map(log_rot)))
|
|
== so3_exponential_map(log_rot)`
|
|
for a randomly generated batch of rotation matrix logarithms `log_rot`.
|
|
Unlike `test_so3_log_to_exp_to_log`, this test allows to check the
|
|
correctness of converting `log_rot` which contains values > math.pi.
|
|
"""
|
|
log_rot = 2.0 * TestSO3.init_log_rot(batch_size=batch_size)
|
|
# check also the singular cases where rot. angle = {0, pi, 2pi, 3pi}
|
|
log_rot[:3] = 0
|
|
log_rot[1, 0] = math.pi
|
|
log_rot[2, 0] = 2.0 * math.pi
|
|
log_rot[3, 0] = 3.0 * math.pi
|
|
rot = so3_exponential_map(log_rot, eps=1e-8)
|
|
rot_ = so3_exponential_map(so3_log_map(rot, eps=1e-8), eps=1e-8)
|
|
angles = so3_relative_angle(rot, rot_)
|
|
self.assertClose(angles, torch.zeros_like(angles), atol=0.01)
|
|
|
|
def test_so3_log_to_exp_to_log(self, batch_size: int = 100):
|
|
"""
|
|
Check that `so3_log_map(so3_exponential_map(log_rot))==log_rot` for
|
|
a randomly generated batch of rotation matrix logarithms `log_rot`.
|
|
"""
|
|
log_rot = TestSO3.init_log_rot(batch_size=batch_size)
|
|
# check also the singular cases where rot. angle = 0
|
|
log_rot[:1] = 0
|
|
log_rot_ = so3_log_map(so3_exponential_map(log_rot))
|
|
self.assertClose(log_rot, log_rot_, atol=1e-4)
|
|
|
|
def test_so3_exp_to_log_to_exp(self, batch_size: int = 100):
|
|
"""
|
|
Check that `so3_exponential_map(so3_log_map(R))==R` for
|
|
a batch of randomly generated rotation matrices `R`.
|
|
"""
|
|
rot = TestSO3.init_rot(batch_size=batch_size)
|
|
rot_ = so3_exponential_map(so3_log_map(rot, eps=1e-8), eps=1e-8)
|
|
angles = so3_relative_angle(rot, rot_)
|
|
# TODO: a lot of precision lost here ...
|
|
self.assertClose(angles, torch.zeros_like(angles), atol=0.1)
|
|
|
|
def test_so3_cos_angle(self, batch_size: int = 100):
|
|
"""
|
|
Check that `so3_relative_angle(R1, R2, cos_angle=False).cos()`
|
|
is the same as `so3_relative_angle(R1, R2, cos_angle=True)`
|
|
batches of randomly generated rotation matrices `R1` and `R2`.
|
|
"""
|
|
rot1 = TestSO3.init_rot(batch_size=batch_size)
|
|
rot2 = TestSO3.init_rot(batch_size=batch_size)
|
|
angles = so3_relative_angle(rot1, rot2, cos_angle=False).cos()
|
|
angles_ = so3_relative_angle(rot1, rot2, cos_angle=True)
|
|
self.assertClose(angles, angles_)
|
|
|
|
@staticmethod
|
|
def so3_expmap(batch_size: int = 10):
|
|
log_rot = TestSO3.init_log_rot(batch_size=batch_size)
|
|
torch.cuda.synchronize()
|
|
|
|
def compute_rots():
|
|
so3_exponential_map(log_rot)
|
|
torch.cuda.synchronize()
|
|
|
|
return compute_rots
|
|
|
|
@staticmethod
|
|
def so3_logmap(batch_size: int = 10):
|
|
log_rot = TestSO3.init_rot(batch_size=batch_size)
|
|
torch.cuda.synchronize()
|
|
|
|
def compute_logs():
|
|
so3_log_map(log_rot)
|
|
torch.cuda.synchronize()
|
|
|
|
return compute_logs
|