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matrix_to_quaternion corner case

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Summary: Issue #119. The function `sqrt(max(x, 0))` is not convex and has infinite gradient at 0, but 0 is a subgradient at 0. Here we implement it in such a way as to give 0 as the gradient.

Reviewed By: gkioxari

Differential Revision: D24306294

fbshipit-source-id: 48d136faca083babad4d64970be7ea522dbe9e09
This commit is contained in:
Jeremy Reizenstein 2020-10-15 03:19:51 -07:00 committed by Facebook GitHub Bot
parent 2d39723610
commit 4d52f9fb8b
2 changed files with 29 additions and 5 deletions
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20
pytorch3d/transforms/rotation_conversions.py
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@ -82,6 +82,17 @@ def _copysign(a, b):
return torch.where(signs_differ, -a, a) return torch.where(signs_differ, -a, a)
def _sqrt_positive_part(x):
"""
Returns torch.sqrt(torch.max(0, x))
but with a zero subgradient where x is 0.
"""
ret = torch.zeros_like(x)
positive_mask = x > 0
ret[positive_mask] = torch.sqrt(x[positive_mask])
return ret
def matrix_to_quaternion(matrix): def matrix_to_quaternion(matrix):
""" """
Convert rotations given as rotation matrices to quaternions. Convert rotations given as rotation matrices to quaternions.
@ -94,14 +105,13 @@ def matrix_to_quaternion(matrix):
""" """
if matrix.size(-1) != 3 or matrix.size(-2) != 3: if matrix.size(-1) != 3 or matrix.size(-2) != 3:
raise ValueError(f"Invalid rotation matrix shape f{matrix.shape}.") raise ValueError(f"Invalid rotation matrix shape f{matrix.shape}.")
zero = matrix.new_zeros((1,))
m00 = matrix[..., 0, 0] m00 = matrix[..., 0, 0]
m11 = matrix[..., 1, 1] m11 = matrix[..., 1, 1]
m22 = matrix[..., 2, 2] m22 = matrix[..., 2, 2]
o0 = 0.5 * torch.sqrt(torch.max(zero, 1 + m00 + m11 + m22)) o0 = 0.5 * _sqrt_positive_part(1 + m00 + m11 + m22)
x = 0.5 * torch.sqrt(torch.max(zero, 1 + m00 - m11 - m22)) x = 0.5 * _sqrt_positive_part(1 + m00 - m11 - m22)
y = 0.5 * torch.sqrt(torch.max(zero, 1 - m00 + m11 - m22)) y = 0.5 * _sqrt_positive_part(1 - m00 + m11 - m22)
z = 0.5 * torch.sqrt(torch.max(zero, 1 - m00 - m11 + m22)) z = 0.5 * _sqrt_positive_part(1 - m00 - m11 + m22)
o1 = _copysign(x, matrix[..., 2, 1] - matrix[..., 1, 2]) o1 = _copysign(x, matrix[..., 2, 1] - matrix[..., 1, 2])
o2 = _copysign(y, matrix[..., 0, 2] - matrix[..., 2, 0]) o2 = _copysign(y, matrix[..., 0, 2] - matrix[..., 2, 0])
o3 = _copysign(z, matrix[..., 1, 0] - matrix[..., 0, 1]) o3 = _copysign(z, matrix[..., 1, 0] - matrix[..., 0, 1])

14
tests/test_rotation_conversions.py
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@ -145,6 +145,20 @@ class TestRotationConversion(TestCaseMixin, unittest.TestCase):
self.assertEqual(ab.shape, ab_from_matrix.shape) self.assertEqual(ab.shape, ab_from_matrix.shape)
self.assertTrue(torch.allclose(ab, ab_from_matrix)) self.assertTrue(torch.allclose(ab, ab_from_matrix))
def test_matrix_to_quaternion_corner_case(self):
"""Check no bad gradients from sqrt(0)."""
matrix = torch.eye(3, requires_grad=True)
target = torch.Tensor([0.984808, 0, 0.174, 0])
optimizer = torch.optim.Adam([matrix], lr=0.05)
optimizer.zero_grad()
q = matrix_to_quaternion(matrix)
loss = torch.sum((q - target) ** 2)
loss.backward()
optimizer.step()
self.assertClose(matrix, 0.95 * torch.eye(3))
def test_quaternion_application(self): def test_quaternion_application(self):
"""Applying a quaternion is the same as applying the matrix.""" """Applying a quaternion is the same as applying the matrix."""
quaternions = random_quaternions(3, torch.float64, requires_grad=True) quaternions = random_quaternions(3, torch.float64, requires_grad=True)