SO3 log map fix for singularity at PI

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

pytorch3d/transforms/so3.py

@@ -152,11 +152,14 @@ def so3_log_map(R, eps: float = 0.0001):
 
     phi = so3_rotation_angle(R)
 
-    phi_valid = torch.clamp(phi.abs(), eps) * phi.sign()
+    phi_sin = phi.sin()
 
-    log_rot_hat = (phi_valid / (2.0 * phi_valid.sin()))[:, None, None] * (
-        R - R.permute(0, 2, 1)
+    phi_denom = (
+        torch.clamp(phi_sin.abs(), eps) * phi_sin.sign()
+        + (phi_sin == 0).type_as(phi) * eps
     )
+
+    log_rot_hat = (phi / (2.0 * phi_denom))[:, None, None] * (R - R.permute(0, 2, 1))
     log_rot = hat_inv(log_rot_hat)
 
     return log_rot

tests/test_so3.py

@@ -1,10 +1,12 @@
 # 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,
@@ -13,7 +15,7 @@
 )
 
 
-class TestSO3(unittest.TestCase):
+class TestSO3(TestCaseMixin, unittest.TestCase):
     def setUp(self) -> None:
         super().setUp()
         torch.manual_seed(42)
@@ -55,9 +57,8 @@ def test_determinant(self):
         """
         log_rot = TestSO3.init_log_rot(batch_size=30)
         Rs = so3_exponential_map(log_rot)
-        for R in Rs:
-            det = np.linalg.det(R.cpu().numpy())
-            self.assertAlmostEqual(float(det), 1.0, 5)
+        dets = torch.det(Rs)
+        self.assertClose(dets, torch.ones_like(dets), atol=1e-4)
 
     def test_cross(self):
         """
@@ -70,8 +71,7 @@ def test_cross(self):
         hat_a = hat(a)
         cross = torch.bmm(hat_a, b[:, :, None])[:, :, 0]
         torch_cross = torch.cross(a, b, dim=1)
-        max_df = (cross - torch_cross).abs().max()
-        self.assertAlmostEqual(float(max_df), 0.0, 5)
+        self.assertClose(torch_cross, cross, atol=1e-4)
 
     def test_bad_so3_input_value_err(self):
         """
@@ -126,37 +126,63 @@ def test_so3_log_singularity(self, batch_size: int = 100):
         """
         # generate random rotations with a tiny angle
         device = torch.device("cuda:0")
-        r = torch.eye(3, device=device)[None].repeat((batch_size, 1, 1))
-        r += torch.randn((batch_size, 3, 3), device=device) * 1e-3
-        r = torch.stack([torch.qr(r_)[0] for r_ in r])
+        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))
-        max_df = (log_rot - log_rot_).abs().max()
-        self.assertAlmostEqual(float(max_df), 0.0, 4)
+        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))
+        rot_ = so3_exponential_map(so3_log_map(rot, eps=1e-8), eps=1e-8)
         angles = so3_relative_angle(rot, rot_)
-        max_angle = angles.max()
-        # a lot of precision lost here :(
-        # TODO: fix this test??
-        self.assertTrue(np.allclose(float(max_angle), 0.0, atol=0.1))
+        # 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):
         """
@@ -168,7 +194,7 @@ def test_so3_cos_angle(self, batch_size: int = 100):
         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.assertTrue(torch.allclose(angles, angles_))
+        self.assertClose(angles, angles_)
 
     @staticmethod
     def so3_expmap(batch_size: int = 10):