code: def _corresponding_cameras_alignment_test_case(
      self,
      cameras,
      R_align_gt,
      T_align_gt,
      s_align_gt,
      estimate_scale,
      mode,
      add_noise,
  ):
      batch_size = cameras.R.shape[0]
  
      # get target camera centers
      R_new = torch.bmm(
          R_align_gt[None].expand_as(cameras.R), cameras.R
      )
      T_new = (
          torch.bmm(
              T_align_gt[None, None].repeat(batch_size, 1, 1), cameras.R
          )[:, 0]
          + cameras.T
      ) * s_align_gt
  
      if add_noise != 0.0:
          R_new = torch.bmm(
              R_new, so3_exp_map(torch.randn_like(T_new) * add_noise)
          )
          T_new += torch.randn_like(T_new) * add_noise
  
      # create new cameras from R_new and T_new
      cameras_tgt = cameras.clone()
      cameras_tgt.R = R_new
      cameras_tgt.T = T_new
  
      # align cameras and cameras_tgt
      cameras_aligned = corresponding_cameras_alignment(
          cameras, cameras_tgt, estimate_scale=estimate_scale, mode=mode
      )
  
      if batch_size <= 2 and mode == "centers":
          # underdetermined case - check only the center alignment error
          # since the rotation and translation are ambiguous here
          self.assertClose(
              cameras_aligned.get_camera_center(),
              cameras_tgt.get_camera_center(),
              atol=max(add_noise * 7.0, 1e-4),
          )
  
      else:
  
          def _rmse(a):
              return (torch.norm(a, dim=1, p=2) ** 2).mean().sqrt()
  
          if add_noise != 0.0:
              # in a noisy case check mean rotation/translation error for
              # extrinsic alignment and root mean center error for center alignment
              if mode == "centers":
                  self.assertNormsClose(
                      cameras_aligned.get_camera_center(),
                      cameras_tgt.get_camera_center(),
                      _rmse,
                      atol=max(add_noise * 10.0, 1e-4),
                  )
              elif mode == "extrinsics":
                  angle_err = so3_relative_angle(
                      cameras_aligned.R, cameras_tgt.R, cos_angle=True
                  ).mean()
                  self.assertClose(
                      angle_err,
                      torch.ones_like(angle_err),
                      atol=add_noise * 0.03,
                  )
                  self.assertNormsClose(
                      cameras_aligned.T,
                      cameras_tgt.T,
                      _rmse,
                      atol=add_noise * 7.0,
                  )
              else:
                  raise ValueError(mode)
  
          else:
              # compare the rotations and translations of cameras
              self.assertClose(
                  cameras_aligned.R, cameras_tgt.R, atol=3e-4
              )
              self.assertClose(
                  cameras_aligned.T, cameras_tgt.T, atol=3e-4
              )
              # compare the centers
              self.assertClose(
                  cameras_aligned.get_camera_center(),
                  cameras_tgt.get_camera_center(),
                  atol=3e-4,
              )
  
file_path: pytorch3d/tests/test_cameras_alignment.py
imports: import unittest
  import numpy
  import torch
  from pytorch3d.ops import corresponding_cameras_alignment
  from pytorch3d.renderer.cameras import OpenGLOrthographicCameras, OpenGLPerspectiveCameras, SfMOrthographicCameras, SfMPerspectiveCameras
  from pytorch3d.transforms.rotation_conversions import random_rotations
  from pytorch3d.transforms.so3 import so3_exp_map, so3_relative_angle
  from .common_testing import TestCaseMixin
  from .test_cameras import init_random_cameras
label_desc: Use image node_id 3 for calling the TestCamerasAlignment obj's underlying member method code with example usage: obj._corresponding_cameras_alignment_test_case(cameras, R_align_gt, T_align_gt, s_align_gt, estimate_scale, mode, add_noise) and returns: unknown