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_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] # add random rotations and random almost orthonormal matrices r.extend([ qr(identity + torch.randn_like(identity) * 1e-4)[0] + float(i > batch_size // 2) * (0.5 - torch.rand_like(identity)) * 1e-3 # this adds random noise to the second half # of the random orthogonal matrices to generate # near-orthogonal matrices for i in range(batch_size - 2) ]) r = torch.stack(r) r.requires_grad = True # the log of the rotation matrix r r_log = so3_log_map(r, cos_bound=1e-4, eps=1e-2) # tests whether all outputs are finite self.assertTrue(torch.isfinite(r_log).all()) # tests whether the gradient is not None and all finite loss = r.sum() loss.backward() self.assertIsNotNone(r.grad) self.assertTrue(torch.isfinite(r.grad).all())
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) 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)
def test_so3_log_to_exp_to_log(self, batch_size: int = 100): """ Check that `so3_log_map(so3_exp_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_exp_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_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)) 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))
def test_so3_exp_to_log_to_exp(self, batch_size: int = 100): """ Check that `so3_exp_map(so3_log_map(R))==R` for a batch of randomly generated rotation matrices `R`. """ rot = TestSO3.init_rot(batch_size=batch_size) non_singular = (so3_rotation_angle(rot) - math.pi).abs() > 1e-2 rot = rot[non_singular] rot_ = so3_exp_map(so3_log_map(rot, eps=1e-8, cos_bound=1e-8), eps=1e-8) self.assertClose(rot_, rot, atol=0.1) angles = so3_relative_angle(rot, rot_, cos_bound=1e-4) self.assertClose(angles, torch.zeros_like(angles), atol=0.1)
def test_se3_log_zero_translation(self, batch_size: int = 100): """ Check that `se3_log_map` with zero translation gives the same result as corresponding `so3_log_map`. """ transform = TestSE3.init_transform(batch_size=batch_size) transform[:, 3, :3] *= 0.0 log_transform = se3_log_map(transform, eps=1e-8, cos_bound=1e-4) log_transform_so3 = so3_log_map(transform[:, :3, :3], eps=1e-8, cos_bound=1e-4) self.assertClose(log_transform[:, 3:], -log_transform_so3, atol=1e-4) self.assertClose(log_transform[:, :3], torch.zeros_like(log_transform[:, :3]), atol=1e-4)
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") 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]) # 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_exp_map(so3_log_map(so3_exp_map(log_rot))) == so3_exp_map(log_rot)` for a randomly generated batch of rotation matrix logarithms `log_rot`. Unlike `test_so3_log_to_exp_to_log`, this test checks the correctness of converting a `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, 2pi} log_rot[:2] = 0 log_rot[1, 0] = 2.0 * math.pi - 1e-6 rot = so3_exp_map(log_rot, eps=1e-4) rot_ = so3_exp_map(so3_log_map(rot, eps=1e-4, cos_bound=1e-6), eps=1e-6) self.assertClose(rot, rot_, atol=0.01) angles = so3_relative_angle(rot, rot_, cos_bound=1e-6) self.assertClose(angles, torch.zeros_like(angles), atol=0.01)
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_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 compute_logs(): so3_log_map(log_rot) torch.cuda.synchronize()
def main(args): # set for reproducibility torch.manual_seed(42) if args.dtype == "float": args.dtype = torch.float32 elif args.dtype == "double": args.dtype = torch.float64 # ## 1. Set up Cameras and load ground truth positions # load the SE3 graph of relative/absolute camera positions if (args.input_folder / "images.bin").isfile(): ext = '.bin' elif (args.input_folder / "images.txt").isfile(): ext = '.txt' else: print('error') return cameras, images, points3D = read_model(args.input_folder, ext) images_df = pd.DataFrame.from_dict(images, orient="index").set_index("id") cameras_df = pd.DataFrame.from_dict(cameras, orient="index").set_index("id") points_df = pd.DataFrame.from_dict(points3D, orient="index").set_index("id") print(points_df) print(images_df) print(cameras_df) ref_pointcloud = PyntCloud.from_file(args.ply) ref_pointcloud = torch.from_numpy(ref_pointcloud.xyz).to(device, dtype=args.dtype) points_3d = np.stack(points_df["xyz"].values) points_3d = torch.from_numpy(points_3d).to(device, dtype=args.dtype) cameras_R = np.stack( [qvec2rotmat(q) for _, q in images_df["qvec"].iteritems()]) cameras_R = torch.from_numpy(cameras_R).to(device, dtype=args.dtype).transpose( 1, 2) cameras_T = torch.from_numpy(np.stack(images_df["tvec"].values)).to( device, dtype=args.dtype) cameras_params = torch.from_numpy(np.stack( cameras_df["params"].values)).to(device, dtype=args.dtype) cameras_params = cameras_params[:, :4] print(cameras_params) # Constructu visibility map, True at (frame, point) if point is visible by frame, False otherwise # Thus, we can ignore reprojection errors for invisible points visibility = np.full((cameras_R.shape[0], points_3d.shape[0]), False) visibility = pd.DataFrame(visibility, index=images_df.index, columns=points_df.index) points_2D_gt = [] for idx, (pts_ids, xy) in images_df[["point3D_ids", "xys"]].iterrows(): pts_ids_clean = pts_ids[pts_ids != -1] pts_2D = pd.DataFrame(xy[pts_ids != -1], index=pts_ids_clean) pts_2D = pts_2D[~pts_2D.index.duplicated(keep=False)].reindex( points_df.index).dropna() points_2D_gt.append(pts_2D.values) visibility.loc[idx, pts_2D.index] = True print(visibility) visibility = torch.from_numpy(visibility.values).to(device) eps = 1e-3 # Visibility map is very sparse. So we can use Pytorch3d's function to reduce points_2D size # to (num_frames, max points seen by frame) points_2D_gt = list_to_padded([torch.from_numpy(p) for p in points_2D_gt], pad_value=eps).to(device, dtype=args.dtype) print(points_2D_gt) cameras_df["raw_id"] = np.arange(len(cameras_df)) cameras_id_per_image = torch.from_numpy( cameras_df["raw_id"][images_df["camera_id"]].values).to(device) # the number of absolute camera positions N = len(images_df) nonzer = (points_2D_gt != eps).all(dim=-1) # print(padded) # print(points_2D_gt, points_2D_gt.shape) # ## 2. Define optimization functions # # ### Relative cameras and camera distance # We now define two functions crucial for the optimization. # # **`calc_camera_distance`** compares a pair of cameras. # This function is important as it defines the loss that we are minimizing. # The method utilizes the `so3_relative_angle` function from the SO3 API. # # **`get_relative_camera`** computes the parameters of a relative camera # that maps between a pair of absolute cameras. Here we utilize the `compose` # and `inverse` class methods from the PyTorch3D Transforms API. def calc_camera_distance(cam_1, cam_2): """ Calculates the divergence of a batch of pairs of cameras cam_1, cam_2. The distance is composed of the cosine of the relative angle between the rotation components of the camera extrinsics and the l2 distance between the translation vectors. """ # rotation distance R_distance = ( 1. - so3_relative_angle(cam_1.R, cam_2.R, cos_angle=True)).mean() # translation distance T_distance = ((cam_1.T - cam_2.T)**2).sum(1).mean() # the final distance is the sum return R_distance + T_distance # ## 3. Optimization # Finally, we start the optimization of the absolute cameras. # # We use SGD with momentum and optimize over `log_R_absolute` and `T_absolute`. # # As mentioned earlier, `log_R_absolute` is the axis angle representation of the # rotation part of our absolute cameras. We can obtain the 3x3 rotation matrix # `R_absolute` that corresponds to `log_R_absolute` with: # # `R_absolute = so3_exponential_map(log_R_absolute)` # fxfyu0v0 = cameras_params[cameras_id_per_image] cameras_absolute_gt = PerspectiveCameras( focal_length=fxfyu0v0[:, :2], principal_point=fxfyu0v0[:, 2:], R=cameras_R, T=cameras_T, device=device, ) # Normally, the points_2d are the one we should use to minimize reprojection errors. # But we have been dealing with unstability, so we can reproject the 3D points instead and use their reprojection # since we assume Colmap's bundle adjuster to have converged alone before. use_3d_points = True if use_3d_points: with torch.no_grad(): padded_points = list_to_padded( [points_3d[visibility[c]] for c in range(N)], pad_value=1e-3) points_2D_gt = cameras_absolute_gt.transform_points( padded_points, eps=1e-4)[:, :, :2] relative_points_gt = padded_points @ cameras_R + cameras_T # Starting point is normally points_3d and camera_R and camera_T # For stability test, you can try to add noise and see if the otpitmization # gets back to intial state (spoiler alert, it's complicated) # Set noise and shift to 0 for a normal starting point noise = 0 shift = 0.1 points_init = points_3d + noise * torch.randn( points_3d.shape, dtype=torch.float32, device=device) + shift log_R_init = so3_log_map(cameras_R) + noise * torch.randn( N, 3, dtype=torch.float32, device=device) T_init = cameras_T + noise * torch.randn( cameras_T.shape, dtype=torch.float32, device=device) - shift cams_init = cameras_params # + noise * torch.randn(cameras_params.shape, dtype=torch.float32, device=device) # instantiate a copy of the initialization of log_R / T log_R = log_R_init.clone().detach() log_R.requires_grad = True T = T_init.clone().detach() T.requires_grad = True cams_params = cams_init.clone().detach() cams_params.requires_grad = True points = points_init.clone().detach() points.requires_grad = True # init the optimizer # Different learning rates per parameter ? By intuition I'd say that it should be higher for T and lower for log_R # Params could be optimized as well but it's unlikely to be interesting param_groups = [{ 'params': points, 'lr': args.lr }, { 'params': log_R, 'lr': 0.1 * args.lr }, { 'params': T, 'lr': 2 * args.lr }, { 'params': cams_params, 'lr': 0 }] optimizer = torch.optim.SGD(param_groups, lr=args.lr, momentum=0.9) # run the optimization n_iter = 200000 # fix the number of iterations # Compute inliers # In the model, some 3d points have their reprojection way off compared to the # target 2d point. It is potentially a great source of instability. inliers is # keeping track of those problematic points to discard them from optimization discard_outliers = True if discard_outliers: with torch.no_grad(): padded_points = list_to_padded( [points_3d[visibility[c]] for c in range(N)], pad_value=1e-3) projected_points = cameras_absolute_gt.transform_points( padded_points, eps=1e-4)[:, :, :2] points_distance = ((projected_points[nonzer] - points_2D_gt[nonzer])**2).sum(dim=1) inliers = (points_distance < 100).clone().detach() print(inliers) else: inliers = points_2D_gt[nonzer] == points_2D_gt[ nonzer] # All true, except NaNs loss_log = [] cam_dist_log = [] pts_dist_log = [] for it in range(n_iter): # re-init the optimizer gradients optimizer.zero_grad() R = so3_exponential_map(log_R) fxfyu0v0 = cams_params[cameras_id_per_image] # get the current absolute cameras cameras_absolute = PerspectiveCameras( focal_length=fxfyu0v0[:, :2], principal_point=fxfyu0v0[:, 2:], R=R, T=T, device=device, ) padded_points = list_to_padded( [points[visibility[c]] for c in range(N)], pad_value=1e-3) # two ways of optimizing : # 1) minimize 2d projection error. Potentially unstable, especially with very close points. # This is problematic as close points are the ones with which we want the pose modification to be low # but gradient descent makes them with the highest step size. We can maybe use Adam, but unstability remains. # # 2) minimize 3d relative position error (initial 3d relative position is considered groundtruth). No more unstability for very close points. # 2d reprojection error is not guaranteed to be minimized though minimize_2d = True chamfer_weight = 1e3 verbose = True chamfer_dist = chamfer_distance(ref_pointcloud[None], points[None])[0] if minimize_2d: projected_points_3D = cameras_absolute.transform_points( padded_points, eps=1e-4)[..., :2] projected_points = projected_points_3D[:, :, :2] # Discard points with a depth < 0 (theoretically impossible) inliers = inliers & (projected_points_3D[:, :, 2][nonzer] > 0) # Plot point distants for first image # distances = (projected_points[0] - points_2D_gt[0]).norm(dim=-1).detach().cpu().numpy() # from matplotlib import pyplot as plt # plt.plot(distances[:(visibility[0]).sum()]) # Different loss functions for reprojection error minimization # points_distance = smooth_l1_loss(projected_points, points_2D_gt) # points_distance = (smooth_l1_loss(projected_points, points_2D_gt, reduction='none')[nonzer]).sum(dim=1) proj_error = ((projected_points[nonzer] - points_2D_gt[nonzer])**2).sum(dim=1) proj_error_filtered = proj_error[inliers] else: projected_points_3D = padded_points @ R + T # Plot point distants for first image # distances = (projected_points_3D[0] - relative_points_gt[0]).norm(dim=-1).detach().cpu().numpy() # from matplotlib import pyplot as plt # plt.plot(distances[:(visibility[0]).sum()]) # Different loss functions for reprojection error minimization # points_distance = smooth_l1_loss(projected_points, points_2D_gt) # points_distance = (smooth_l1_loss(projected_points, points_2D_gt, reduction='none')[nonzer]).sum(dim=1) proj_error = ((projected_points_3D[nonzer] - relative_points_gt[nonzer])**2).sum(dim=1) proj_error_filtered = proj_error[inliers] loss = proj_error_filtered.mean() + chamfer_weight * chamfer_dist loss.backward() if verbose: print("faulty elements (with nan grad) :") faulty_points = torch.arange( points.shape[0])[points.grad[:, 0] != points.grad[:, 0]] faulty_images = torch.arange( log_R.shape[0])[log_R.grad[:, 0] != log_R.grad[:, 0]] faulty_cams = torch.arange(cams_params.shape[0])[ cams_params.grad[:, 0] != cams_params.grad[:, 0]] faulty_projected_points = torch.arange( projected_points.shape[1])[torch.isnan( projected_points.grad).any(dim=2)[0]] # Print Tensor that would become NaN, should the gradient be applied print("Faulty Rotation (log) and translation") print(faulty_images) print(log_R[faulty_images]) print(T[faulty_images]) print("Faulty 3D colmap points") print(faulty_points) print(points[faulty_points]) print("Faulty Cameras") print(faulty_cams) print(cams_params[faulty_cams]) print("Faulty 2D points") print(projected_points[faulty_projected_points]) first_faulty_point = points_df.iloc[int(faulty_points[0])] related_faulty_images = images_df.loc[ first_faulty_point["image_ids"][0]] print("First faulty point, and images where it is seen") print(first_faulty_point) print(related_faulty_images) # apply the gradients optimizer.step() # plot and print status message if it % 2000 == 0 or it == n_iter - 1: camera_distance = calc_camera_distance(cameras_absolute, cameras_absolute_gt) print( 'iteration = {}; loss = {}, chamfer distance = {}, camera_distance = {}' .format(it, loss, chamfer_distance, camera_distance)) loss_log.append(loss.item()) pts_dist_log.append(chamfer_distance.item()) cam_dist_log.append(camera_distance.item()) if it % 20000 == 0 or it == n_iter - 1: with torch.no_grad(): from matplotlib import pyplot as plt plt.hist( torch.sqrt(proj_error_filtered).detach().cpu().numpy()) if it % 200000 == 0 or it == n_iter - 1: plt.figure() plt.plot(loss_log) plt.figure() plt.plot(pts_dist_log, label="chamfer_dist") plt.plot(cam_dist_log, label="cam_dist") plt.legend() plot_camera_scene( cameras_absolute, cameras_absolute_gt, points, ref_pointcloud, 'iteration={}; chamfer distance={}'.format( it, chamfer_distance)) print('Optimization finished.')