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.')
