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# Copyright (c) 2025 ByteDance Ltd. and/or its affiliates
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import torch
import torch.nn.functional as F
def extri_intri_to_pose_encoding(
extrinsics,
intrinsics,
image_size_hw=None,
):
"""Convert camera extrinsics and intrinsics to a compact pose encoding."""
# extrinsics: BxSx3x4
# intrinsics: BxSx3x3
R = extrinsics[:, :, :3, :3] # BxSx3x3
T = extrinsics[:, :, :3, 3] # BxSx3
quat = mat_to_quat(R)
# Note the order of h and w here
H, W = image_size_hw
fov_h = 2 * torch.atan((H / 2) / intrinsics[..., 1, 1])
fov_w = 2 * torch.atan((W / 2) / intrinsics[..., 0, 0])
pose_encoding = torch.cat([T, quat, fov_h[..., None], fov_w[..., None]], dim=-1).float()
return pose_encoding
def pose_encoding_to_extri_intri(
pose_encoding,
image_size_hw=None,
):
"""Convert a pose encoding back to camera extrinsics and intrinsics."""
T = pose_encoding[..., :3]
quat = pose_encoding[..., 3:7]
fov_h = pose_encoding[..., 7]
fov_w = pose_encoding[..., 8]
R = quat_to_mat(quat)
extrinsics = torch.cat([R, T[..., None]], dim=-1)
H, W = image_size_hw
fy = (H / 2.0) / torch.clamp(torch.tan(fov_h / 2.0), 1e-6)
fx = (W / 2.0) / torch.clamp(torch.tan(fov_w / 2.0), 1e-6)
intrinsics = torch.zeros(pose_encoding.shape[:2] + (3, 3), device=pose_encoding.device)
intrinsics[..., 0, 0] = fx
intrinsics[..., 1, 1] = fy
intrinsics[..., 0, 2] = W / 2
intrinsics[..., 1, 2] = H / 2
intrinsics[..., 2, 2] = 1.0 # Set the homogeneous coordinate to 1
return extrinsics, intrinsics
def quat_to_mat(quaternions: torch.Tensor) -> torch.Tensor:
"""
Quaternion Order: XYZW or say ijkr, scalar-last
Convert rotations given as quaternions to rotation matrices.
Args:
quaternions: quaternions with real part last,
as tensor of shape (..., 4).
Returns:
Rotation matrices as tensor of shape (..., 3, 3).
"""
i, j, k, r = torch.unbind(quaternions, -1)
two_s = 2.0 / (quaternions * quaternions).sum(-1)
o = torch.stack(
(
1 - two_s * (j * j + k * k),
two_s * (i * j - k * r),
two_s * (i * k + j * r),
two_s * (i * j + k * r),
1 - two_s * (i * i + k * k),
two_s * (j * k - i * r),
two_s * (i * k - j * r),
two_s * (j * k + i * r),
1 - two_s * (i * i + j * j),
),
-1,
)
return o.reshape(quaternions.shape[:-1] + (3, 3))
def mat_to_quat(matrix: torch.Tensor) -> torch.Tensor:
"""
Convert rotations given as rotation matrices to quaternions.
Args:
matrix: Rotation matrices as tensor of shape (..., 3, 3).
Returns:
quaternions with real part last, as tensor of shape (..., 4).
Quaternion Order: XYZW or say ijkr, scalar-last
"""
if matrix.size(-1) != 3 or matrix.size(-2) != 3:
raise ValueError(f"Invalid rotation matrix shape {matrix.shape}.")
batch_dim = matrix.shape[:-2]
m00, m01, m02, m10, m11, m12, m20, m21, m22 = torch.unbind(
matrix.reshape(batch_dim + (9,)), dim=-1
)
q_abs = _sqrt_positive_part(
torch.stack(
[
1.0 + m00 + m11 + m22,
1.0 + m00 - m11 - m22,
1.0 - m00 + m11 - m22,
1.0 - m00 - m11 + m22,
],
dim=-1,
)
)
quat_by_rijk = torch.stack(
[
torch.stack([q_abs[..., 0] ** 2, m21 - m12, m02 - m20, m10 - m01], dim=-1),
torch.stack([m21 - m12, q_abs[..., 1] ** 2, m10 + m01, m02 + m20], dim=-1),
torch.stack([m02 - m20, m10 + m01, q_abs[..., 2] ** 2, m12 + m21], dim=-1),
torch.stack([m10 - m01, m20 + m02, m21 + m12, q_abs[..., 3] ** 2], dim=-1),
],
dim=-2,
)
flr = torch.tensor(0.1).to(dtype=q_abs.dtype, device=q_abs.device)
quat_candidates = quat_by_rijk / (2.0 * q_abs[..., None].max(flr))
out = quat_candidates[F.one_hot(q_abs.argmax(dim=-1), num_classes=4) > 0.5, :].reshape(
batch_dim + (4,)
)
out = out[..., [1, 2, 3, 0]]
out = standardize_quaternion(out)
return out
def _sqrt_positive_part(x: torch.Tensor) -> torch.Tensor:
"""
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
if torch.is_grad_enabled():
ret[positive_mask] = torch.sqrt(x[positive_mask])
else:
ret = torch.where(positive_mask, torch.sqrt(x), ret)
return ret
def standardize_quaternion(quaternions: torch.Tensor) -> torch.Tensor:
"""
Convert a unit quaternion to a standard form: one in which the real
part is non negative.
Args:
quaternions: Quaternions with real part last,
as tensor of shape (..., 4).
Returns:
Standardized quaternions as tensor of shape (..., 4).
"""
return torch.where(quaternions[..., 3:4] < 0, -quaternions, quaternions)
def cam_quat_xyzw_to_world_quat_wxyz(cam_quat_xyzw, c2w):
# cam_quat_xyzw: (b, n, 4) in xyzw
# c2w: (b, n, 4, 4)
b, n = cam_quat_xyzw.shape[:2]
# 1. xyzw -> wxyz
cam_quat_wxyz = torch.cat(
[
cam_quat_xyzw[..., 3:4], # w
cam_quat_xyzw[..., 0:1], # x
cam_quat_xyzw[..., 1:2], # y
cam_quat_xyzw[..., 2:3], # z
],
dim=-1,
)
# 2. Quaternion to matrix
cam_quat_wxyz_flat = cam_quat_wxyz.reshape(-1, 4)
rotmat_cam = quat_to_mat(cam_quat_wxyz_flat).reshape(b, n, 3, 3)
# 3. Transform to world space
rotmat_c2w = c2w[..., :3, :3]
rotmat_world = torch.matmul(rotmat_c2w, rotmat_cam)
# 4. Matrix to quaternion (wxyz)
rotmat_world_flat = rotmat_world.reshape(-1, 3, 3)
world_quat_wxyz_flat = mat_to_quat(rotmat_world_flat)
world_quat_wxyz = world_quat_wxyz_flat.reshape(b, n, 4)
return world_quat_wxyz
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