# 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