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# python3.8
"""Contains some functions related to cameras, including rotation
transformation, projection, etc."""
import torch
import torch.nn.functional as F
def camera_9d_to_16d(d9):
d6, translation = d9[..., :6], d9[..., 6:]
rotation = rotation_6d_to_matrix(d6)
RT = torch.eye(4).to(device=d9.device, dtype=d9.dtype).reshape(
1, 4, 4).repeat(d6.size(0), 1, 1)
RT[:, :3, :3] = rotation
RT[:, :3, -1] = translation
return RT.reshape(-1, 16)
def rotation_6d_to_matrix(d6: torch.Tensor) -> torch.Tensor:
"""
Converts 6D rotation representation by Zhou et al. [1] to rotation matrix
using Gram--Schmidt orthogonalization per Section B of [1].
Args:
d6: 6D rotation representation, of size (*, 6)
Returns:
batch of rotation matrices of size (*, 3, 3)
[1] Zhou, Y., Barnes, C., Lu, J., Yang, J., & Li, H.
On the Continuity of Rotation Representations in Neural Networks.
IEEE Conference on Computer Vision and Pattern Recognition, 2019.
Retrieved from http://arxiv.org/abs/1812.07035.
"""
a1, a2 = d6[..., :3], d6[..., 3:]
b1 = F.normalize(a1, dim=-1)
b2 = a2 - (b1 * a2).sum(-1, keepdim=True) * b1
b2 = F.normalize(b2, dim=-1)
b3 = torch.cross(b1, b2, dim=-1)
return torch.stack((b1, b2, b3), dim=-2) |