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