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| from typing import Optional | |
| import torch | |
| from torch.nn import functional as F | |
| def aa_to_rotmat(theta: torch.Tensor): | |
| """ | |
| Convert axis-angle representation to rotation matrix. | |
| Works by first converting it to a quaternion. | |
| Args: | |
| theta (torch.Tensor): Tensor of shape (B, 3) containing axis-angle representations. | |
| Returns: | |
| torch.Tensor: Corresponding rotation matrices with shape (B, 3, 3). | |
| """ | |
| norm = torch.norm(theta + 1e-8, p = 2, dim = 1) | |
| angle = torch.unsqueeze(norm, -1) | |
| normalized = torch.div(theta, angle) | |
| angle = angle * 0.5 | |
| v_cos = torch.cos(angle) | |
| v_sin = torch.sin(angle) | |
| quat = torch.cat([v_cos, v_sin * normalized], dim = 1) | |
| return quat_to_rotmat(quat) | |
| def quat_to_rotmat(quat: torch.Tensor) -> torch.Tensor: | |
| """ | |
| Convert quaternion representation to rotation matrix. | |
| Args: | |
| quat (torch.Tensor) of shape (B, 4); 4 <===> (w, x, y, z). | |
| Returns: | |
| torch.Tensor: Corresponding rotation matrices with shape (B, 3, 3). | |
| """ | |
| norm_quat = quat | |
| norm_quat = norm_quat/norm_quat.norm(p=2, dim=1, keepdim=True) | |
| w, x, y, z = norm_quat[:,0], norm_quat[:,1], norm_quat[:,2], norm_quat[:,3] | |
| B = quat.size(0) | |
| w2, x2, y2, z2 = w.pow(2), x.pow(2), y.pow(2), z.pow(2) | |
| wx, wy, wz = w*x, w*y, w*z | |
| xy, xz, yz = x*y, x*z, y*z | |
| rotMat = torch.stack([w2 + x2 - y2 - z2, 2*xy - 2*wz, 2*wy + 2*xz, | |
| 2*wz + 2*xy, w2 - x2 + y2 - z2, 2*yz - 2*wx, | |
| 2*xz - 2*wy, 2*wx + 2*yz, w2 - x2 - y2 + z2], dim=1).view(B, 3, 3) | |
| return rotMat | |
| def rot6d_to_rotmat(x: torch.Tensor) -> torch.Tensor: | |
| """ | |
| Convert 6D rotation representation to 3x3 rotation matrix. | |
| Based on Zhou et al., "On the Continuity of Rotation Representations in Neural Networks", CVPR 2019 | |
| Args: | |
| x (torch.Tensor): (B,6) Batch of 6-D rotation representations. | |
| Returns: | |
| torch.Tensor: Batch of corresponding rotation matrices with shape (B,3,3). | |
| """ | |
| x = x.reshape(-1,2,3).permute(0, 2, 1).contiguous() | |
| a1 = x[:, :, 0] | |
| a2 = x[:, :, 1] | |
| b1 = F.normalize(a1) | |
| b2 = F.normalize(a2 - torch.einsum('bi,bi->b', b1, a2).unsqueeze(-1) * b1) | |
| b3 = torch.cross(b1, b2) | |
| return torch.stack((b1, b2, b3), dim=-1) | |
| def perspective_projection(points: torch.Tensor, | |
| translation: torch.Tensor, | |
| focal_length: torch.Tensor, | |
| camera_center: Optional[torch.Tensor] = None, | |
| rotation: Optional[torch.Tensor] = None) -> torch.Tensor: | |
| """ | |
| Computes the perspective projection of a set of 3D points. | |
| Args: | |
| points (torch.Tensor): Tensor of shape (B, N, 3) containing the input 3D points. | |
| translation (torch.Tensor): Tensor of shape (B, 3) containing the 3D camera translation. | |
| focal_length (torch.Tensor): Tensor of shape (B, 2) containing the focal length in pixels. | |
| camera_center (torch.Tensor): Tensor of shape (B, 2) containing the camera center in pixels. | |
| rotation (torch.Tensor): Tensor of shape (B, 3, 3) containing the camera rotation. | |
| Returns: | |
| torch.Tensor: Tensor of shape (B, N, 2) containing the projection of the input points. | |
| """ | |
| batch_size = points.shape[0] | |
| if rotation is None: | |
| rotation = torch.eye(3, device=points.device, dtype=points.dtype).unsqueeze(0).expand(batch_size, -1, -1) | |
| if camera_center is None: | |
| camera_center = torch.zeros(batch_size, 2, device=points.device, dtype=points.dtype) | |
| # Populate intrinsic camera matrix K. | |
| K = torch.zeros([batch_size, 3, 3], device=points.device, dtype=points.dtype) | |
| K[:,0,0] = focal_length[:,0] | |
| K[:,1,1] = focal_length[:,1] | |
| K[:,2,2] = 1. | |
| K[:,:-1, -1] = camera_center | |
| # Transform points | |
| points = torch.einsum('bij,bkj->bki', rotation, points) | |
| points = points + translation.unsqueeze(1) | |
| # Apply perspective distortion | |
| projected_points = points / points[:,:,-1].unsqueeze(-1) | |
| # Apply camera intrinsics | |
| projected_points = torch.einsum('bij,bkj->bki', K, projected_points) | |
| return projected_points[:, :, :-1] |