Function get_extrinsics

flowmap/model/projection.py:187–210

Convert the inverse relative transformations from ModelOutput to extrinsics. Each inverse relative transformation transforms points from frame {i + 1}'s camera space to frame i's camera space. Since our extrinsics are in camera-to-world format, this means that expressed in terms of camer

(
    inverse_relative_transformations: Float[Tensor, "*batch pair 4 4"],
)

def get_extrinsics(
    inverse_relative_transformations: Float[Tensor, "*batch pair 4 4"],
) -> Float[Tensor, "*batch pair+1 4 4"]:
    """Convert the inverse relative transformations from ModelOutput to extrinsics.
    Each inverse relative transformation transforms points from frame {i + 1}'s
    camera space to frame i's camera space. Since our extrinsics are in
    camera-to-world format, this means that expressed in terms of camera poses, each
    inverse relative transformation is (P_i^-1 @ P_{i + 1}). If we assume that P_0
    is I (the identity pose), we can thus extract camera poses as follows:

    P_n = (I @ P_1) @ (P_1^-1 @ P_2) @ ... @ (P_{n - 1}^-1 @ P_n)

    This is slightly counterintuitive, since transformations are generally composed
    by right-to-left multiplication.
    """
    *batch, step, _, _ = inverse_relative_transformations.shape
    device = inverse_relative_transformations.device
    pose = torch.eye(4, dtype=torch.float32, device=device)
    pose = pose.expand((*batch, 4, 4)).contiguous()
    result = [pose]
    for i in range(step):
        pose = pose @ inverse_relative_transformations[..., i, :, :]
        result.append(pose)
    return torch.stack(result, dim=-3)


def align_surfaces(