depth_anything_3/model/utils/transform.py

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#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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#   http://www.apache.org/licenses/LICENSE-2.0
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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