xhs-note-crawling/python/py/Lib/site-packages/kornia/geometry/epipolar/projection.py

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# Copyright 2018 Kornia Team
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# Licensed under the Apache License, Version 2.0 (the "License");
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#     http://www.apache.org/licenses/LICENSE-2.0
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"""Module for image projections."""

from typing import Tuple, Union

import torch
from torch.linalg import qr as linalg_qr

from kornia.core import Tensor, concatenate, pad, stack
from kornia.core.check import KORNIA_CHECK_SHAPE
from kornia.utils import eye_like, vec_like
from kornia.utils.helpers import _torch_svd_cast

from .numeric import cross_product_matrix


def intrinsics_like(focal: float, input: Tensor) -> Tensor:
    r"""Return a 3x3 intrinsics matrix, with same size as the input.

    The center of projection will be based in the input image size.

    Args:
        focal: the focal length for the camera matrix.
        input: image tensor that will determine the batch size and image height
          and width. It is assumed to be a tensor in the shape of :math:`(B, C, H, W)`.

    Returns:
        The camera matrix with the shape of :math:`(B, 3, 3)`.

    """
    if len(input.shape) != 4:
        raise AssertionError(input.shape)
    if focal <= 0:
        raise AssertionError(focal)

    _, _, H, W = input.shape

    intrinsics = eye_like(3, input)
    intrinsics[..., 0, 0] *= focal
    intrinsics[..., 1, 1] *= focal
    intrinsics[..., 0, 2] += 1.0 * W / 2
    intrinsics[..., 1, 2] += 1.0 * H / 2
    return intrinsics


def random_intrinsics(low: Union[float, Tensor], high: Union[float, Tensor]) -> Tensor:
    r"""Generate a random camera matrix based on a given uniform distribution.

    Args:
        low: lower range (inclusive).
        high: upper range (exclusive).

    Returns:
        the random camera matrix with the shape of :math:`(1, 3, 3)`.

    """
    sampler = torch.distributions.Uniform(low, high)
    params = sampler.sample((4,))
    fx, fy, cx, cy = params[0], params[1], params[2], params[3]
    camera_matrix = torch.tensor([[fx, 0.0, cx], [0.0, fy, cy], [0.0, 0.0, 1.0]], dtype=fx.dtype, device=fx.device)
    return camera_matrix.unsqueeze(0)


def scale_intrinsics(camera_matrix: Tensor, scale_factor: Union[float, Tensor]) -> Tensor:
    r"""Scale a camera matrix containing the intrinsics.

    Applies the scaling factor to the focal length and center of projection.

    Args:
        camera_matrix: the camera calibration matrix containing the intrinsic
          parameters. The expected shape for the tensor is :math:`(B, 3, 3)`.
        scale_factor: the scaling factor to be applied.

    Returns:
        The scaled camera matrix with shame shape as input :math:`(B, 3, 3)`.

    """
    K_scale = camera_matrix.clone()
    K_scale[..., 0, 0] *= scale_factor
    K_scale[..., 1, 1] *= scale_factor
    K_scale[..., 0, 2] *= scale_factor
    K_scale[..., 1, 2] *= scale_factor
    return K_scale


def projection_from_KRt(K: Tensor, R: Tensor, t: Tensor) -> Tensor:
    r"""Get the projection matrix P from K, R and t.

    This function estimate the projection matrix by solving the following equation: :math:`P = K * [R|t]`.

    Args:
       K: the camera matrix with the intrinsics with shape :math:`(B, 3, 3)`.
       R: The rotation matrix with shape :math:`(B, 3, 3)`.
       t: The translation vector with shape :math:`(B, 3, 1)`.

    Returns:
       The projection matrix P with shape :math:`(B, 4, 4)`.

    """
    KORNIA_CHECK_SHAPE(K, ["*", "3", "3"])
    KORNIA_CHECK_SHAPE(R, ["*", "3", "3"])
    KORNIA_CHECK_SHAPE(t, ["*", "3", "1"])
    if not len(K.shape) == len(R.shape) == len(t.shape):
        raise AssertionError

    Rt = concatenate([R, t], dim=-1)  # 3x4
    Rt_h = pad(Rt, [0, 0, 0, 1], "constant", 0.0)  # 4x4
    Rt_h[..., -1, -1] += 1.0

    K_h = pad(K, [0, 1, 0, 1], "constant", 0.0)  # 4x4
    K_h[..., -1, -1] += 1.0

    return K @ Rt


def KRt_from_projection(P: Tensor, eps: float = 1e-6) -> Tuple[Tensor, Tensor, Tensor]:
    r"""Decompose the Projection matrix into Camera-Matrix, Rotation Matrix and Translation vector.

    Args:
        P: the projection matrix with shape :math:`(B, 3, 4)`.
        eps: epsilon for numerical stability.

    Returns:
        - The Camera matrix with shape :math:`(B, 3, 3)`.
        - The Rotation matrix with shape :math:`(B, 3, 3)`.
        - The Translation vector with shape :math:`(B, 3)`.

    """
    KORNIA_CHECK_SHAPE(P, ["*", "3", "4"])
    submat_3x3 = P[:, 0:3, 0:3]
    last_column = P[:, 0:3, 3].unsqueeze(-1)

    # Trick to turn QR-decomposition into RQ-decomposition
    reverse = torch.tensor([[0, 0, 1], [0, 1, 0], [1, 0, 0]], device=P.device, dtype=P.dtype).unsqueeze(0)
    submat_3x3 = torch.matmul(reverse, submat_3x3).permute(0, 2, 1)
    ortho_mat, upper_mat = linalg_qr(submat_3x3)
    ortho_mat = torch.matmul(reverse, ortho_mat.permute(0, 2, 1))
    upper_mat = torch.matmul(reverse, torch.matmul(upper_mat.permute(0, 2, 1), reverse))

    # Turning the `upper_mat's` diagonal elements to positive.
    diagonals = torch.diagonal(upper_mat, dim1=-2, dim2=-1) + eps
    signs = torch.sign(diagonals)
    signs_mat = torch.diag_embed(signs)

    K = torch.matmul(upper_mat, signs_mat)
    R = torch.matmul(signs_mat, ortho_mat)
    t = torch.matmul(torch.inverse(K), last_column)

    return K, R, t


def depth_from_point(R: Tensor, t: Tensor, X: Tensor) -> Tensor:
    r"""Return the depth of a point transformed by a rigid transform.

    Args:
       R: The rotation matrix with shape :math:`(*, 3, 3)`.
       t: The translation vector with shape :math:`(*, 3, 1)`.
       X: The 3d points with shape :math:`(*, 3)`.

    Returns:
       The depth value per point with shape :math:`(*, 1)`.

    """
    X_tmp = R @ X.transpose(-2, -1)
    X_out = X_tmp[..., 2, :] + t[..., 2, :]
    return X_out


# adapted from:
# https://github.com/opencv/opencv_contrib/blob/master/modules/sfm/src/fundamental.cpp#L61
# https://github.com/mapillary/OpenSfM/blob/master/opensfm/multiview.py#L14
def _nullspace(A: Tensor) -> Tuple[Tensor, Tensor]:
    """Compute the null space of A.

    Return the smallest singular value and the corresponding vector.
    """
    _, s, v = _torch_svd_cast(A)
    return s[..., -1], v[..., -1]


def projections_from_fundamental(F_mat: Tensor) -> Tensor:
    r"""Get the projection matrices from the Fundamental Matrix.

    Args:
       F_mat: the fundamental matrix with the shape :math:`(B, 3, 3)`.

    Returns:
        The projection matrices with shape :math:`(B, 3, 4, 2)`.

    """
    KORNIA_CHECK_SHAPE(F_mat, ["*", "3", "3"])

    R1 = eye_like(3, F_mat)  # Bx3x3
    t1 = vec_like(3, F_mat)  # Bx3

    Ft_mat = F_mat.transpose(-2, -1)

    _, e2 = _nullspace(Ft_mat)

    R2 = cross_product_matrix(e2) @ F_mat  # Bx3x3
    t2 = e2[..., :, None]  # Bx3x1

    P1 = torch.cat([R1, t1], dim=-1)  # Bx3x4
    P2 = torch.cat([R2, t2], dim=-1)  # Bx3x4

    return stack([P1, P2], dim=-1)