def get_affine_matrix2d(translations: torch.Tensor, center: torch.Tensor, scale: torch.Tensor, angle: torch.Tensor,
sx: Optional[torch.Tensor] = None, sy: Optional[torch.Tensor] = None) -> torch.Tensor:
r"""Composes affine matrix Bx3x3 from the components
Returns:
torch.Tensor: params to be passed to the affine transformation.
"""
transform: torch.Tensor = get_rotation_matrix2d(center, -angle, scale)
transform[..., 2] += translations # tx/ty
# pad transform to get Bx3x3
transform_h = convert_affinematrix_to_homography(transform)
if sx is not None:
x, y = torch.split(center, 1, dim=-1)
x = x.view(-1)
y = y.view(-1)
sx_tan = torch.tan(sx) # type: ignore
sy_tan = torch.tan(sy) # type: ignore
zeros = torch.zeros_like(sx) # type: ignore
ones = torch.ones_like(sx) # type: ignore
shear_mat = torch.stack([ones, -sx_tan, sx_tan * x, # type: ignore # noqa: E241
-sy_tan, ones + sx_tan * sy_tan, sy_tan * (-sx_tan * x + y)], # noqa: E241
dim=-1).view(-1, 2, 3)
shear_mat = convert_affinematrix_to_homography(shear_mat)
transform_h = transform_h @ shear_mat
return transform_h
def invert_affine_transform(matrix: torch.Tensor) -> torch.Tensor:
r"""Invert an affine transformation.
The function computes an inverse affine transformation represented by
2×3 matrix:
.. math::
\begin{bmatrix}
a_{11} & a_{12} & b_{1} \\
a_{21} & a_{22} & b_{2} \\
\end{bmatrix}
The result is also a 2×3 matrix of the same type as M.
Args:
matrix: original affine transform. The tensor must be
in the shape of :math:`(B, 2, 3)`.
Return:
the reverse affine transform with shape :math:`(B, 2, 3)`.
.. note::
This function is often used in conjunction with :func:`warp_affine`.
"""
if not isinstance(matrix, torch.Tensor):
raise TypeError(f"Input matrix type is not a torch.Tensor. Got {type(matrix)}")
if not (len(matrix.shape) == 3 and matrix.shape[-2:] == (2, 3)):
raise ValueError(f"Input matrix must be a Bx2x3 tensor. Got {matrix.shape}")
matrix_tmp: torch.Tensor = convert_affinematrix_to_homography(matrix)
matrix_inv: torch.Tensor = torch.inverse(matrix_tmp)
return matrix_inv[..., :2, :3]
def invert_affine_transform(matrix: torch.Tensor) -> torch.Tensor:
r"""Inverts an affine transformation.
The function computes an inverse affine transformation represented by
2×3 matrix:
.. math::
\begin{bmatrix}
a_{11} & a_{12} & b_{1} \\
a_{21} & a_{22} & b_{2} \\
\end{bmatrix}
The result is also a 2×3 matrix of the same type as M.
Args:
matrix (torch.Tensor): original affine transform. The tensor must be
in the shape of (B, 2, 3).
Return:
torch.Tensor: the reverse affine transform.
"""
if not torch.is_tensor(matrix):
raise TypeError("Input matrix type is not a torch.Tensor. Got {}"
.format(type(matrix)))
if not (len(matrix.shape) == 3 and matrix.shape[-2:] == (2, 3)):
raise ValueError("Input matrix must be a Bx2x3 tensor. Got {}"
.format(matrix.shape))
matrix_tmp: torch.Tensor = convert_affinematrix_to_homography(matrix)
matrix_inv: torch.Tensor = torch.inverse(matrix_tmp)
return matrix_inv[..., :2, :3]
def get_affine_matrix2d(
translations: torch.Tensor,
center: torch.Tensor,
scale: torch.Tensor,
angle: torch.Tensor,
sx: Optional[torch.Tensor] = None,
sy: Optional[torch.Tensor] = None,
) -> torch.Tensor:
r"""Composes affine matrix from the components.
Args:
translations: tensor containing the translation vector with shape :math:`(B, 2)`.
center: tensor containing the center vector with shape :math:`(B, 2)`.
scale: tensor containing the scale factor with shape :math:`(B, 2)`.
angle: tensor of angles in degrees :math:`(B)`.
sx: tensor containing the shear factor in the x-direction with shape :math:`(B)`.
sy: tensor containing the shear factor in the y-direction with shape :math:`(B)`.
Returns:
the affine transformation matrix :math:`(B, 3, 3)`.
.. note::
This function is often used in conjuntion with :func:`warp_affine`, :func:`warp_perspective`.
"""
transform: torch.Tensor = get_rotation_matrix2d(center, -angle, scale)
transform[..., 2] += translations # tx/ty
# pad transform to get Bx3x3
transform_h = convert_affinematrix_to_homography(transform)
if any(s is not None for s in [sx, sy]):
shear_mat = get_shear_matrix2d(center, sx, sy)
transform_h = transform_h @ shear_mat
return transform_h
def warp_affine(src: torch.Tensor, M: torch.Tensor,
dsize: Tuple[int, int], flags: str = 'bilinear',
padding_mode: str = 'zeros',
align_corners: bool = False) -> torch.Tensor:
r"""Applies an affine transformation to a tensor.
The function warp_affine transforms the source tensor using
the specified matrix:
.. math::
\text{dst}(x, y) = \text{src} \left( M_{11} x + M_{12} y + M_{13} ,
M_{21} x + M_{22} y + M_{23} \right )
Args:
src (torch.Tensor): input tensor of shape :math:`(B, C, H, W)`.
M (torch.Tensor): affine transformation of shape :math:`(B, 2, 3)`.
dsize (Tuple[int, int]): size of the output image (height, width).
mode (str): interpolation mode to calculate output values
'bilinear' | 'nearest'. Default: 'bilinear'.
padding_mode (str): padding mode for outside grid values
'zeros' | 'border' | 'reflection'. Default: 'zeros'.
align_corners (bool): mode for grid_generation. Default: False.
Returns:
torch.Tensor: the warped tensor with shape :math:`(B, C, H, W)`.
.. note::
See a working example `here <https://kornia.readthedocs.io/en/latest/
tutorials/warp_affine.html>`__.
"""
if not isinstance(src, torch.Tensor):
raise TypeError("Input src type is not a torch.Tensor. Got {}"
.format(type(src)))
if not isinstance(M, torch.Tensor):
raise TypeError("Input M type is not a torch.Tensor. Got {}"
.format(type(M)))
if not len(src.shape) == 4:
raise ValueError("Input src must be a BxCxHxW tensor. Got {}"
.format(src.shape))
if not (len(M.shape) == 3 or M.shape[-2:] == (2, 3)):
raise ValueError("Input M must be a Bx2x3 tensor. Got {}"
.format(M.shape))
B, C, H, W = src.size()
dsize_src = (H, W)
out_size = dsize
# we generate a 3x3 transformation matrix from 2x3 affine
M_3x3: torch.Tensor = convert_affinematrix_to_homography(M)
dst_norm_trans_src_norm: torch.Tensor = normalize_homography(
M_3x3, dsize_src, out_size)
src_norm_trans_dst_norm = torch.inverse(dst_norm_trans_src_norm)
grid = F.affine_grid(src_norm_trans_dst_norm[:, :2, :],
[B, C, out_size[0], out_size[1]],
align_corners=align_corners)
return F.grid_sample(src, grid,
align_corners=align_corners,
mode=flags,
padding_mode=padding_mode)
def get_affine_matrix2d(translations: torch.Tensor,
center: torch.Tensor,
scale: torch.Tensor,
angle: torch.Tensor,
sx: Optional[torch.Tensor] = None,
sy: Optional[torch.Tensor] = None) -> torch.Tensor:
r"""Composes affine matrix from the components.
Args:
translations (torch.Tensor): tensor containing the translation vector with shape :math:`(B, 2)`.
center (torch.Tensor): tensor containing the center vector with shape :math:`(B, 2)`.
scale (torch.Tensor): tensor containing the scale factor with shape :math:`(B, 2)`.
sx (torch.Tensor, optional): tensor containing the shear factor in the x-direction with shape :math:`(B)`.
sy (torch.Tensor, optional): tensor containing the shear factor in the y-direction with shape :math:`(B)`.
Returns:
torch.Tensor: the affine transformation matrix :math:`(B, 2, 3)`.
"""
transform: torch.Tensor = get_rotation_matrix2d(center, -angle, scale)
transform[..., 2] += translations # tx/ty
# pad transform to get Bx3x3
transform_h = convert_affinematrix_to_homography(transform)
if any([s is not None for s in [sx, sy]]):
shear_mat = get_shear_matrix2d(center, sx, sy)
transform_h = transform_h @ shear_mat
return transform_h
def get_shear_matrix2d(center: torch.Tensor,
sx: Optional[torch.Tensor] = None,
sy: Optional[torch.Tensor] = None):
r"""Composes shear matrix Bx4x4 from the components.
Note: Ordered shearing, shear x-axis then y-axis.
.. math::
\begin{bmatrix}
1 & b \\
a & ab + 1 \\
\end{bmatrix}
Args:
center: shearing center coordinates of (x, y).
sx: shearing degree along x axis.
sy: shearing degree along y axis.
Returns:
params to be passed to the affine transformation with shape :math:`(B, 3, 3)`.
Examples:
>>> rng = torch.manual_seed(0)
>>> sx = torch.randn(1)
>>> sx
tensor([1.5410])
>>> center = torch.tensor([[0., 0.]]) # Bx2
>>> get_shear_matrix2d(center, sx=sx)
tensor([[[ 1.0000, -33.5468, 0.0000],
[ -0.0000, 1.0000, 0.0000],
[ 0.0000, 0.0000, 1.0000]]])
.. note::
This function is often used in conjuntion with :func:`warp_affine`, :func:`warp_perspective`.
"""
sx = torch.tensor([0.0]).repeat(center.size(0)) if sx is None else sx
sy = torch.tensor([0.0]).repeat(center.size(0)) if sy is None else sy
x, y = torch.split(center, 1, dim=-1)
x, y = x.view(-1), y.view(-1)
sx_tan = torch.tan(sx) # type: ignore
sy_tan = torch.tan(sy) # type: ignore
ones = torch.ones_like(sx) # type: ignore
shear_mat = torch.stack(
[
ones,
-sx_tan,
sx_tan * y, # type: ignore # noqa: E241
-sy_tan,
ones + sx_tan * sy_tan,
sy_tan * (sx_tan * y + x), # noqa: E241
],
dim=-1,
).view(-1, 2, 3)
shear_mat = convert_affinematrix_to_homography(shear_mat)
return shear_mat
def forward(self) -> torch.Tensor:
r"""Single-batch similarity transform".
Returns:
Similarity with shape :math:`(1, 3, 3)`"""
rot = self.scale * angle_to_rotation_matrix(self.rot)
out = convert_affinematrix_to_homography(
torch.cat([rot, self.shift], dim=2))
return out
def warp_affine(
src: torch.Tensor,
M: torch.Tensor,
dsize: Tuple[int, int],
mode: str = 'bilinear',
padding_mode: str = 'zeros',
align_corners: Optional[bool] = None,
) -> torch.Tensor:
r"""Applies an affine transformation to a tensor.
.. image:: _static/img/warp_affine.png
The function warp_affine transforms the source tensor using
the specified matrix:
.. math::
\text{dst}(x, y) = \text{src} \left( M_{11} x + M_{12} y + M_{13} ,
M_{21} x + M_{22} y + M_{23} \right )
Args:
src: input tensor of shape :math:`(B, C, H, W)`.
M: affine transformation of shape :math:`(B, 2, 3)`.
dsize: size of the output image (height, width).
mode: interpolation mode to calculate output values ``'bilinear'`` | ``'nearest'``.
padding_mode (str): padding mode for outside grid values ``'zeros'`` | ``'border'`` | ``'reflection'``.
align_corners : mode for grid_generation.
Returns:
the warped tensor with shape :math:`(B, C, H, W)`.
Example:
>>> img = torch.rand(1, 4, 5, 6)
>>> A = torch.eye(2, 3)[None]
>>> out = warp_affine(img, A, (4, 2), align_corners=True)
>>> print(out.shape)
torch.Size([1, 4, 4, 2])
.. note::
This function is often used in conjuntion with :func:`get_rotation_matrix2d`,
:func:`get_shear_matrix2d`, :func:`get_affine_matrix2d`, :func:`invert_affine_transform`.
.. note::
See a working example `here <https://kornia.readthedocs.io/en/latest/
tutorials/warp_affine.html>`__.
"""
if not isinstance(src, torch.Tensor):
raise TypeError("Input src type is not a torch.Tensor. Got {}".format(
type(src)))
if not isinstance(M, torch.Tensor):
raise TypeError("Input M type is not a torch.Tensor. Got {}".format(
type(M)))
if not len(src.shape) == 4:
raise ValueError("Input src must be a BxCxHxW tensor. Got {}".format(
src.shape))
if not (len(M.shape) == 3 or M.shape[-2:] == (2, 3)):
raise ValueError("Input M must be a Bx2x3 tensor. Got {}".format(
M.shape))
# TODO: remove the statement below in kornia v0.6
if align_corners is None:
message: str = (
"The align_corners default value has been changed. By default now is set True "
"in order to match cv2.warpAffine. In case you want to keep your previous "
"behaviour set it to False. This warning will disappear in kornia > v0.6."
)
warnings.warn(message)
# set default value for align corners
align_corners = True
B, C, H, W = src.size()
# we generate a 3x3 transformation matrix from 2x3 affine
M_3x3: torch.Tensor = convert_affinematrix_to_homography(M)
dst_norm_trans_src_norm: torch.Tensor = normalize_homography(
M_3x3, (H, W), dsize)
# src_norm_trans_dst_norm = torch.inverse(dst_norm_trans_src_norm)
src_norm_trans_dst_norm = _torch_inverse_cast(dst_norm_trans_src_norm)
grid = F.affine_grid(src_norm_trans_dst_norm[:, :2, :],
[B, C, dsize[0], dsize[1]],
align_corners=align_corners)
return F.grid_sample(src,
grid,
align_corners=align_corners,
mode=mode,
padding_mode=padding_mode)
def warp_affine(
src: torch.Tensor,
M: torch.Tensor,
dsize: Tuple[int, int],
mode: str = 'bilinear',
padding_mode: str = 'zeros',
align_corners: bool = True,
) -> torch.Tensor:
r"""Apply an affine transformation to a tensor.
.. image:: _static/img/warp_affine.png
The function warp_affine transforms the source tensor using
the specified matrix:
.. math::
\text{dst}(x, y) = \text{src} \left( M_{11} x + M_{12} y + M_{13} ,
M_{21} x + M_{22} y + M_{23} \right )
Args:
src: input tensor of shape :math:`(B, C, H, W)`.
M: affine transformation of shape :math:`(B, 2, 3)`.
dsize: size of the output image (height, width).
mode: interpolation mode to calculate output values ``'bilinear'`` | ``'nearest'``.
padding_mode (str): padding mode for outside grid values ``'zeros'`` | ``'border'`` | ``'reflection'``.
align_corners : mode for grid_generation.
Returns:
the warped tensor with shape :math:`(B, C, H, W)`.
.. note::
This function is often used in conjunction with :func:`get_rotation_matrix2d`,
:func:`get_shear_matrix2d`, :func:`get_affine_matrix2d`, :func:`invert_affine_transform`.
.. note::
See a working example `here <https://kornia-tutorials.readthedocs.io/en/latest/
rotate_affine.html>`__.
Example:
>>> img = torch.rand(1, 4, 5, 6)
>>> A = torch.eye(2, 3)[None]
>>> out = warp_affine(img, A, (4, 2), align_corners=True)
>>> print(out.shape)
torch.Size([1, 4, 4, 2])
"""
if not isinstance(src, torch.Tensor):
raise TypeError(f"Input src type is not a torch.Tensor. Got {type(src)}")
if not isinstance(M, torch.Tensor):
raise TypeError(f"Input M type is not a torch.Tensor. Got {type(M)}")
if not len(src.shape) == 4:
raise ValueError(f"Input src must be a BxCxHxW tensor. Got {src.shape}")
if not (len(M.shape) == 3 or M.shape[-2:] == (2, 3)):
raise ValueError(f"Input M must be a Bx2x3 tensor. Got {M.shape}")
B, C, H, W = src.size()
# we generate a 3x3 transformation matrix from 2x3 affine
M_3x3: torch.Tensor = convert_affinematrix_to_homography(M)
dst_norm_trans_src_norm: torch.Tensor = normalize_homography(M_3x3, (H, W), dsize)
# src_norm_trans_dst_norm = torch.inverse(dst_norm_trans_src_norm)
src_norm_trans_dst_norm = _torch_inverse_cast(dst_norm_trans_src_norm)
grid = F.affine_grid(src_norm_trans_dst_norm[:, :2, :], [B, C, dsize[0], dsize[1]], align_corners=align_corners)
return F.grid_sample(src, grid, align_corners=align_corners, mode=mode, padding_mode=padding_mode)