Source code for kornia.geometry.linalg

import warnings

import torch

import kornia
from kornia.geometry.bbox import transform_bbox as _transform_bbox
from kornia.geometry.conversions import convert_points_from_homogeneous, convert_points_to_homogeneous
from kornia.testing import check_is_tensor

__all__ = [
    "compose_transformations",
    "relative_transformation",
    "inverse_transformation",
    "transform_points",
    "transform_boxes",
    "perspective_transform_lafs",
]


[docs]def compose_transformations(trans_01: torch.Tensor, trans_12: torch.Tensor) -> torch.Tensor: r"""Functions that composes two homogeneous transformations. .. math:: T_0^{2} = \begin{bmatrix} R_0^1 R_1^{2} & R_0^{1} t_1^{2} + t_0^{1} \\ \mathbf{0} & 1\end{bmatrix} Args: trans_01: tensor with the homogeneous transformation from a reference frame 1 respect to a frame 0. The tensor has must have a shape of :math:`(B, 4, 4)` or :math:`(4, 4)`. trans_12: tensor with the homogeneous transformation from a reference frame 2 respect to a frame 1. The tensor has must have a shape of :math:`(B, 4, 4)` or :math:`(4, 4)`. Returns: the transformation between the two frames with shape :math:`(N, 4, 4)` or :math:`(4, 4)`. Example:: >>> trans_01 = torch.eye(4) # 4x4 >>> trans_12 = torch.eye(4) # 4x4 >>> trans_02 = compose_transformations(trans_01, trans_12) # 4x4 """ if not torch.is_tensor(trans_01): raise TypeError(f"Input trans_01 type is not a torch.Tensor. Got {type(trans_01)}") if not torch.is_tensor(trans_12): raise TypeError(f"Input trans_12 type is not a torch.Tensor. Got {type(trans_12)}") if not trans_01.dim() in (2, 3) and trans_01.shape[-2:] == (4, 4): raise ValueError("Input trans_01 must be a of the shape Nx4x4 or 4x4." " Got {}".format(trans_01.shape)) if not trans_12.dim() in (2, 3) and trans_12.shape[-2:] == (4, 4): raise ValueError("Input trans_12 must be a of the shape Nx4x4 or 4x4." " Got {}".format(trans_12.shape)) if not trans_01.dim() == trans_12.dim(): raise ValueError(f"Input number of dims must match. Got {trans_01.dim()} and {trans_12.dim()}") # unpack input data rmat_01: torch.Tensor = trans_01[..., :3, :3] # Nx3x3 rmat_12: torch.Tensor = trans_12[..., :3, :3] # Nx3x3 tvec_01: torch.Tensor = trans_01[..., :3, -1:] # Nx3x1 tvec_12: torch.Tensor = trans_12[..., :3, -1:] # Nx3x1 # compute the actual transforms composition rmat_02: torch.Tensor = torch.matmul(rmat_01, rmat_12) tvec_02: torch.Tensor = torch.matmul(rmat_01, tvec_12) + tvec_01 # pack output tensor trans_02: torch.Tensor = torch.zeros_like(trans_01) trans_02[..., :3, 0:3] += rmat_02 trans_02[..., :3, -1:] += tvec_02 trans_02[..., -1, -1:] += 1.0 return trans_02
[docs]def inverse_transformation(trans_12): r"""Function that inverts a 4x4 homogeneous transformation :math:`T_1^{2} = \begin{bmatrix} R_1 & t_1 \\ \mathbf{0} & 1 \end{bmatrix}` The inverse transformation is computed as follows: .. math:: T_2^{1} = (T_1^{2})^{-1} = \begin{bmatrix} R_1^T & -R_1^T t_1 \\ \mathbf{0} & 1\end{bmatrix} Args: trans_12: transformation tensor of shape :math:`(N, 4, 4)` or :math:`(4, 4)`. Returns: tensor with inverted transformations with shape :math:`(N, 4, 4)` or :math:`(4, 4)`. Example: >>> trans_12 = torch.rand(1, 4, 4) # Nx4x4 >>> trans_21 = inverse_transformation(trans_12) # Nx4x4 """ if not torch.is_tensor(trans_12): raise TypeError(f"Input type is not a torch.Tensor. Got {type(trans_12)}") if not trans_12.dim() in (2, 3) and trans_12.shape[-2:] == (4, 4): raise ValueError(f"Input size must be a Nx4x4 or 4x4. Got {trans_12.shape}") # unpack input tensor rmat_12: torch.Tensor = trans_12[..., :3, 0:3] # Nx3x3 tvec_12: torch.Tensor = trans_12[..., :3, 3:4] # Nx3x1 # compute the actual inverse rmat_21: torch.Tensor = torch.transpose(rmat_12, -1, -2) tvec_21: torch.Tensor = torch.matmul(-rmat_21, tvec_12) # pack to output tensor trans_21: torch.Tensor = torch.zeros_like(trans_12) trans_21[..., :3, 0:3] += rmat_21 trans_21[..., :3, -1:] += tvec_21 trans_21[..., -1, -1:] += 1.0 return trans_21
[docs]def relative_transformation(trans_01: torch.Tensor, trans_02: torch.Tensor) -> torch.Tensor: r"""Function that computes the relative homogeneous transformation from a reference transformation :math:`T_1^{0} = \begin{bmatrix} R_1 & t_1 \\ \mathbf{0} & 1 \end{bmatrix}` to destination :math:`T_2^{0} = \begin{bmatrix} R_2 & t_2 \\ \mathbf{0} & 1 \end{bmatrix}`. The relative transformation is computed as follows: .. math:: T_1^{2} = (T_0^{1})^{-1} \cdot T_0^{2} Args: trans_01: reference transformation tensor of shape :math:`(N, 4, 4)` or :math:`(4, 4)`. trans_02: destination transformation tensor of shape :math:`(N, 4, 4)` or :math:`(4, 4)`. Returns: the relative transformation between the transformations with shape :math:`(N, 4, 4)` or :math:`(4, 4)`. Example:: >>> trans_01 = torch.eye(4) # 4x4 >>> trans_02 = torch.eye(4) # 4x4 >>> trans_12 = relative_transformation(trans_01, trans_02) # 4x4 """ if not torch.is_tensor(trans_01): raise TypeError(f"Input trans_01 type is not a torch.Tensor. Got {type(trans_01)}") if not torch.is_tensor(trans_02): raise TypeError(f"Input trans_02 type is not a torch.Tensor. Got {type(trans_02)}") if not trans_01.dim() in (2, 3) and trans_01.shape[-2:] == (4, 4): raise ValueError("Input must be a of the shape Nx4x4 or 4x4." " Got {}".format(trans_01.shape)) if not trans_02.dim() in (2, 3) and trans_02.shape[-2:] == (4, 4): raise ValueError("Input must be a of the shape Nx4x4 or 4x4." " Got {}".format(trans_02.shape)) if not trans_01.dim() == trans_02.dim(): raise ValueError(f"Input number of dims must match. Got {trans_01.dim()} and {trans_02.dim()}") trans_10: torch.Tensor = inverse_transformation(trans_01) trans_12: torch.Tensor = compose_transformations(trans_10, trans_02) return trans_12
[docs]def transform_points(trans_01: torch.Tensor, points_1: torch.Tensor) -> torch.Tensor: r"""Function that applies transformations to a set of points. Args: trans_01 (torch.Tensor): tensor for transformations of shape :math:`(B, D+1, D+1)`. points_1 (torch.Tensor): tensor of points of shape :math:`(B, N, D)`. Returns: torch.Tensor: tensor of N-dimensional points. Shape: - Output: :math:`(B, N, D)` Examples: >>> points_1 = torch.rand(2, 4, 3) # BxNx3 >>> trans_01 = torch.eye(4).view(1, 4, 4) # Bx4x4 >>> points_0 = transform_points(trans_01, points_1) # BxNx3 """ check_is_tensor(trans_01) check_is_tensor(points_1) if not trans_01.shape[0] == points_1.shape[0] and trans_01.shape[0] != 1: raise ValueError("Input batch size must be the same for both tensors or 1") if not trans_01.shape[-1] == (points_1.shape[-1] + 1): raise ValueError("Last input dimensions must differ by one unit") # We reshape to BxNxD in case we get more dimensions, e.g., MxBxNxD shape_inp = list(points_1.shape) points_1 = points_1.reshape(-1, points_1.shape[-2], points_1.shape[-1]) trans_01 = trans_01.reshape(-1, trans_01.shape[-2], trans_01.shape[-1]) # We expand trans_01 to match the dimensions needed for bmm trans_01 = torch.repeat_interleave(trans_01, repeats=points_1.shape[0] // trans_01.shape[0], dim=0) # to homogeneous points_1_h = convert_points_to_homogeneous(points_1) # BxNxD+1 # transform coordinates points_0_h = torch.bmm(points_1_h, trans_01.permute(0, 2, 1)) points_0_h = torch.squeeze(points_0_h, dim=-1) # to euclidean points_0 = convert_points_from_homogeneous(points_0_h) # BxNxD # reshape to the input shape shape_inp[-2] = points_0.shape[-2] shape_inp[-1] = points_0.shape[-1] points_0 = points_0.reshape(shape_inp) return points_0
[docs]def transform_boxes(trans_mat: torch.Tensor, boxes: torch.Tensor, mode: str = "xyxy") -> torch.Tensor: r"""Function that applies a transformation matrix to a box or batch of boxes. Boxes must be a tensor of the shape (N, 4) or a batch of boxes (B, N, 4) and trans_mat must be a (3, 3) transformation matrix or a batch of transformation matrices (B, 3, 3) Args: trans_mat: The transformation matrix to be applied. boxes: The boxes to be transformed. mode: The format in which the boxes are provided. If set to 'xyxy' the boxes are assumed to be in the format (xmin, ymin, xmax, ymax). If set to 'xywh' the boxes are assumed to be in the format (xmin, ymin, width, height). Returns: The set of transformed points in the specified mode. """ warnings.warn( "`kornia.geometry.linalg.transform_boxes` is deprecated and will be removed > 0.6.0. " "Please use `kornia.geometry.bbox.transform_bbox instead.`", DeprecationWarning, stacklevel=2, ) return _transform_bbox(trans_mat, boxes, mode)
[docs]def perspective_transform_lafs(trans_01: torch.Tensor, lafs_1: torch.Tensor) -> torch.Tensor: r"""Function that applies perspective transformations to a set of local affine frames (LAFs). Args: trans_01: tensor for perspective transformations of shape :math:`(B, 3, 3)`. lafs_1: tensor of lafs of shape :math:`(B, N, 2, 3)`. Returns: tensor of N-dimensional points of shape :math:`(B, N, 2, 3)`. Examples: >>> rng = torch.manual_seed(0) >>> lafs_1 = torch.rand(2, 4, 2, 3) # BxNx2x3 >>> lafs_1 tensor([[[[0.4963, 0.7682, 0.0885], [0.1320, 0.3074, 0.6341]], <BLANKLINE> [[0.4901, 0.8964, 0.4556], [0.6323, 0.3489, 0.4017]], <BLANKLINE> [[0.0223, 0.1689, 0.2939], [0.5185, 0.6977, 0.8000]], <BLANKLINE> [[0.1610, 0.2823, 0.6816], [0.9152, 0.3971, 0.8742]]], <BLANKLINE> <BLANKLINE> [[[0.4194, 0.5529, 0.9527], [0.0362, 0.1852, 0.3734]], <BLANKLINE> [[0.3051, 0.9320, 0.1759], [0.2698, 0.1507, 0.0317]], <BLANKLINE> [[0.2081, 0.9298, 0.7231], [0.7423, 0.5263, 0.2437]], <BLANKLINE> [[0.5846, 0.0332, 0.1387], [0.2422, 0.8155, 0.7932]]]]) >>> trans_01 = torch.eye(3).repeat(2, 1, 1) # Bx3x3 >>> trans_01.shape torch.Size([2, 3, 3]) >>> lafs_0 = perspective_transform_lafs(trans_01, lafs_1) # BxNx2x3 """ kornia.feature.laf.raise_error_if_laf_is_not_valid(lafs_1) if not torch.is_tensor(trans_01): raise TypeError("Input type is not a torch.Tensor") if not trans_01.device == lafs_1.device: raise TypeError("Tensor must be in the same device") if not trans_01.shape[0] == lafs_1.shape[0]: raise ValueError("Input batch size must be the same for both tensors") if (not (trans_01.shape[-1] == 3)) or (not (trans_01.shape[-2] == 3)): raise ValueError("Transformation should be homography") bs, n, _, _ = lafs_1.size() # First, we convert LAF to points threepts_1 = kornia.feature.laf.laf_to_three_points(lafs_1) points_1 = threepts_1.permute(0, 1, 3, 2).reshape(bs, n * 3, 2) # First, transform the points points_0 = transform_points(trans_01, points_1) # Back to LAF format threepts_0 = points_0.view(bs, n, 3, 2).permute(0, 1, 3, 2) return kornia.feature.laf.laf_from_three_points(threepts_0)
# TODO: # - project_points: from opencv # layer api # NOTE: is it needed ? '''class TransformPoints(nn.Module): r"""Creates an object to transform a set of points. Args: dst_pose_src (torhc.Tensor): tensor for transformations of shape :math:`(B, D+1, D+1)`. Returns: torch.Tensor: tensor of N-dimensional points. Shape: - Input: :math:`(B, D, N)` - Output: :math:`(B, N, D)` Examples: >>> input = torch.rand(2, 4, 3) # BxNx3 >>> transform = torch.eye(4).view(1, 4, 4) # Bx4x4 >>> transform_op = kornia.TransformPoints(transform) >>> output = transform_op(input) # BxNx3 """ def __init__(self, dst_homo_src: torch.Tensor) -> None: super(TransformPoints, self).__init__() self.dst_homo_src: torch.Tensor = dst_homo_src def forward(self, points_src: torch.Tensor) -> torch.Tensor: # type: ignore return transform_points(self.dst_homo_src, points_src) class InversePose(nn.Module): r"""Creates a transformation that inverts a 4x4 pose. Args: points (Tensor): tensor with poses. Returns: Tensor: tensor with inverted poses. Shape: - Input: :math:`(N, 4, 4)` - Output: :math:`(N, 4, 4)` Example: >>> pose = torch.rand(1, 4, 4) # Nx4x4 >>> transform = kornia.InversePose() >>> pose_inv = transform(pose) # Nx4x4 """ def __init__(self): super(InversePose, self).__init__() def forward(self, input): return inverse_pose(input)'''