kornia.geometry.conversions¶

rad2deg(tensor: torch.Tensor) → torch.Tensor[source]¶

Function that converts angles from radians to degrees.

Parameters: tensor (torch.Tensor) – Tensor of arbitrary shape.
Returns: Tensor with same shape as input.
Return type: torch.Tensor

Example

>>> input = torch.tensor(3.1415926535) * torch.rand(1, 3, 3)
>>> output = rad2deg(input)

deg2rad(tensor: torch.Tensor) → torch.Tensor[source]¶

Function that converts angles from degrees to radians.

Parameters: tensor (torch.Tensor) – Tensor of arbitrary shape.
Returns: tensor with same shape as input.
Return type: torch.Tensor

Examples:

>>> input = 360. * torch.rand(1, 3, 3)
>>> output = deg2rad(input)

pol2cart(rho: torch.Tensor, phi: torch.Tensor) → Tuple[torch.Tensor, torch.Tensor][source]¶

Function that converts polar coordinates to cartesian coordinates.

Parameters

rho (torch.Tensor) – Tensor of arbitrary shape.
phi (torch.Tensor) – Tensor of same arbitrary shape.

Returns

Tensor with same shape as input.

Return type

torch.Tensor, torch.Tensor

Example

>>> rho = torch.rand(1, 3, 3)
>>> phi = torch.rand(1, 3, 3)
>>> x, y = pol2cart(rho, phi)

cart2pol(x: torch.Tensor, y: torch.Tensor, eps: float = 1e-08) → Tuple[torch.Tensor, torch.Tensor][source]¶

Function that converts cartesian coordinates to polar coordinates.

Parameters

rho (torch.Tensor) – Tensor of arbitrary shape.
phi (torch.Tensor) – Tensor of same arbitrary shape.
eps (float) – To avoid division by zero. Default is 1e-8

Returns

Tensor with same shape as input.

Return type

torch.Tensor, torch.Tensor

Example

>>> x = torch.rand(1, 3, 3)
>>> y = torch.rand(1, 3, 3)
>>> rho, phi = cart2pol(x, y)

convert_points_from_homogeneous(points: torch.Tensor, eps: float = 1e-08) → torch.Tensor[source]¶

Function that converts points from homogeneous to Euclidean space.

Examples:

>>> input = torch.rand(2, 4, 3)  # BxNx3
>>> output = convert_points_from_homogeneous(input)  # BxNx2

convert_points_to_homogeneous(points: torch.Tensor) → torch.Tensor[source]¶

Function that converts points from Euclidean to homogeneous space.

Examples:

>>> input = torch.rand(2, 4, 3)  # BxNx3
>>> output = convert_points_to_homogeneous(input)  # BxNx4

convert_affinematrix_to_homography(A: torch.Tensor) → torch.Tensor[source]¶

Function that converts batch of affine matrices from [Bx2x3] to [Bx3x3].

Examples:

>>> input = torch.rand(2, 2, 3)  # Bx2x3
>>> output = convert_affinematrix_to_homography(input)  # Bx3x3

rotation_matrix_to_angle_axis(rotation_matrix: torch.Tensor) → torch.Tensor[source]¶

Convert 3x3 rotation matrix to Rodrigues vector.

Parameters: rotation_matrix (torch.Tensor) – rotation matrix.
Returns: Rodrigues vector transformation.
Return type: torch.Tensor

Shape:

Input: \((N, 3, 3)\)
Output: \((N, 3)\)

Example

>>> input = torch.rand(2, 3, 3)  # Nx3x3
>>> output = rotation_matrix_to_angle_axis(input)  # Nx3

rotation_matrix_to_quaternion(rotation_matrix: torch.Tensor, eps: float = 1e-08) → torch.Tensor[source]¶

Convert 3x3 rotation matrix to 4d quaternion vector. The quaternion vector has components in (x, y, z, w) format.

Parameters

rotation_matrix (torch.Tensor) – the rotation matrix to convert.
eps (float) – small value to avoid zero division. Default: 1e-8.

Returns

the rotation in quaternion.

Return type

torch.Tensor

Shape:

Input: \((*, 3, 3)\)
Output: \((*, 4)\)

Example

>>> input = torch.rand(4, 3, 3)  # Nx3x3
>>> output = rotation_matrix_to_quaternion(input)  # Nx4

quaternion_to_angle_axis(quaternion: torch.Tensor) → torch.Tensor[source]¶

Convert quaternion vector to angle axis of rotation. The quaternion should be in (x, y, z, w) format.

Adapted from ceres C++ library: ceres-solver/include/ceres/rotation.h

Parameters: quaternion (torch.Tensor) – tensor with quaternions.
Returns: tensor with angle axis of rotation.
Return type: torch.Tensor

Shape:

Input: \((*, 4)\) where * means, any number of dimensions
Output: \((*, 3)\)

Example

>>> quaternion = torch.rand(2, 4)  # Nx4
>>> angle_axis = quaternion_to_angle_axis(quaternion)  # Nx3

quaternion_to_rotation_matrix(quaternion: torch.Tensor) → torch.Tensor[source]¶

Converts a quaternion to a rotation matrix. The quaternion should be in (x, y, z, w) format.

Parameters: quaternion (torch.Tensor) – a tensor containing a quaternion to be converted. The tensor can be of shape \((*, 4)\).
Returns: the rotation matrix of shape \((*, 3, 3)\).
Return type: torch.Tensor

Example

>>> quaternion = torch.tensor([0., 0., 1., 0.])
>>> quaternion_to_rotation_matrix(quaternion)
tensor([[-1.,  0.,  0.],
        [ 0., -1.,  0.],
        [ 0.,  0.,  1.]])

quaternion_log_to_exp(quaternion: torch.Tensor, eps: float = 1e-08) → torch.Tensor[source]¶

Applies exponential map to log quaternion. The quaternion should be in (x, y, z, w) format.

Parameters: quaternion (torch.Tensor) – a tensor containing a quaternion to be converted. The tensor can be of shape \((*, 3)\).
Returns: the quaternion exponential map of shape \((*, 4)\).
Return type: torch.Tensor

Example

>>> quaternion = torch.tensor([0., 0., 0.])
>>> quaternion_log_to_exp(quaternion)
tensor([0., 0., 0., 1.])

quaternion_exp_to_log(quaternion: torch.Tensor, eps: float = 1e-08) → torch.Tensor[source]¶

Applies the log map to a quaternion. The quaternion should be in (x, y, z, w) format.

Parameters: quaternion (torch.Tensor) – a tensor containing a quaternion to be converted. The tensor can be of shape \((*, 4)\).
Returns: the quaternion log map of shape \((*, 3)\).
Return type: torch.Tensor

Example

>>> quaternion = torch.tensor([0., 0., 0., 1.])
>>> quaternion_exp_to_log(quaternion)
tensor([0., 0., 0.])

angle_axis_to_quaternion(angle_axis: torch.Tensor) → torch.Tensor[source]¶

Convert an angle axis to a quaternion. The quaternion vector has components in (x, y, z, w) format.

Adapted from ceres C++ library: ceres-solver/include/ceres/rotation.h

Parameters: angle_axis (torch.Tensor) – tensor with angle axis.
Returns: tensor with quaternion.
Return type: torch.Tensor

Shape:

Input: \((*, 3)\) where * means, any number of dimensions
Output: \((*, 4)\)

Example

>>> angle_axis = torch.rand(2, 3)  # Nx3
>>> quaternion = angle_axis_to_quaternion(angle_axis)  # Nx4

angle_axis_to_rotation_matrix(angle_axis: torch.Tensor) → torch.Tensor[source]¶

Convert 3d vector of axis-angle rotation to 3x3 rotation matrix

Parameters: angle_axis (torch.Tensor) – tensor of 3d vector of axis-angle rotations.
Returns: tensor of 3x3 rotation matrices.
Return type: torch.Tensor

Shape:

Input: \((N, 3)\)
Output: \((N, 3, 3)\)

Example

>>> input = torch.rand(1, 3)  # Nx3
>>> output = angle_axis_to_rotation_matrix(input)  # Nx3x3

denormalize_pixel_coordinates(pixel_coordinates: torch.Tensor, height: int, width: int, eps: float = 1e-08) → torch.Tensor[source]¶

Denormalize pixel coordinates.

The input is assumed to be -1 if on extreme left, 1 if on extreme right (x = w-1).

Parameters

pixel_coordinates (torch.Tensor) – the normalized grid coordinates. Shape can be \((*, 2)\).
width (int) – the maximum width in the x-axis.
height (int) – the maximum height in the y-axis.
eps (float) – safe division by zero. (default 1e-8).

Returns

the denormalized pixel coordinates.

Return type

torch.Tensor

normalize_pixel_coordinates(pixel_coordinates: torch.Tensor, height: int, width: int, eps: float = 1e-08) → torch.Tensor[source]¶

Normalize pixel coordinates between -1 and 1.

Normalized, -1 if on extreme left, 1 if on extreme right (x = w-1).

Parameters

pixel_coordinates (torch.Tensor) – the grid with pixel coordinates. Shape can be \((*, 2)\).
width (int) – the maximum width in the x-axis.
height (int) – the maximum height in the y-axis.
eps (float) – safe division by zero. (default 1e-8).

Returns

the normalized pixel coordinates.

Return type

torch.Tensor

denormalize_pixel_coordinates3d(pixel_coordinates: torch.Tensor, depth: int, height: int, width: int, eps: float = 1e-08) → torch.Tensor[source]¶

Denormalize pixel coordinates.

The input is assumed to be -1 if on extreme left, 1 if on extreme right (x = w-1).

Parameters

pixel_coordinates (torch.Tensor) – the normalized grid coordinates. Shape can be \((*, 3)\).
depth (int) – the maximum depth in the x-axis.
height (int) – the maximum height in the y-axis.
width (int) – the maximum width in the x-axis.
eps (float) – safe division by zero. (default 1e-8).

Returns

the denormalized pixel coordinates.

Return type

torch.Tensor

normalize_pixel_coordinates3d(pixel_coordinates: torch.Tensor, depth: int, height: int, width: int, eps: float = 1e-08) → torch.Tensor[source]¶

Normalize pixel coordinates between -1 and 1.

Normalized, -1 if on extreme left, 1 if on extreme right (x = w-1).

Parameters

pixel_coordinates (torch.Tensor) – the grid with pixel coordinates. Shape can be \((*, 3)\).
depth (int) – the maximum depth in the z-axis.
height (int) – the maximum height in the y-axis.
width (int) – the maximum width in the x-axis.
eps (float) – safe division by zero. (default 1e-8).

Returns

the normalized pixel coordinates.

Return type

torch.Tensor

normalize_quaternion(quaternion: torch.Tensor, eps: float = 1e-12) → torch.Tensor[source]¶

Normalizes a quaternion. The quaternion should be in (x, y, z, w) format.

Parameters

quaternion (torch.Tensor) – a tensor containing a quaternion to be normalized. The tensor can be of shape \((*, 4)\).
eps (Optional[bool]) – small value to avoid division by zero. Default: 1e-12.

Returns

the normalized quaternion of shape \((*, 4)\).

Return type

torch.Tensor

Example

>>> quaternion = torch.tensor([1., 0., 1., 0.])
>>> normalize_quaternion(quaternion)
tensor([0.7071, 0.0000, 0.7071, 0.0000])