kornia.geometry.conversions

rad2deg(tensor: torch.Tensor) → torch.Tensor

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 = kornia.pi * torch.rand(1, 3, 3)
>>> output = kornia.rad2deg(input)

deg2rad(tensor: torch.Tensor) → torch.Tensor

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 = kornia.deg2rad(input)

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

Function that converts points from homogeneous to Euclidean space.

Examples:

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

convert_points_to_homogeneous(points: torch.Tensor) → torch.Tensor

Function that converts points from Euclidean to homogeneous space.

Examples:

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

rotation_matrix_to_angle_axis(rotation_matrix: torch.Tensor) → torch.Tensor

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 = kornia.rotation_matrix_to_angle_axis(input)  # Nx3

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

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 = kornia.rotation_matrix_to_quaternion(input)  # Nx4

quaternion_to_angle_axis(quaternion: torch.Tensor) → torch.Tensor

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 = kornia.quaternion_to_angle_axis(quaternion)  # Nx3

quaternion_to_rotation_matrix(quaternion: torch.Tensor) → torch.Tensor

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.])
>>> kornia.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

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

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

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.])
>>> kornia.quaternion_exp_to_log(quaternion)
tensor([0., 0., 0.])

angle_axis_to_quaternion(angle_axis: torch.Tensor) → torch.Tensor

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, 4)  # Nx4
>>> quaternion = kornia.angle_axis_to_quaternion(angle_axis)  # Nx3

angle_axis_to_rotation_matrix(angle_axis: torch.Tensor) → torch.Tensor

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 4x4 rotation matrices. Return type:torch.Tensor

Shape:

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

Example

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

denormalize_pixel_coordinates(pixel_coordinates: torch.Tensor, height: int, width: int) → torch.Tensor

Denormalize pixel coordinates.

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

Parameters:

• pixel_coordinate (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.

Returns:

the denormalized pixel coordinates.

Return type:

torch.Tensor

normalize_pixel_coordinates(pixel_coordinates: torch.Tensor, height: int, width: int) → torch.Tensor

Normalize pixel coordinates between -1 and 1.

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

Parameters:

• pixel_coordinate (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.

Returns:

the normalized pixel coordinates.

Return type:

torch.Tensor

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

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.])
>>> kornia.normalize_quaternion(quaternion)
tensor([0.7071, 0.0000, 0.7071, 0.0000])