kornia.geometry.conversions¶

Angles¶

kornia.geometry.conversions.rad2deg(tensor)[source]¶

Function that converts angles from radians to degrees.

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

Example

>>> input = torch.tensor(3.1415926535)
>>> rad2deg(input)
tensor(180.)

kornia.geometry.conversions.deg2rad(tensor)[source]¶

Function that converts angles from degrees to radians.

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

Examples

>>> input = torch.tensor(180.)
>>> deg2rad(input)
tensor(3.1416)

kornia.geometry.conversions.pol2cart(rho, phi)[source]¶

Function that converts polar coordinates to cartesian coordinates.

Parameters

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

Return type

Tuple[Tensor, Tensor]

Returns

Tensor with same shape as input.

Example

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

kornia.geometry.conversions.cart2pol(x, y, eps=1e-08)[source]¶

Function that converts cartesian coordinates to polar coordinates.

Parameters

rho – Tensor of arbitrary shape.
phi – Tensor of same arbitrary shape.
eps (float, optional) – To avoid division by zero. Default: 1e-08

Return type

Tuple[Tensor, Tensor]

Returns

Tensor with same shape as input.

Example

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

kornia.geometry.conversions.angle_to_rotation_matrix(angle)[source]¶

Create a rotation matrix out of angles in degrees.

Parameters: angle (Tensor) – tensor of angles in degrees, any shape \((*)\).
Return type: Tensor
Returns: tensor of rotation matrices with shape \((*, 2, 2)\).

Example

>>> input = torch.rand(1, 3)  # Nx3
>>> output = angle_to_rotation_matrix(input)  # Nx3x2x2

Coordinates¶

kornia.geometry.conversions.convert_points_from_homogeneous(points, eps=1e-08)[source]¶

Function that converts points from homogeneous to Euclidean space.

Parameters

points (Tensor) – the points to be transformed of shape \((B, N, D)\).
eps (float, optional) – to avoid division by zero. Default: 1e-08

Return type

Tensor

Returns

the points in Euclidean space \((B, N, D-1)\).

Examples

>>> input = torch.tensor([[0., 0., 1.]])
>>> convert_points_from_homogeneous(input)
tensor([[0., 0.]])

kornia.geometry.conversions.convert_points_to_homogeneous(points)[source]¶

Function that converts points from Euclidean to homogeneous space.

Parameters: points (Tensor) – the points to be transformed with shape \((B, N, D)\).
Return type: Tensor
Returns: the points in homogeneous coordinates \((B, N, D+1)\).

Examples

>>> input = torch.tensor([[0., 0.]])
>>> convert_points_to_homogeneous(input)
tensor([[0., 0., 1.]])

kornia.geometry.conversions.convert_affinematrix_to_homography(A)[source]¶

Function that converts batch of affine matrices.

Parameters: A (Tensor) – the affine matrix with shape \((B,2,3)\).
Return type: Tensor
Returns: the homography matrix with shape of \((B,3,3)\).

Examples

>>> A = torch.tensor([[[1., 0., 0.],
...                    [0., 1., 0.]]])
>>> convert_affinematrix_to_homography(A)
tensor([[[1., 0., 0.],
         [0., 1., 0.],
         [0., 0., 1.]]])

kornia.geometry.conversions.denormalize_pixel_coordinates(pixel_coordinates, height, width, eps=1e-08)[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 (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, optional) – safe division by zero. Default: 1e-08

Return type

Tensor

Returns

the denormalized pixel coordinates with shape \((*, 2)\).

Examples

>>> coords = torch.tensor([[-1., -1.]])
>>> denormalize_pixel_coordinates(coords, 100, 50)
tensor([[0., 0.]])

kornia.geometry.conversions.normalize_pixel_coordinates(pixel_coordinates, height, width, eps=1e-08)[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 (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, optional) – safe division by zero. Default: 1e-08

Return type

Tensor

Returns

the normalized pixel coordinates with shape \((*, 2)\).

Examples

>>> coords = torch.tensor([[50., 100.]])
>>> normalize_pixel_coordinates(coords, 100, 50)
tensor([[1.0408, 1.0202]])

kornia.geometry.conversions.denormalize_pixel_coordinates3d(pixel_coordinates, depth, height, width, eps=1e-08)[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 (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, optional) – safe division by zero. Default: 1e-08

Return type

Tensor

Returns

the denormalized pixel coordinates.

kornia.geometry.conversions.normalize_pixel_coordinates3d(pixel_coordinates, depth, height, width, eps=1e-08)[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 (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, optional) – safe division by zero. Default: 1e-08

Return type

Tensor

Returns

the normalized pixel coordinates.

Homography¶

kornia.geometry.conversions.normalize_homography(dst_pix_trans_src_pix, dsize_src, dsize_dst)[source]¶

Normalize a given homography in pixels to [-1, 1].

Parameters

dst_pix_trans_src_pix (Tensor) – homography/ies from source to destination to be normalized. \((B, 3, 3)\)
dsize_src (Tuple[int, int]) – size of the source image (height, width).
dsize_dst (Tuple[int, int]) – size of the destination image (height, width).

Return type

Tensor

Returns

the normalized homography of shape \((B, 3, 3)\).

kornia.geometry.conversions.denormalize_homography(dst_pix_trans_src_pix, dsize_src, dsize_dst)[source]¶

De-normalize a given homography in pixels from [-1, 1] to actual height and width.

Parameters

dst_pix_trans_src_pix (Tensor) – homography/ies from source to destination to be denormalized. \((B, 3, 3)\)
dsize_src (Tuple[int, int]) – size of the source image (height, width).
dsize_dst (Tuple[int, int]) – size of the destination image (height, width).

Return type

Tensor

Returns

the denormalized homography of shape \((B, 3, 3)\).

kornia.geometry.conversions.normalize_homography3d(dst_pix_trans_src_pix, dsize_src, dsize_dst)[source]¶

Normalize a given homography in pixels to [-1, 1].

Parameters

dst_pix_trans_src_pix (Tensor) – homography/ies from source to destination to be normalized. \((B, 4, 4)\)
dsize_src (Tuple[int, int, int]) – size of the source image (depth, height, width).
dsize_src – size of the destination image (depth, height, width).

Return type

Tensor

Returns

the normalized homography.

Shape:: Output: \((B, 4, 4)\)

Quaternion¶

kornia.geometry.conversions.quaternion_to_angle_axis(quaternion, order=QuaternionCoeffOrder.XYZW)[source]¶

Convert quaternion vector to angle axis of rotation in radians.

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

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

Parameters

quaternion (Tensor) – tensor with quaternions.
order (QuaternionCoeffOrder, optional) – quaternion coefficient order. Note: ‘xyzw’ will be deprecated in favor of ‘wxyz’. Default: QuaternionCoeffOrder.XYZW

Return type

Tensor

Returns

tensor with angle axis of rotation.

Shape:

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

Example

>>> quaternion = torch.tensor((1., 0., 0., 0.))
>>> quaternion_to_angle_axis(quaternion)
tensor([3.1416, 0.0000, 0.0000])

kornia.geometry.conversions.quaternion_to_rotation_matrix(quaternion, order=QuaternionCoeffOrder.XYZW)[source]¶

Convert a quaternion to a rotation matrix.

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

Parameters

quaternion (Tensor) – a tensor containing a quaternion to be converted. The tensor can be of shape \((*, 4)\).
order (QuaternionCoeffOrder, optional) – quaternion coefficient order. Note: ‘xyzw’ will be deprecated in favor of ‘wxyz’. Default: QuaternionCoeffOrder.XYZW

Return type

Tensor

Returns

the rotation matrix of shape \((*, 3, 3)\).

Example

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

kornia.geometry.conversions.quaternion_log_to_exp(quaternion, eps=1e-08, order=QuaternionCoeffOrder.XYZW)[source]¶

Apply exponential map to log quaternion.

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

Parameters

quaternion (Tensor) – a tensor containing a quaternion to be converted. The tensor can be of shape \((*, 3)\).
eps (float, optional) – a small number for clamping. Default: 1e-08
order (QuaternionCoeffOrder, optional) – quaternion coefficient order. Note: ‘xyzw’ will be deprecated in favor of ‘wxyz’. Default: QuaternionCoeffOrder.XYZW

Return type

Tensor

Returns

the quaternion exponential map of shape \((*, 4)\).

Example

>>> quaternion = torch.tensor((0., 0., 0.))
>>> quaternion_log_to_exp(quaternion, eps=torch.finfo(quaternion.dtype).eps,
...                       order=QuaternionCoeffOrder.WXYZ)
tensor([1., 0., 0., 0.])

kornia.geometry.conversions.quaternion_exp_to_log(quaternion, eps=1e-08, order=QuaternionCoeffOrder.XYZW)[source]¶

Apply the log map to a quaternion.

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

Parameters

quaternion (Tensor) – a tensor containing a quaternion to be converted. The tensor can be of shape \((*, 4)\).
eps (float, optional) – a small number for clamping. Default: 1e-08
order (QuaternionCoeffOrder, optional) – quaternion coefficient order. Note: ‘xyzw’ will be deprecated in favor of ‘wxyz’. Default: QuaternionCoeffOrder.XYZW

Return type

Tensor

Returns

the quaternion log map of shape \((*, 3)\).

Example

>>> quaternion = torch.tensor((1., 0., 0., 0.))
>>> quaternion_exp_to_log(quaternion, eps=torch.finfo(quaternion.dtype).eps,
...                       order=QuaternionCoeffOrder.WXYZ)
tensor([0., 0., 0.])

kornia.geometry.conversions.normalize_quaternion(quaternion, eps=1e-12)[source]¶

Normalize a quaternion.

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

Parameters

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

Return type

Tensor

Returns

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

Example

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

Rotation Matrix¶

kornia.geometry.conversions.rotation_matrix_to_angle_axis(rotation_matrix)[source]¶

Convert 3x3 rotation matrix to Rodrigues vector in radians.

Parameters: rotation_matrix (Tensor) – rotation matrix of shape \((N, 3, 3)\).
Return type: Tensor
Returns: Rodrigues vector transformation of shape \((N, 3)\).

Example

>>> input = torch.tensor([[1., 0., 0.],
...                       [0., 1., 0.],
...                       [0., 0., 1.]])
>>> rotation_matrix_to_angle_axis(input)
tensor([0., 0., 0.])

>>> input = torch.tensor([[1., 0., 0.],
...                       [0., 0., -1.],
...                       [0., 1., 0.]])
>>> rotation_matrix_to_angle_axis(input)
tensor([1.5708, 0.0000, 0.0000])

kornia.geometry.conversions.rotation_matrix_to_quaternion(rotation_matrix, eps=1e-08, order=QuaternionCoeffOrder.XYZW)[source]¶

Convert 3x3 rotation matrix to 4d quaternion vector.

The quaternion vector has components in (w, x, y, z) or (x, y, z, w) format.

Note

The (x, y, z, w) order is going to be deprecated in favor of efficiency.

Parameters

rotation_matrix (Tensor) – the rotation matrix to convert with shape \((*, 3, 3)\).
eps (float, optional) – small value to avoid zero division. Default: 1e-08
order (QuaternionCoeffOrder, optional) – quaternion coefficient order. Note: ‘xyzw’ will be deprecated in favor of ‘wxyz’. Default: QuaternionCoeffOrder.XYZW

Return type

Tensor

Returns

the rotation in quaternion with shape \((*, 4)\).

Example

>>> input = torch.tensor([[1., 0., 0.],
...                       [0., 1., 0.],
...                       [0., 0., 1.]])
>>> rotation_matrix_to_quaternion(input, eps=torch.finfo(input.dtype).eps,
...                               order=QuaternionCoeffOrder.WXYZ)
tensor([1., 0., 0., 0.])

Angle Axis¶

kornia.geometry.conversions.angle_axis_to_quaternion(angle_axis, order=QuaternionCoeffOrder.XYZW)[source]¶

Convert an angle axis to a quaternion.

The quaternion vector has components in (x, y, z, w) or (w, x, y, z) format.

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

Parameters

angle_axis (Tensor) – tensor with angle axis in radians.
order (QuaternionCoeffOrder, optional) – quaternion coefficient order. Note: ‘xyzw’ will be deprecated in favor of ‘wxyz’. Default: QuaternionCoeffOrder.XYZW

Return type

Tensor

Returns

tensor with quaternion.

Shape:

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

Example

>>> angle_axis = torch.tensor((0., 1., 0.))
>>> angle_axis_to_quaternion(angle_axis, order=QuaternionCoeffOrder.WXYZ)
tensor([0.8776, 0.0000, 0.4794, 0.0000])

kornia.geometry.conversions.angle_axis_to_rotation_matrix(angle_axis)[source]¶

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

Parameters: angle_axis (Tensor) – tensor of 3d vector of axis-angle rotations in radians with shape \((N, 3)\).
Return type: Tensor
Returns: tensor of rotation matrices of shape \((N, 3, 3)\).

Example

>>> input = torch.tensor([[0., 0., 0.]])
>>> angle_axis_to_rotation_matrix(input)
tensor([[[1., 0., 0.],
         [0., 1., 0.],
         [0., 0., 1.]]])

>>> input = torch.tensor([[1.5708, 0., 0.]])
>>> angle_axis_to_rotation_matrix(input)
tensor([[[ 1.0000e+00,  0.0000e+00,  0.0000e+00],
         [ 0.0000e+00, -3.6200e-06, -1.0000e+00],
         [ 0.0000e+00,  1.0000e+00, -3.6200e-06]]])