kornia.geometry.linalg¶
- kornia.geometry.linalg.relative_transformation(trans_01, trans_02)¶
Function that computes the relative homogeneous transformation from a reference transformation.
\(T_1^{0} = \begin{bmatrix} R_1 & t_1 \\ \mathbf{0} & 1 \end{bmatrix}\) to destination \(T_2^{0} = \begin{bmatrix} R_2 & t_2 \\ \mathbf{0} & 1 \end{bmatrix}\).
The relative transformation is computed as follows:
\[T_1^{2} = (T_0^{1})^{-1} \cdot T_0^{2}\]- Parameters:
- Return type:
- Returns:
the relative transformation between the transformations with shape \((N, 4, 4)\) or \((4, 4)\).
- Example::
>>> trans_01 = torch.eye(4) # 4x4 >>> trans_02 = torch.eye(4) # 4x4 >>> trans_12 = relative_transformation(trans_01, trans_02) # 4x4
- kornia.geometry.linalg.compose_transformations(trans_01, trans_12)¶
Function that composes two homogeneous transformations.
\[\begin{split}T_0^{2} = \begin{bmatrix} R_0^1 R_1^{2} & R_0^{1} t_1^{2} + t_0^{1} \\ \mathbf{0} & 1\end{bmatrix}\end{split}\]- Parameters:
trans_01 (
Tensor) – tensor with the homogeneous transformation from a reference frame 1 respect to a frame 0. The tensor has must have a shape of \((N, 4, 4)\) or \((4, 4)\).trans_12 (
Tensor) – tensor with the homogeneous transformation from a reference frame 2 respect to a frame 1. The tensor has must have a shape of \((N, 4, 4)\) or \((4, 4)\).
- Return type:
- Returns:
the transformation between the two frames with shape \((N, 4, 4)\) or \((4, 4)\).
- Example::
>>> trans_01 = torch.eye(4) # 4x4 >>> trans_12 = torch.eye(4) # 4x4 >>> trans_02 = compose_transformations(trans_01, trans_12) # 4x4
- kornia.geometry.linalg.inverse_transformation(trans_12)¶
Function that inverts a 4x4 homogeneous transformation.
\(T_1^{2} = \begin{bmatrix} R_1 & t_1 \\ \mathbf{0} & 1 \end{bmatrix}\)
The inverse transformation is computed as follows:
\[\begin{split}T_2^{1} = (T_1^{2})^{-1} = \begin{bmatrix} R_1^T & -R_1^T t_1 \\ \mathbf{0} & 1\end{bmatrix}\end{split}\]- Parameters:
trans_12 (
Tensor) – transformation tensor of shape \((N, 4, 4)\) or \((4, 4)\).- Return type:
- Returns:
tensor with inverted transformations with shape \((N, 4, 4)\) or \((4, 4)\).
Example
>>> trans_12 = torch.rand(1, 4, 4) # Nx4x4 >>> trans_21 = inverse_transformation(trans_12) # Nx4x4
- kornia.geometry.linalg.transform_points(trans_01, points_1)¶
Function that applies transformations to a set of points.
- Parameters:
- Return type:
- Returns:
a tensor of N-dimensional points.
- Shape:
Output: \((B, N, D)\)
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
- kornia.geometry.linalg.point_line_distance(point, line, eps=1e-9)¶
Return the distance from points to lines.
- Parameters:
- Return type:
- Returns:
the computed distance with shape \((*, N)\).
- kornia.geometry.linalg.squared_norm(x, keepdim=False)¶
Return the squared norm of a vector.
- Return type:
- kornia.geometry.linalg.batched_dot_product(x, y, keepdim=False)¶
Return a batched version of .dot()
- Return type:
- kornia.geometry.linalg.euclidean_distance(x, y, keepdim=False, eps=1e-6)¶
Compute the Euclidean distance between two set of n-dimensional points.
More: https://en.wikipedia.org/wiki/Euclidean_distance
- Parameters:
- Return type: