kornia.geometry.camera¶
Projections¶
- kornia.geometry.camera.project_points_z1(points_in_camera)¶
Project one or more points from the camera frame into the canonical z=1 plane through perspective division.
\[\begin{split}\begin{bmatrix} u \\ v \\ w \end{bmatrix} = \begin{bmatrix} x \\ y \\ z \end{bmatrix} / z\end{split}\]Note
This function has a precondition that the points are in front of the camera, i.e. z > 0. If this is not the case, the points will be projected to the canonical plane, but the resulting points will be behind the camera and causing numerical issues for z == 0.
- Parameters:
points_in_camera (
Tensor) – Tensor representing the points to project with shape (…, 3).- Return type:
- Returns:
Tensor representing the projected points with shape (…, 2).
Example
>>> points = torch.tensor([1., 2., 3.]) >>> project_points_z1(points) tensor([0.3333, 0.6667])
- kornia.geometry.camera.unproject_points_z1(points_in_cam_canonical, extension=None)¶
Unproject one or more points from the canonical z=1 plane into the camera frame.
\[\begin{split}\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} u \\ v \end{bmatrix} \cdot w\end{split}\]- Parameters:
- Return type:
- Returns:
Tensor representing the unprojected points with shape (…, 3).
Example
>>> points = torch.tensor([1., 2.]) >>> extension = torch.tensor([3.]) >>> unproject_points_z1(points, extension) tensor([3., 6., 3.])
- kornia.geometry.camera.dx_project_points_z1(points_in_camera)¶
Compute the derivative of the x projection with respect to the x coordinate.
Returns point derivative of inverse depth point projection with respect to the x coordinate.
\[\begin{split}\frac{\partial \pi}{\partial x} = \begin{bmatrix} \frac{1}{z} & 0 & -\frac{x}{z^2} \\ 0 & \frac{1}{z} & -\frac{y}{z^2} \end{bmatrix}\end{split}\]Note
This function has a precondition that the points are in front of the camera, i.e. z > 0. If this is not the case, the points will be projected to the canonical plane, but the resulting points will be behind the camera and causing numerical issues for z == 0.
- Parameters:
points_in_camera (
Tensor) – Tensor representing the points to project with shape (…, 3).- Return type:
- Returns:
Tensor representing the derivative of the x projection with respect to the x coordinate with shape (…, 2, 3).
Example
>>> points = torch.tensor([1., 2., 3.]) >>> dx_project_points_z1(points) tensor([[ 0.3333, 0.0000, -0.1111], [ 0.0000, 0.3333, -0.2222]])
- kornia.geometry.camera.project_points_orthographic(points_in_camera)¶
Project one or more points from the camera frame into the canonical z=1 plane through orthographic projection.
\[\begin{split}\begin{bmatrix} u \\ v \end{bmatrix} = \begin{bmatrix} x \\ y \\ z \end{bmatrix}\end{split}\]- Parameters:
points_in_camera (
Tensor) – Tensor representing the points to project.- Return type:
- Returns:
Tensor representing the projected points.
Example
>>> points = torch.tensor([1., 2., 3.]) >>> project_points_orthographic(points) tensor([1., 2.])
- kornia.geometry.camera.unproject_points_orthographic(points_in_camera, extension)¶
Unproject one or more points from the canonical z=1 plane into the camera frame.
\[\begin{split}\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} u \\ v \\ w \end{bmatrix}\end{split}\]- Parameters:
- Return type:
- Returns:
Tensor representing the unprojected points with shape (…, 3).
Example
>>> points = torch.tensor([1., 2.]) >>> extension = torch.tensor([3.]) >>> unproject_points_orthographic(points, extension) tensor([1., 2., 3.])
- kornia.geometry.camera.dx_project_points_orthographic(points_in_camera)¶
Compute the derivative of the x projection with respect to the x coordinate.
\[\frac{\partial u}{\partial x} = 1\]- Parameters:
points_in_camera (
Tensor) – Tensor representing the points to project.- Return type:
- Returns:
Tensor representing the derivative of the x projection with respect to the x coordinate.
Example
>>> points = torch.tensor([1., 2., 3.]) >>> dx_project_points_orthographic(points) tensor([1.])
Distortion¶
- kornia.geometry.camera.distort_points_affine(projected_points_in_camera_z1_plane, params)¶
Distort one or more points from the canonical z=1 plane into the camera frame.
\[\begin{split}\begin{bmatrix} u \\ v \end{bmatrix} = \begin{bmatrix} f_x & 0 \\ 0 & f_y \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix} c_x \\ c_y \end{bmatrix}\end{split}\]- Parameters:
- Return type:
- Returns:
Tensor representing the distorted points with shape (…, 2).
Example
>>> points = torch.tensor([319.5, 239.5]) # center of a 640x480 image >>> params = torch.tensor([600., 600., 319.5, 239.5]) >>> distort_points_affine(points, params) tensor([192019.5000, 143939.5000])
- kornia.geometry.camera.undistort_points_affine(distorted_points_in_camera, params)¶
Undistort one or more points from the camera frame into the canonical z=1 plane.
\[\begin{split}\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} u \\ v \end{bmatrix} - \begin{bmatrix} c_x \\ c_y \end{bmatrix} \begin{bmatrix} f_x & 0 \\ 0 & f_y \end{bmatrix}^{-1}\end{split}\]- Parameters:
- Return type:
- Returns:
Tensor representing the undistorted points with shape (…, 2).
Example
>>> points = torch.tensor([319.5, 239.5]) # center of a 640x480 image >>> params = torch.tensor([600., 600., 319.5, 239.5]) >>> undistort_points_affine(points, params) tensor([0., 0.])
- kornia.geometry.camera.dx_distort_points_affine(projected_points_in_camera_z1_plane, params)¶
Compute the derivative of the x distortion with respect to the x coordinate.
\[\begin{split}\frac{\partial u}{\partial x} = \begin{bmatrix} f_x & 0 \\ 0 & f_y \end{bmatrix}\end{split}\]- Parameters:
- Return type:
- Returns:
Tensor representing the derivative of the x distortion with respect to the x coordinate with shape (…, 2).
Example
>>> points = torch.tensor([319.5, 239.5]) # center of a 640x480 image >>> params = torch.tensor([600., 600., 319.5, 239.5]) >>> dx_distort_points_affine(points, params) tensor([[600., 0.], [ 0., 600.]])
- kornia.geometry.camera.distort_points_kannala_brandt(projected_points_in_camera_z1_plane, params)¶
Distort one or more points from the canonical z=1 plane into the camera frame using the Kannala-Brandt model.
- Parameters:
- Return type:
- Returns:
Tensor representing the distorted points with shape (…, 2).
Example
>>> points = torch.tensor([319.5, 239.5]) # center of a 640x480 image >>> params = torch.tensor([1000.0, 1000.0, 320.0, 280.0, 0.1, 0.01, 0.001, 0.0001]) >>> distort_points_kannala_brandt(points, params) tensor([1982.6832, 1526.3619])
- kornia.geometry.camera.undistort_points_kannala_brandt(distorted_points_in_camera, params)¶
Undistort one or more points from the camera frame into the canonical z=1 plane using the Kannala-Brandt model.
- Parameters:
- Return type:
- Returns:
Tensor representing the undistorted points with shape (…, 2).
Example
>>> points = torch.tensor([319.5, 239.5]) # center of a 640x480 image >>> params = torch.tensor([1000.0, 1000.0, 320.0, 280.0, 0.1, 0.01, 0.001, 0.0001]) >>> undistort_points_kannala_brandt(points, params).shape torch.Size([2])
- kornia.geometry.camera.dx_distort_points_kannala_brandt(projected_points_in_camera_z1_plane, params)¶
Compute the derivative of the x distortion with respect to the x coordinate.
\[\begin{split}\frac{\partial u}{\partial x} = \begin{bmatrix} f_x & 0 \\ 0 & f_y \end{bmatrix}\end{split}\]- Parameters:
- Return type:
- Returns:
Tensor representing the derivative of the x distortion with respect to the x coordinate with shape (…, 2).
Example
>>> points = torch.tensor([1., 2.]) >>> params = torch.tensor([1000.0, 1000.0, 320.0, 280.0, 0.1, 0.01, 0.001, 0.0001]) >>> dx_distort_points_kannala_brandt(points, params) tensor([[ 486.0507, -213.5573], [-213.5573, 165.7147]])