Perspective Camera

kornia.geometry.camera.perspective.project_points(point_3d, camera_matrix)

Project a 3d point onto the 2d camera plane.

See the Convention block on PinholeCamera.

Convention:

• point_3d is a camera-frame point and camera_matrix the \((*, 3, 3)\) K; the function takes no extrinsics, so it does not move between frames.

• the input must be at least rank 2: an unbatched \((3,)\) point raises ValueError.

Warning

At abs(z) <= 1e-8 the divide is skipped and K is applied to the undivided point, giving the finite placeholder fx x + cx; the other projection entry points do not follow this rule yet: #4267. Neither that placeholder nor a point behind the camera is flagged as invalid: #4555.

Parameters:

• point_3d (Tensor) – tensor containing the 3d points to be projected to the camera plane. The shape of the tensor can be \((*, 3)\).

• camera_matrix (Tensor) – tensor containing the intrinsics camera matrix. The tensor shape must be \((*, 3, 3)\).

Return type:

Tensor

Returns:

tensor of (u, v) cam coordinates with shape \((*, 2)\).

Example

>>> _ = torch.manual_seed(0)
>>> X = torch.rand(1, 3)
>>> K = torch.eye(3)[None]
>>> project_points(X, K)
tensor([[5.6088, 8.6827]])

kornia.geometry.camera.perspective.unproject_points(point_2d, depth, camera_matrix, normalize=False)

Unproject a 2d point in 3d.

Transform coordinates in the pixel frame to the camera frame.

See the Convention block on PinholeCamera.

Convention:

• point_2d is a pixel coordinate and the result is in the camera frame: the function takes no extrinsics, so it cannot return world coordinates. unproject() is the world-frame counterpart.

• depth is the camera-frame z of the result. With normalize=True it is read as the Euclidean ray length instead, so the result has that norm and a smaller z.

Parameters:

• point_2d (Tensor) – tensor containing the 2d points to be projected to the camera frame. The shape of the tensor can be \((*, 2)\).

• depth (Tensor) – tensor containing the depth value of each 2d points. The tensor shape must be equal to point2d \((*, 1)\).

• camera_matrix (Tensor) – tensor containing the intrinsics camera matrix. The tensor shape must be \((*, 3, 3)\).

• normalize (bool, optional) – whether to normalize the pointcloud. This must be set to True when the depth is represented as the Euclidean ray length from the camera position. Default: False

Return type:

Tensor

Returns:

tensor of (x, y, z) camera coordinates with shape \((*, 3)\).

Example

>>> _ = torch.manual_seed(0)
>>> x = torch.rand(1, 2)
>>> depth = torch.ones(1, 1)
>>> K = torch.eye(3)[None]
>>> unproject_points(x, depth, K)
tensor([[0.4963, 0.7682, 1.0000]])