# Pinhole Camera¶

In this module we have all the functions and data structures needed to describe the projection of a 3D scene space onto a 2D image plane.

In computer vision, we can map between the 3D world and a 2D image using projective geometry. The module implements the simplest camera model, the Pinhole Camera, which is the most basic model for general projective cameras from the finite cameras group.

The Pinhole Camera model is shown in the following figure:

Using this model, a scene view can be formed by projecting 3D points into the image plane using a perspective transformation.

$s \; m' = K [R|t] M'$

or

$\begin{split}s \begin{bmatrix} u \\ v \\ 1\end{bmatrix} = \begin{bmatrix} f_x & 0 & u_0 \\ 0 & f_y & v_0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_1 \\ r_{21} & r_{22} & r_{23} & t_2 \\ r_{31} & r_{32} & r_{33} & t_3 \end{bmatrix} \begin{bmatrix} X \\ Y \\ Z \\ 1 \end{bmatrix}\end{split}$
where:
• $$M'$$ is a 3D point in space with coordinates $$[X,Y,Z]^T$$ expressed in a Euclidean coordinate system.

• $$m'$$ is the projection of the 3D point $$M'$$ onto the image plane with coordinates $$[u,v]^T$$ expressed in pixel units.

• $$K$$ is the camera calibration matrix, also refered as the instrinsics parameters matrix.

• $$C$$ is the principal point offset with coordinates $$[u_0, v_0]^T$$ at the origin in the image plane.

• $$fx, fy$$ are the focal lengths expressed in pixel units.

The camera rotation and translation are expressed in terms of Euclidean coordinate frame, also known as the world coordinates system. This terms are usually expressed by the joint rotation-translation matrix $$[R|t]$$, or also called as the extrinsics parameters matrix. It is used to describe the camera pose around a static scene and translates the coordinates of a 3D point $$(X,Y,Z)$$ to a coordinate sytstem respect to the camera.

class PinholeCamera(intrinsics: torch.Tensor, extrinsics: torch.Tensor, height: torch.Tensor, width: torch.Tensor)[source]

Class that represents a Pinhole Camera model.

Parameters
• intrinsics (torch.Tensor) – tensor with shape $$(B, 4, 4)$$ containing the full 4x4 camera calibration matrix.

• extrinsics (torch.Tensor) – tensor with shape $$(B, 4, 4)$$ containing the full 4x4 rotation-translation matrix.

• height (torch.Tensor) – tensor with shape $$(B)$$ containing the image height.

• width (torch.Tensor) – tensor with shape $$(B)$$ containing the image width.

Note

We assume that the class attributes are in batch form in order to take advantage of PyTorch parallelism to boost computing performce.

property batch_size

Returns the batch size of the storage.

Returns

scalar with the batch size

Return type

int

property camera_matrix

Returns the 3x3 camera matrix containing the intrinsics.

Returns

tensor of shape $$(B, 3, 3)$$

Return type

torch.Tensor

clone() → kornia.geometry.camera.pinhole.PinholeCamera[source]

Returns a deep copy of the current object instance.

property cx

Returns the x-coordinate of the principal point.

Returns

tensor of shape $$(B)$$

Return type

torch.Tensor

property cy

Returns the y-coordinate of the principal point.

Returns

tensor of shape $$(B)$$

Return type

torch.Tensor

property extrinsics

The full 4x4 extrinsics matrix.

Returns

tensor of shape $$(B, 4, 4)$$

Return type

torch.Tensor

property fx

Returns the focal lenght in the x-direction.

Returns

tensor of shape $$(B)$$

Return type

torch.Tensor

property fy

Returns the focal lenght in the y-direction.

Returns

tensor of shape $$(B)$$

Return type

torch.Tensor

property intrinsics

The full 4x4 intrinsics matrix.

Returns

tensor of shape $$(B, 4, 4)$$

Return type

torch.Tensor

intrinsics_inverse() → torch.Tensor[source]

Returns the inverse of the 4x4 instrisics matrix.

Returns

tensor of shape $$(B, 4, 4)$$

Return type

torch.Tensor

property rotation_matrix

Returns the 3x3 rotation matrix from the extrinsics.

Returns

tensor of shape $$(B, 3, 3)$$

Return type

torch.Tensor

property rt_matrix

Returns the 3x4 rotation-translation matrix.

Returns

tensor of shape $$(B, 3, 4)$$

Return type

torch.Tensor

scale(scale_factor) → kornia.geometry.camera.pinhole.PinholeCamera[source]

Scales the pinhole model.

Parameters

scale_factor (torch.Tensor) – a tensor with the scale factor. It has to be broadcastable with class members. The expected shape is $$(B)$$ or $$(1)$$.

Returns

the camera model with scaled parameters.

Return type

PinholeCamera

scale_(scale_factor) → kornia.geometry.camera.pinhole.PinholeCamera[source]

Scales the pinhole model in-place.

Parameters

scale_factor (torch.Tensor) – a tensor with the scale factor. It has to be broadcastable with class members. The expected shape is $$(B)$$ or $$(1)$$.

Returns

the camera model with scaled parameters.

Return type

PinholeCamera

property translation_vector

Returns the translation vector from the extrinsics.

Returns

tensor of shape $$(B, 3, 1)$$

Return type

torch.Tensor

property tx

Returns the x-coordinate of the translation vector.

Returns

tensor of shape $$(B)$$

Return type

torch.Tensor

property ty

Returns the y-coordinate of the translation vector.

Returns

tensor of shape $$(B)$$

Return type

torch.Tensor

property tz

Returns the z-coordinate of the translation vector.

Returns

tensor of shape $$(B)$$

Return type

torch.Tensor

cam2pixel(cam_coords_src: torch.Tensor, dst_proj_src: torch.Tensor, eps: Optional[float] = 1e-06) → torch.Tensor[source]

Transform coordinates in the camera frame to the pixel frame.

Parameters
• cam_coords (torch.Tensor) – pixel coordinates defined in the first camera coordinates system. Shape must be BxHxWx3.

• dst_proj_src (torch.Tensor) – the projection matrix between the reference and the non reference camera frame. Shape must be Bx4x4.

Returns

array of [-1, 1] coordinates of shape BxHxWx2.

Return type

torch.Tensor

pixel2cam(depth: torch.Tensor, intrinsics_inv: torch.Tensor, pixel_coords: torch.Tensor) → torch.Tensor[source]

Transform coordinates in the pixel frame to the camera frame.

Parameters
• depth (torch.Tensor) – the source depth maps. Shape must be Bx1xHxW.

• intrinsics_inv (torch.Tensor) – the inverse intrinsics camera matrix. Shape must be Bx4x4.

• pixel_coords (torch.Tensor) – the grid with the homogeneous camera coordinates. Shape must be BxHxWx3.

Returns

array of (u, v, 1) cam coordinates with shape BxHxWx3.

Return type

torch.Tensor