class SphericalCameraCal(focal_length, principal_point, distortion_coeffs=(0.0, 0.0, 0.0, 0.0, 0.0, 0.0), critical_theta=None, max_theta=3.141592653589793)[source]#

Bases: CameraCal

Kannala-Brandt camera model, where radial distortion is modeled relative to the 3D angle theta off the optical axis as opposed to radius within the image plane (i.e. ATANCamera)

I.e. the radius in the image plane as a function of the angle theta from the camera z-axis is assumed to be given by:

r(theta) = theta + d[0] * theta^3 + d[1] * theta^5 + d[2] * theta^7 + d[3] * theta^9

This model also includes two tangential coefficients, implemented similar to the Brown-Conrady model. For details, see the Fisheye62 model from Project Aria:

With no tangential coefficients, this model is over-parameterized in that we may scale all the distortion coefficients by a constant, and the focal length by the inverse of that constant. To fix this issue, we peg the first coefficient at 1. So while the distortion dimension is ‘4’, the actual total number of coeffs is 5.

Additionally, the storage for this class includes the critical theta, the maximum angle from the optical axis where projection is invertible; although the critical theta is a function of the other parameters, this function requires polynomial root finding, so it should be computed externally at runtime and set to the computed value.


A generic camera model and calibration method for conventional, wide-angle, and fish-eye lenses
Kannala, Juho; Brandt, Sami S.
PAMI 2006

This is the simpler “P9” model without any non-radially-symmetric distortion params, but also includes two tangential distortion params similar to the Brown-Conrady model.

The storage for this class is:

[ fx fy cx cy critical_theta d0 d1 d2 d3 p0 p1]

  • focal_length (T.Sequence[T.Scalar]) –

  • principal_point (T.Sequence[T.Scalar]) –

  • distortion_coeffs (T.Sequence[T.Scalar]) –

  • critical_theta (T.Optional[T.Scalar]) –

  • max_theta (T.Scalar) –

classmethod from_distortion_coeffs(focal_length, principal_point, distortion_coeffs=(), **kwargs)[source]#

Construct a Camera Cal of type cls from the focal_length, principal_point, and distortion_coeffs.

kwargs are additional arguments which will be passed to the constructor.

Symbolic arguments may only be passed if the kwarg critical_theta is passed.

Return type:


classmethod storage_order()[source]#

Return list of the names of values returned in the storage paired with the dimension of each value.

Return type:

Tuple[Tuple[str, int], …]

classmethod storage_dim()[source]#

Dimension of underlying storage

Return type:



Flat list representation of the underlying storage, length of storage_dim(). This is used purely for plumbing, it is NOT like a tangent space.

Return type:


classmethod from_storage(vec)[source]#

Construct from a flat list representation. Opposite of to_storage().


vec (Sequence[float]) –

Return type:


classmethod symbolic(name, **kwargs)[source]#

Construct a symbolic element with the given name prefix. Kwargs are forwarded to sf.Symbol (for example, sympy assumptions).

  • name (str) –

  • kwargs (Any) –

Return type:


pixel_from_camera_point(point, epsilon=0.0)[source]#

Project a 3D point in the camera frame into 2D pixel coordinates.

  • pixel – (x, y) coordinate in pixels if valid

  • is_valid – 1 if the operation is within bounds else 0

Return type:

Tuple[Matrix21, float]

camera_ray_from_pixel(pixel, epsilon=0)[source]#

Backproject a 2D pixel coordinate into a 3D ray in the camera frame.

  • camera_ray – The ray in the camera frame (NOT normalized)

  • is_valid – 1 if the operation is within bounds else 0

Return type:

Tuple[Matrix31, float]