About calibration code

[qianyu220]

Hi, I am trying your calibration code (projection.py) on fisheye images. I found the distortion coefficients k1-k4 are very different from the standard format in OpenCV (their number is smaller than 1, while yours is hundreds). Could your please share your calibration code and how to correspond your coeff with Opencv's?

[sleepywitti]

Hello,
we do not use the OpenCV calibration model, but a 4th order polynomial described e.g. by Davide Scaramuzza. Both models can not be derived from each other and therefore have no equivalent representations.

The following text is an excerpt from the calibration description that can be found along with the calibrations.

The intrinsic calibration is given in a calibration model that describes the radial distortion using a 4th order polynomial
rho(theta) = k1 * theta + k2 * theta ** 2 + k3 * theta ** 3 + k4 * theta ** 4,
where theta is the angle of incidence with respect to the optical axis and rho is the distance between the image center and projected point. The coefficients k1, k2, k3 and k4 are given in the calibration files.
The image width and height as well as the offset (cx, cy) of the principal point are given in pixels.

For completeness, the projection of a 3D point (X, Y, Z) given in camera coordinates to image coordinates (u, v) looks like:

chi = sqrt( X ** 2 + Y ** 2)
theta = arctan2( chi, Z ) = pi / 2 - arctan2( Z, chi )
rho = rho(theta)
u’ = rho * X / chi if chi != 0 else 0
v’ = rho * Y / chi if chi != 0 else 0
u = u’ + cx + width / 2 - 0.5
v = v’ * aspect_ratio + cy + height / 2 - 0.5

The last two lines show the final conversion to image coordinates assuming that the origin of the image coordinate system is located in the upper left corner with the upper left pixel at (0, 0). The projection itself is implemented in projection.py which can be found at https://github.com/valeoai/WoodScape/tree/master/scripts/calibration.

[sandeepnmenon]

@sleepywitti
Thank you for the explanation. Can you provide the data/images used for your calibration so that people who wants to use the OpenCV model can calibrate accordingly.