Technical Details

This implementation is based on [1] and [2].

pyfisheye uses trust-region constrained optimization (trust-constr) as a replacement for MATLAB’s lsqlin function.

This approach converges quickly and supports linear constraints, useful for enforcing monotonicity during calibration.

Note the following:

• The original toolbox enforces a monotonic increasing function; pyfisheye finds parameters for a monotonic decreasing function, resulting in a coordinate system where the positive z-axis is forward (see Projection).

• During linear optimization, radial distances are normalized by the image radius — defined as the maximum distance from the distortion centre to any valid pixel coordinate — to improve numerical stability.

• Intrinsic parameters are unnormalized before nonlinear refinement.

• Instead of a high-degree polynomial for inverse mapping, pyfisheye uses a precomputed lookup table with linear interpolation.

This method is less prone to numerical instability but about 5x slower: on a 640x480 image, the lookup takes ~50 ms versus ~10 ms for polynomial evaluation (tested on an AMD Ryzen 7 5800H).

Polynomial support for inverse mapping will be implemented in a future release (contributions welcome).

References

[1]

Scaramuzza et al., “Omnidirectional Camera Calibration,” IEEE IROS 2006, https://doi.org/10.1109/IROS.2006.282372

[2]

Urban et al., “Improved omnidirectional camera calibration,” ISPRS Journal 2015, https://doi.org/10.1016/j.isprsjprs.2015.06.005