View source on GitHub
|
Quadratic radial lens distortion and un-distortion functions.
Given a vector in homogeneous coordinates, (x/z, y/z, 1), we define
r^2 = (x/z)^2 + (y/z)^2. We use the simplest form of distortion function,
f(r) = 1 + k * r^2. The distorted vector is given by
(f(r) * x/z, f(r) * y/z, 1).
To apply the undistortion, we need the inverse of f(r), g = f^{-1}. In this library we use the approximate formula for the undistortion function given here https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4934233/, and refine the solution using Newton-Raphson iterations (https://en.wikipedia.org/wiki/Newtons_method).
Restricting the distortion function to quadratic form allows to easily detect
the cases where r goes beyond the monotonically-increasing range of f (which
we refer to as overflow).
Functions
distortion_factor(...): Calculates a quadratic distortion factor given squared radii.
undistortion_factor(...): Calculates the inverse quadratic distortion function given squared radii.