Analytically solving radial distortion parameters

Most camera calibration algorithms consider parameters that define the lens distortion mapping. The usual way to determine these parameters is to minimize a nonlinear optimization problem in the final step of a calibration algorithm. This neglects the fact that given the projection matrix and the calibration data the parameters of a radial distortion can be determined analytically. In this article we show that the problem can be solved in a closed form. We present an algorithm in which this is done and compare it to classic approaches.