Correcting Radial Distortion by Circle Fitting

A powerful and popular approach for estimating radial lens distortion parameters is to use the fact that lines which are straight in the scene should be imaged as straight lines under the pinhole camera model. This paper revisits this problem using the division model to parameterise the lens distortion. This turns out to have significant advantages over the more conventional parameterisation, especially for a single parameter model. In particular, we demonstrate that the locus of distorted points from a straight line is a circular arc. This allows distortion estimation to be reformulated as circle-fitting for which many algorithms are available. We compare a number of suboptimal methods offering closed-form solutions with an optimal, iterative technique which minimises a cost function on the actual image plane as opposed to existing techniques which suffer from a bias due to the fact that they optimise a geometric cost function on the undistorted image plane.