Modeling of radial asymmetry in lens distortion facilitated by modern optimization techniques

Abstract

Most current lens distortion models use only a few terms of Brown's model, which assumes that the radial distortion is dependant only on the distance from the distortion centre, and an additive tangential distortion can be used to correct lens de-centering. This paper shows that the characterization of lens distortion can be improved by over 79% compared to prevailing methods. This is achieved by using modern numerical optimization techniques such as the Leapfrog algorithm, and sensitivity-normalized parameter scaling to reliably and repeatably determine more terms for Brown's model. An additional novel feature introduced in this paper is to allow the distortion to vary not only with polar distance but with the angle too. Two models for radially asymmetrical distortion (i.e. distortion that is dependant on both polar angle and distance) are discussed, implemented and contrasted to results obtained when no asymmetry is modelled. A sample of 32 cameras exhibiting extreme barrel distortion (due to their 6.0mm focal lengths) is used to show that these new techniques can straighten lines to within 7 hundredths of a pixel RMS over the entire image.