Lens distortion calibration by explicit straight-line to distorted-line geometric mapping

Abstract

Medium and wide-angle off-shelf cameras are often used in computer-vision applications despite their large lens distortion. Algorithms to correct for radial and tangential distortion are available; however, they often use non-linear optimization search methods that rely on carefully chosen starting points. This paper presents a method to correct for both radial symmetric lens distortion and decentering lens distortion using an iterative geometric approach to find the distortion center, and a closed-form solution for all other distortion parameters. The method is based on deriving an equivalent radial symmetric distortion model that accounts for both radial and tangential distortion. The technique uses the simple geometric relationship between a straight line and its distorted counterpart under this distortion model. The distortion calibration involves firstly determining the axis of symmetry of several distorted lines. The intersection of these axes is then computed and considered as the point of best radial symmetry (PBRS). The inclinations of the axes of symmetry of the distorted lines are then used in a closed-form solution to determine the distortion coefficients. One advantage of this approach is that higher-order coefficients can be included as needed, with their computation still achieved in closed form. The simplicity of the lens distortion calibration technique has been demonstrated in a simulation using synthetic images.