The calibration of wide-angle lens cameras using perspective and non-perspective projections in the context of real-time tracking applications

Abstract

In most close-range photogrammetry applications, the cameras are modelled as imaging systems with perspective projection combined with the lens distortion correction as proposed by Brown in 1971. In the 1980s, the calibration of video cameras received considerable attention. This required compensation for further systematic effects caused by the digitization of the analogue image signal. Modelling the image process in that manner has become the widely-applied standard since then. To take advantage of the increased field of view of individual cameras, the use of wide angle as well as fisheye lenses became common in computer vision and close-range photogrammetry, again requiring appropriate modelling of the imaging process to ensure high accuracies. A.R.T. provides real-time tracking systems with infra-red cameras, which are in some cases equipped with short focal length lenses for the purpose of increased fields of view, resulting in larger trackable object volumes. Unfortunately the lens distortion of these cameras reaches magnitudes which can not be sufficiently modelled with the customary Brown model as - mainly at high excentricities such as image corners - the calculation of the correction is not applicable. Considerations to avoid modelling these lenses as fisheye projections led to an alternate and rather pragmatic approach, where the distortion model is extended by a fourth radial distortion coefficient. Due to numeric instabilities, a stepwise camera calibration is required to achieve convergence in the bundle adjustment process. This paper presents the modified lens distortion model, describes the stepwise calibration procedure and compares results in respect to the conventional approach. The results are also compared to the approach wherein the camera lens is modelled as a fisheye projection. The introduction of a fourth radial lens distortion parameter allows the correction of lens distortion effects over the full sensor area of wide angle lenses, which increases the usable field of view of that specific camera and therefore the size of the trackable observed object volume. The approaches with the extended lens distortion model and the fisheye projection were successfully implemented and tested, and are on target to become part of the A.R.T. product range.