Determination of the Center of Radial Distortion for a Camera Lens

Abstract

A precise determination of the center of radial distortion (CoD) improves the characterization of the distortion introduced by the lens, and hence, supports a better description of the perspective projection process. Nonetheless, its value is often neglected and approximated by the center of the image. In our research, we aim to determine a lens CoD with high accuracy using derivative instruments. To that end, we introduce a method that bounds the region containing the CoD within one pixel of uncertainty by characterizing the residual of a straight line (RSL) fitting process. The procedure is further refined to obtain an estimate for the CoD position by first inferring straight lines (ISL) crossing it and then finding the intersection between these lines. Later on, we explore the introduction of the division model assumption (DMA) for lens distortion in the estimation of the CoD. The RSL approach becomes relevant as we compare the ISL and DMA methods with alternatives from the literature as it provides a reference value containing the CoD. In our experiments, we take images of a straightness gauge by moving a camera with a coordinate measuring machine at regular and accurate steps. At each location, we estimate undistorted lines at different orientations of the camera and find the CoD from their intersections. Our approach permits the establishment of the CoD with high accuracy for a camera lens with radial distortion.