Accurate calibration with highly distorted images

Abstract

Camera calibration is a two-step process where first a linear algebraic approximation is followed by a nonlinear minimization. The nonlinear minimization adjusts the pin-hole and lens distortion models to the calibrating data. Since both models are coupled, nonlinear minimization can converge to a local solution easily. Moreover, nonlinear minimization is poorly conditioned since parameters with different effects in the minimization function are calculated simultaneously (some are in pixels, some in world coordinates, and some are lens distortion parameters). A local solution is adapted to parameters, which minimize the function easily, and the remaining parameters are just adapted to this solution. We propose a calibration method where traditional calibration steps are inverted. First, a nonlinear minimization is done, and after, camera parameters are computed in a linear step. Using projective geometry constraints in a nonlinear minimization process, detected point locations in the images are corrected. The pin-hole and lens distortion models are computed separately with corrected point locations. The proposed method avoids the coupling between both models. Also, the condition of nonlinear minimization increases since points coordinates are computed alone.