CAMERA CALIBRATION WITH IRRATIONAL RADIAL DISTORTION MODEL WITH ANALYTICAL SOLUTIONS

Abstract. Consumer grade digital cameras are widely used in many applications including Photogrammetric mapping and 3D modelling. One common limitation found in such cameras is radial lens distortions. To produce wide angle lenses camera manufacturers reduce the amount of barrel distortion by minimizing both the central and edge distortion profiles, resulting in a mixture of pincushion and barrel distortions for a single lens. These lenses also lack symmetry, making some of the existing distortion models almost ineffective. The mostly used model for radial distortion corrections is the polynomial model which is difficult to solve analytically especially when the model possesses many quadratic terms. Suggestions were made for division models but such models are not suitable when the lens field of view exceeds 180 degrees and exhibit some instabilities when dealing with large magnitude of distortion coefficients. Moreover mathematical formulations of some models cannot handle negative distortion coefficients. Attempts to improve the division models were made with proposals for rational models which present the advantage of handling larger distortion magnitude with fewer terms. However some of these models do not account for all the distortion coefficients in their solutions, limiting the potential of the techniques. This study presents an irrational distortion model with analytical solutions. The proposed model was tested with imagery captured by wide angle lenses and the experimental results reveal that the technique produced the best estimates of radial distortion coefficients. The proposed model was also able to capture image distortions originating from projection errors by the wide angles lenses used in this study.