Hyperbolic Distortion Model for Radial Distortion Correction

Abstract

ABSTARCTWhen information derived from the imagery is used for metric purposes and not as communication tools the impact of small imaging errors can be significant on the accuracy of derived information. As the number of photogrammetry applications grows and the technology advances, camera calibration becomes more complex. In fact, most lenses suffer from at least one kind of distortion profile such as barrel, pincushion or 'moustache' profiles. Commonly observed on wide angle lenses, barrel distortions curve straight lines inwards to give the image shape of barrel, however most lenses are prone to more than one distortion profile. Proposals for lens correction have been made using line-based approaches as well as division and rational models. The limitations of some of the techniques include the very limited number of distortion profiles they can handle due to their mathematical formulations. For example some can only handle distortion with positive coefficients and would exhibit instabilities when dealing with barrel distortions describe by negative distortion coefficients. In this paper we propose a new class of hyperbolic radial distortion model which handles several distortion profiles. The mathematical formulation of the new approach offers stability of the model since it can handle both positive and negative distortion coefficients -an improvement on some of the current techniques. The calibration results show that the approach produced the best distortion coefficients 1 k and 2 k . The model can handle distortions from panorama imagery as well as 'moustache 'profile produced by wide angle lenses.