Modelling and Removal of Distortions in Images

This thesis investigates the compensation and minimisation of distortions in images. Various forms of non-linear lens distortions are modelled and removed. Projective linear distortions are further minimised to give the closest ideal projection from erroneous cameras. Traditional camera calibration treats lens distortion simultaneously with camera pose and lens scaling factors. This often leads to complex algorithms with multi-image requirements, while alternative so called non-metric methods such as straight line techniques, lack ready usability and insufficient precision. Considering the calibration and compensation of non-idealitys separately, allows greater access to error free projections while considerably simplifying subsequent calibrations. The major contributions of this thesis are the precise calibration and removal of lens distortions and the minimisation of perspective distortions. A simple to use technique is proposed for the closed-form calibration of lens distortion based on a single view of a planar calibration chart. Detailed examinations show its accuracy and suitability for all levels of lens distortion. A related method is proposed for the removal of lateral chromatic aberrations in images. Distortion models and approximate inverses are derived to give precise accuracy over all distortion levels including fish-eye lenses. An analysis of calibration patterns is conducted to determine if the choice of pattern can influence the accuracy of the calibration. It is revealed that only specific patterns offer truly bias free control points. Distortion free images are optimally regenerated to minimise pixel scale distortions. This technique is further developed to uniquely minimise perspective distortions, with application to stereo rectification.