Local Moebius transformations applied to omnidirectional images

Abstract This work presents a new method to transform omnidirectional images based on a combination of Moebius transformations in the complex plane and weighting functions that restrict the action of these mappings to regions of interest. The transformations are calculated based on the specification of the image of three points and the weighting functions are designed to achieve specific goals such as local zoom or straight line rectification. Since no optimization or numerical methods are involved, our implementation of the proposed method can be upgraded to reach real-time performance. We provide a user interface and present many results that illustrate the potential of the proposed technique.