Left: input image with groups of three points and areas (ellipses) that should be affected by the corresponding Moebius transformations. Right: output image with new positions for all points specified on the input (points appear semitransparent). In this example, the user moved the three points around the central building to make it larger in the final result (local zoom) and moved the other points to rectify the underlying straight lines. The final result is a full spherical panorama with a locally zoomed in area and four rectified straight lines.

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.