Complex Plane Transformations for Manipulation and Visualization of Panoramas

We present a method for manipulation and visualization of wide-angle images using transformations defined on the complex plane C. We map the unit sphere S2 to C using the stereographic projection, multiply the complex plane by a given complex number, and map the result back to the sphere using the inverse of the stereographic projection. Since all these transformations preserve angle, we obtain a result containing only distortions due to the latitude/longitude representation of the sphere, which were already present in the input image. We then explore the possibility given by our technique of mapping wide fields of view to narrower ones. This makes possible to apply perspective projection to wider fields of view, leading to a natural generalization of the perspective projection in the context of panoramic images. Our results are generated in real-time and compare competitively with state-of-the-art methods used to project the viewing sphere to the image plane.