Stereographic rectification of omnidirectional stereo pairs

We present a general technique for rectification of a stereo pair acquired by a calibrated omnidirectional camera. Using this technique we formulate a new stereographic rectification method. Our rectification does not map epipolar curves onto lines as common rectification methods, but rather maps epipolar curves onto circles. We show that this rectification in a certain sense minimizes the distortion of the original omnidirectional images. We formulate the rectification for multiple images and show that the choice of the optimal projection center of the rectification is under certain circumstances equivalent to the classical problem of spherical minimax location. We demonstrate the behaviour and the quality of the rectification in real experiments with images from 180 degree field of view fish eye lenses.