Conformal Rectification of Omnidirectional Stereo Pairs

A pair of stereo images are said to be rectified if corresponding image points have the same y-coordinate in their respective images. In this paper we consider the rectification of two omnidirectional cameras, specifically two parabolic catadioptric cameras. Such systems consist of a parabolic mirror and an orthographically projecting lens. We show that if the image coordinates are represented as a point z in the complex plane, then the rectification is specified by coth -1z. This rectification is shown to be conformal, in that it is locally distortionless, and furthermore, it is unique up to scale and transformation. We show an experiment in which two real images have been rectified and a stereo matching performed.