Omni-directional camera has attracted more attentions in computer vision community due to its quick wide-angle imaging. But the great distortion makes the post-processing complex，which limits the algorithm applications of classical perspective camera.This paper deduces an unwarping algorithm from arbitrary ring omni-directional image to cylinder panorama based on the Taylor model of omni-directional imaging system. And we also present an unwarping method to produce a novel kind of panorama which is composed of N perspective planer images. Both two reprojection unwarpings do not depend on a particular model or accurate parameters of omni-directional system. In the unwarped panoramas，each pixel is assigned with a light ray in the 3D space，which makes the applications of stereo rectification and 3D reconstruction simple. Finally，the experimental results with the simulations and real data illustrate the validity of the proposed method.