Departmental Papers (CIS)

Date of this Version

December 2001

Document Type

Journal Article


Postprint version. Published in International Journal of Computer Vision, Volume 45, Number 3, December 2001, pages 223-243. The original publication is available at
Publisher URL:


Catadioptric sensors are devices which utilize mirrors and lenses to form a projection onto the image plane of a camera. Central catadioptric sensors are the class of these devices having a single effective viewpoint. In this paper, we propose a unifying model for the projective geometry induced by these devices and we study its properties as well as its practical implications. We show that a central catadioptric projection is equivalent to a two-step mapping via the sphere. The second step is equivalent to a stereographic projection in the case of parabolic mirrors. Conventional lens-based perspective cameras are also central catadioptric devices with a virtual planar mirror and are, thus, covered by the unifying model. We prove that for each catadioptric projection there exists a dual catadioptric projection based on the duality between points and line images (conics). It turns out that planar and parabolic mirrors build a dual catadioptric projection pair. As a practical example we describe a procedure to estimate focal length and image center from a single view of lines in arbitrary position for a parabolic catadioptric system.


omnidirectional vision, catadioptric systems, conic sections, duality, stereographic projection, calibration



Date Posted: 30 April 2005

This document has been peer reviewed.