Departmental Papers (CIS)

Date of this Version

December 2001

Document Type

Journal Article

Comments

Postprint version. Published in International Journal of Computer Vision, Volume 45, Number 3, December 2001, pages 223-243. The original publication is available at www.springerlink.com.
Publisher URL: http://dx.doi.org/10.1023/A:1013610201135

Abstract

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.

Keywords

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

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Date Posted: 30 April 2005

This document has been peer reviewed.