A Tutorial on Catadioptric Image Formation

Simon Baker and Shree K. Nayar

Department of Computer Science

Columbia University

New York, NY 10027

Email: {simonb,nayar}@cs.columbia.edu

Abstract

Conventional video cameras have limited fields of view which make them restrictive for certain applications in computational vision. A catadioptric sensor uses a combination of lenses and mirrors placed in a carefully arranged configuration to capture a much wider field of view. When designing a catadioptric sensor, the shape of the mirror(s) should ideally be selected to ensure that the complete catadioptric system has a single effective viewpoint. The reason a single viewpoint is so desirable is that it is a requirement for the generation of pure perspective images from the sensed image(s). In this tutorial, we derive the complete class of single-lens single-mirror catadioptric sensors which have a single viewpoint. Some of the solutions turn out to be degenerate with no practical value, while other solutions lead to realizable sensors. We also derive an expression for the spatial resolution of a catadioptric sensor in terms of the resolution of the camera used to construct it, and include detailed analysis of the defocus blur caused by the use of a curved mirror in a catadioptric sensor. This tutorial is a extended version of [Baker and Nayar, 1998].

Keywords: Image formation, sensor design, sensor resolution, defocus blur, omnidirectional imaging, panoramic imaging.