A Theory of Single-Viewpoint Catadioptric Image Formation

  • Authors:

  • Simon Baker;Shree K. Nayar

  • Affiliations:

  • The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA 15213. simonb@cs.cmu.edu;Department of Computer Science, Columbia University, New York, NY 10027. nayar@cs.columbia.edu

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1999

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Abstract

Conventional video cameras have limited fields of view which make themrestrictive for certain applications in computational vision. Acatadioptric sensor uses a combination of lenses and mirrors placed ina carefully arranged configuration to capture a much wider field ofview. One important design goal for catadioptric sensors is choosingthe shapes of the mirrors in a way that ensures that the completecatadioptric system has a single effective viewpoint. The reason asingle viewpoint is so desirable is that it is a requirement for thegeneration of pure perspective images from the sensed images. In thispaper, we derive the complete class of single-lens single-mirrorcatadioptric sensors that have a single viewpoint. We describe all ofthe solutions in detail, including the degenerate ones, with referenceto many of the catadioptric systems that have been proposed in theliterature. In addition, we derive a simple expression for the spatialresolution of a catadioptric sensor in terms of the resolution of thecameras used to construct it. Moreover, we include detailed analysisof the defocus blur caused by the use of a curved mirror in acatadioptric sensor.