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A Theory of Catadioptric Image Formation

Nayar, Shree K.; Baker, Simon

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 paper, we derive and analyze the complete class of single-lens single-mirror catadioptric sensors which satisfy the fixed viewpoint constraint. 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, and include a preliminary analysis of the defocus blur caused by the use of a curved mirror.

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Academic Units
Computer Science
Publisher
Department of Computer Science, Columbia University
Series
Columbia University Computer Science Technical Reports, CUCS-015-97
Published Here
April 25, 2011