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Geometry and Design of General Catadioptric Imaging Systems

Rahul Swaminathan

Monday, February 09, 2004, 02:00pm - 03:00pm

GRASP Lab, University of Pennsylvania

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The imaging system or camera is central to all vision systems.  Typically when one thinks of a camera one imagines a traditional "perspective lens" based system.  Although very useful these cameras do not suit all applications.  For instance it is impossible to acquire a complete panorama as a single image using a perspective camera. A more general imaging system is therefore needed.

The last decade has seen numerous such general designs using both lenses and mirrors (catadioptric systems).  In general these imaging systems can be classified as either (1) single viewpoint or (2) non-single viewpoint.  In this talk we discuss a general framework to describe the imaging geometry of such general catadioptric cameras.  We derive analytic forms for the viewpoint loci of such systems.  In particular we study catadioptric cameras consisting of reflectors with conic profile, including spherical, parabolic, and hyperbolic.

We then turn to the problem of mirror design for catadioptric imaging.  Many techniques have been proposed in the past for individual mirror designs.  Each technique required considerable skill and effort on the part of the designer.  Also, most methods proposed were case specific. We present a general tool to design the mirror for a specified imaging need.  The specification is provided as an image-to-scene map and a known primary sensor (such as perspective camera).  The appropriate mirror shape is then estimated using splines.  We present numerous designs, both old and new, obtained using this tool.

Rahul Swaminathan