Catadioptric Image Formation

Conventional video cameras have limited elds of view that make them restrictive in certain vision applications. A catadioptric sensor uses a combination of lenses and mirrors placed in a carefully designed con guration to capture a much wider eld of view. In particular, the shape of the mirror must be selected to ensure that the complete catadioptric system has a single e ective viewpoint, which is a requirement for the generation of pure perspective images from the sensed image. In this paper, we derive and analyze the complete class of single-lens single-mirror catadioptric sensors which satisfy the xed viewpoint constraint. Some solutions turn out to be degenerate with no practical value while other solutions lead to realizable sensors.