Abstract
In this paper we consider all imaging systems that consist of reflective and refractive components –called catadioptric– and possessing a unique effective viewpoint. Conventional cameras are a special case of such systems if we imagine a planar mirror in front of them. We show that all unique viewpoint catadioptric systems can be modeled with a two-step projection: a central projection to the sphere followed by a projection from the sphere to an image plane. Special cases of this equivalence are parabolic projection, for which the second map is a stereographic projection, and perspective projection, for which the second map is central projection. Certain pairs of catadioptric projections are dual by the mapping which takes conics in the image plane to their foci. The foci of line images are points of another, dual, catadioptric projection; and vice versa, points in the image are foci of line images in the dual projection. The proved unifying model for all central catadioptric projections gives us further insight to practical advantages of catadioptric systems.
The financial support by DOE-GAANN fellowship, ARO/MURI-DAAH04-96-1- 0007, NSF-CISE-CDS-97-03220, DARPA-ITO-MARS-DABT63-99-1-001, and by Advanced Networks and Services is gratefully acknowledged.
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Geyer, C., Daniilidis, K. (2000). Geometric Properties of Central Catadioptric Projections. In: Sommer, G., Zeevi, Y.Y. (eds) Algebraic Frames for the Perception-Action Cycle. AFPAC 2000. Lecture Notes in Computer Science, vol 1888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722492_15
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DOI: https://doi.org/10.1007/10722492_15
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