TITLE: Unifying Image Plane Liftings for Central Catadioptric and
Dioptric Cameras

AUTHORS: Joao P. Barreto
GRASP Laboratory, University of Pennsylvania,
Philadelphia PA, 19104
and
ISR/DEEC, University of Coimbra,
Coimbra, Portugal

Kostas Daniilidis
GRASP Laboratory, University of Pennsylvania,
Philadelphia PA, 19104

ABSTRACT:

In this paper, we study projection systems with a single viewpoint,
including combinations of mirrors and lenses (catadioptric) as well
as just lenses with or without radial distortion (dioptric systems).
Firstly, we extend a well-known unifying model for catadioptric systems to
incorporate a class of dioptric systems with radial distortion. Secondly, we
provide a new representation for the image planes of central systems.
This representation is the lifting through a Veronese map of the original
image plane to the 5D projective space. We study how a
collineation in the original image plane can be transferred to a
collineation in the lifted space and we find that the locus of the lifted
points which correspond to projections of world lines
is a plane in parabolic catadioptric systems and a
hyperplane in case of radial lens distortion.


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