Unifying Image Plane Liftings for Central Catadioptric and Dioptric Cameras

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 wellknown 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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