Geyer, Christopher; Daniilidis, Kostas Catadioptric projective geometry. (English) Zbl 0987.68601 Int. J. Comput. Vis. 45, No. 3, 223-243 (2001). Summary: Catadioptric sensors are devices which utilize mirrors and lenses to form a projection onto the image plane of a camera. Central catadioptric sensors are the class of these devices having a single effective viewpoint. In this paper, we propose a unifying model for the projective geometry induced by these devices and we study its properties as well as its practical implications. We show that a central catadioptric projection is equivalent to a two-step mapping via the sphere. The second step is equivalent to a stereographic projection in the case of parabolic mirrors. Conventional lens-based perspective cameras are also central catadioptric devices with a virtual planar mirror and are, thus, covered by the unifying model. We prove that for each catadioptric projection there exists a dual catadioptric projection based on the duality between points and line images (conics). It turns out that planar and parabolic mirrors build a dual catadioptric projection pair. As a practical example we describe a procedure to estimate focal length and image center from a single view of lines in arbitrary position for a parabolic catadioptric system. Cited in 15 Documents MSC: 68U99 Computing methodologies and applications 68U05 Computer graphics; computational geometry (digital and algorithmic aspects) Keywords:parabolic catadioptric system; stereographic projection PDFBibTeX XMLCite \textit{C. Geyer} and \textit{K. Daniilidis}, Int. J. Comput. Vis. 45, No. 3, 223--243 (2001; Zbl 0987.68601) Full Text: DOI