Abstract
The geometry of two uncalibrated views obtained with a parabolic catadioptric device is the subject of this paper. We introduce the notion of circle space, a natural representation of line images, and the set of incidence preserving transformations on this circle space which happens to equal the Lorentz group. In this space, there is a bilinear constraint on transformed image coordinates in two parabolic catadioptric views involving what we call the catadioptric fundamental matrix. We prove that the angle between corresponding epipolar curves is preserved and that the transformed image of the absolute conic is in the kernel of that matrix, thus enabling a Euclidean reconstruction from two views. We establish the necessary and sufficient conditions for a matrix to be a catadioptric fundamental matrix.
The authors are grateful for support through the following grants: NSF-IIS-0083209, SNF-EIA-0120565, NSF-IIS-0121293, NSF-EIA-9703220, a DARPA/ITO/NGI subcontract to UNC, and a Penn Research Foundation grant.
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© 2002 Springer-Verlag Berlin Heidelberg 2002
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Geyer, C., Daniilidis, K. (2002). Properties of the Catadioptric Fundamental Matrix. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds) Computer Vision — ECCV 2002. ECCV 2002. Lecture Notes in Computer Science, vol 2351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47967-8_10
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DOI: https://doi.org/10.1007/3-540-47967-8_10
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