Abstract
A new method for describing the equivalence of catadioptric and stereographic projections is presented. This method produces a simple projection usable in all central catadioptric systems. A projective model for the sphere is constructed in such a way that it allows the effective use of Clifford algebra in the description of the geometrical entities on the spherical surface.
This work has been supported by DFG grant So-320/2-3.
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Baker, S., Nayar, S.: A theory of catadioptric image formation. In: Proc. Int. Conf. on Computer Vision, pp. 35–42 (1998)
Baker, S., Nayar, S.: A theory of single view-point catadioptric image formation. International Journal of Computer Vision 35, 175–196 (1999)
Bayro-Corrochano, E., López-Franco, C.: Omnidirectional vision: unified model using conformal geometry. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3021, pp. 536–548. Springer, Heidelberg (2004)
Cameron, J.I.: Applications of Geometric Algebra, first year report. Signal Processing Laboratory, Department of Engineering. University of Cambridge, Cambridge (2004)
Geyer, C., Daniilidis, K.: Catadioptric projective geometry. International Journal of Computer Vision 45, 223–243 (2001)
Doran, C., Lasenby, A.: Geometric Algebra for Physicists. Cambridge University Press, Cambridge (2003)
Li, H., Hestenes, D., Rockwood, A.: Spherical conformal geometry with Geometric algebra. In: Sommer, G. (ed.) Geometric Computing with Clifford Algebras, pp. 61–76. Springer, Heidelberg (2001)
McDonald, B.R.: Geometric Algebra over Local Rings. Marcel Dekker, Inc., New York (1976)
Penrose, R., Rindler, W.: Spinors & Space-Time 1. Cambridge University Press, Cambridge (1984)
Perwass, C., Hildenbrand, D.: Aspects of Geometric Algebra in Euclidean, Projective and Conformal Space. Technical Report Nr.0308, University of Kiel (2002)
Rosenhahn, B., Sommer, G.: Pose estimation in conformal geometric algebra, Part II: Real-time pose estimation using extended feature concepts. Journal of Mathematical Imaging and Vision 22, 49–70 (2005)
Rosenhahn, B., Perwass, C., Sommer, G.: Pose Estimation of free-form contours. Int. Journal of Computer Vision 62, 267–289 (2005)
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© 2005 Springer-Verlag Berlin Heidelberg
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Tolvanen, A., Perwass, C., Sommer, G. (2005). Projective Model for Central Catadioptric Cameras Using Clifford Algebra. In: Kropatsch, W.G., Sablatnig, R., Hanbury, A. (eds) Pattern Recognition. DAGM 2005. Lecture Notes in Computer Science, vol 3663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11550518_24
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DOI: https://doi.org/10.1007/11550518_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28703-2
Online ISBN: 978-3-540-31942-9
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