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Epipolar Geometry of Central Panoramic Catadioptric Cameras

T. Pajdla, T. Svoboda and V. Hlavac
Panoramic Vision: Sensors, Theory and Applications
R. Benosman and S.B. Kang, Ed.
Springer, 2001

Abstract

The epipolar geometry of central panoramic catadioptric cameras is presented. Firstly, we show that central panoramic catadioptric cameras are obtained by a combination of (i) a conventional perspective camera with a hyperbolic mirror or (ii) an orthographic camera with a parabolic mirror. Secondly, a complete characterization of the epipolar geometry of central panoramic catadioptric cameras is given as the hyperbolic and the parabolic catadioptric cameras are the only panoramic catadioptric cameras with a single mirror which have a single viewpoint. It is shown that epipolar curves in image become (i) general conics for the hyperbolic camera (ii) ellipses or lines for the parabolic camera. It is advocated that the difference in the estimation of epipolar geometry for conventional and central panoramic cameras consists in image data normalization. A normalization suitable for panoramic cameras is proposed. The effect of normalization is demonstrated for the hyperbolic camera.


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@InCollection{eth_biwi_00232,
  title = {Epipolar Geometry of Central Panoramic Catadioptric Cameras},
  booktitle = {Panoramic Vision: Sensors, Theory and Applications},
  pages = {85-114},
  year = {2001},
  publisher = {Springer},
  keywords = {epipolar geometry}
}