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Properties of the Catadioptric Fundamental Matrix

  • Christopher Geyer
  • Kostas Daniilidis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2351)

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.

Keywords

Image Point Singular Vector Polar Plane Stereographic Projection Line Image 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002 2002

Authors and Affiliations

  • Christopher Geyer
    • 1
  • Kostas Daniilidis
    • 1
  1. 1.GRASP LaboratoryUniversity of PennsylvaniaPhiladelphiaUSA

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