Journal of Mathematical Imaging and Vision

, Volume 32, Issue 2, pp 193–214 | Cite as

Line Geometry and Camera Autocalibration

  • José I. RondaEmail author
  • Antonio Valdés
  • Guillermo Gallego


We provide a completely new rigorous matrix formulation of the absolute quadratic complex (AQC), given by the set of lines intersecting the absolute conic. The new results include closed-form expressions for the camera intrinsic parameters in terms of the AQC, an algorithm to obtain the dual absolute quadric from the AQC using straightforward matrix operations, and an equally direct computation of a Euclidean-upgrading homography from the AQC. We also completely characterize the 6×6 matrices acting on lines which are induced by a spatial homography.

Several algorithmic possibilities arising from the AQC are systematically explored and analyzed in terms of efficiency and computational cost. Experiments include 3D reconstruction from real images.


Camera autocalibration Varying parameters Absolute quadratic complex 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • José I. Ronda
    • 1
    Email author
  • Antonio Valdés
    • 2
  • Guillermo Gallego
    • 1
  1. 1.Grupo de Tratamiento de ImágenesUniversidad Politécnica de MadridMadridSpain
  2. 2.Dep. de Geometría y TopologíaUniversidad Complutense de MadridMadridSpain

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