Line Geometry and Camera Autocalibration

  • Authors:
  • José I. Ronda;Antonio Valdés;Guillermo Gallego

  • Affiliations:
  • Grupo de Tratamiento de Imágenes, Universidad Politécnica de Madrid, Madrid, Spain 28040;Dep. de Geometría y Topología, Universidad Complutense de Madrid, Madrid, Spain 28040;Grupo de Tratamiento de Imágenes, Universidad Politécnica de Madrid, Madrid, Spain 28040

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2008

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Abstract

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脳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.