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Line Geometry and Camera Autocalibration

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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 6×6 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.

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Authors and Affiliations

  1. Grupo de Tratamiento de Imágenes, Universidad Politécnica de Madrid, 28040, Madrid, Spain

    José I. Ronda & Guillermo Gallego

  2. Dep. de Geometría y Topología, Universidad Complutense de Madrid, 28040, Madrid, Spain

    Antonio Valdés

Authors
  1. José I. Ronda
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  2. Antonio Valdés
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  3. Guillermo Gallego
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Corresponding author

Correspondence to José I. Ronda.

Additional information

This work has been partly supported by the Spanish Administration agencies CDTI and CICYT under projects CENIT-VISION 2007-1007 and TEC2007-67764 respectively.

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Ronda, J.I., Valdés, A. & Gallego, G. Line Geometry and Camera Autocalibration. J Math Imaging Vis 32, 193–214 (2008). https://doi.org/10.1007/s10851-008-0095-0

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  • DOI: https://doi.org/10.1007/s10851-008-0095-0

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