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Conic Geometry and Autocalibration from Two Images

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Abstract

We show how the classical theory of projective conics provides new insights and results on the problem of 3D reconstruction from two images taken with uncalibrated cameras. The close relationship between Kruppa equations and Poncelet’s Porism is investigated, leading, in particular, to a closed-form geometrically meaningful parameterization of the set of Euclidean reconstructions compatible with two images taken with cameras with constant intrinsic parameters and known pixel shape. An experiment with real images, showing the applicability of the method, is included.

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Authors and Affiliations

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

    José I. Ronda

  2. Departamento 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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Corresponding author

Correspondence to José I. Ronda.

Additional information

This work has been partially supported by the Ministerio de Educación y Ciencia of the Spanish Government under project TIN2004-07860 (Medusa) and by the Comunidad de Madrid under project S-0505/TIC-0223 (Pro-Multidis).

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Ronda, J.I., Valdés, A. Conic Geometry and Autocalibration from Two Images. J Math Imaging Vis 28, 135–149 (2007). https://doi.org/10.1007/s10851-007-0011-z

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  • DOI: https://doi.org/10.1007/s10851-007-0011-z

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