Conic Geometry and Autocalibration from Two Images

  • Authors:
  • José I. Ronda;Antonio Valdés

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

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2007

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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.