A Closed-Form Solution for Paraperspective Reconstruction

  • Authors:
  • Etienne Grossmann

  • Affiliations:
  • -

  • Venue:
  • ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 1
  • Year:
  • 2000

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Abstract

We address the problem of 3D reconstruction from image features tracked along a sequence. The most precise algorithms compute the Maximum Likelihood (ML) estimate and are iterative. They need an approximate 3D reconstruction as starting position. For that purpose, we propose a closed-form expression of paraperspective reconstruction.A matrix that approximately verifies the properties of a paraperspective projection matrix is first built, as in Christy and Horaud [1] or Poelman and Kanade [3]. Our contribution lies in showing how to transform this matrix so that it exactly verifies the properties of paraperspective projection matrices. This is done by a closed form expression, in which the depth of the camera is also retrieved. The camera position is then found directly, instead of being obtained as the solution of a non-linear optimization problem, like in [3]. As in [1, 5, 3], we assume that calibration is known.