An SVD Decomposition of Essential Matrix with Eight Solutions for the Relative Positions of Two Perspective Cameras

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

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Abstract

We have made two new contributions in this paper to improve the robustness of a Singular Value Decomposition method to compute the relative positions between two calibrated perspective cameras. The first one is an optimal step to constrain the essential matrix E to have two equal non-zero and one zero singular values in the presence of noise, which is the sufficient condition for E to be factored as a rotation matrix R and translation vector t. The other contribution is that we have found four new possible solutions of R and t to the relative positions of two cameras, which have not been reported in any other SVD methods. Furthermore, these eight possible solutions are derived directly from the eight feasible SVD decompositions. Based on the experiments on both simulation data and real images, this method performs very well and the estimation error of R and t are almost at the same level as the noise.