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A QCQP Approach to Triangulation

  • Chris Aholt
  • Sameer Agarwal
  • Rekha Thomas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7572)

Abstract

Triangulation of a three-dimensional point from n ≥ 2 two-dimensional images can be formulated as a quadratically constrained quadratic program. We propose an algorithm to extract candidate solutions to this problem from its semidefinite programming relaxations. We then describe a sufficient condition and a polynomial time test for certifying when such a solution is optimal. This test has no false positives. Experiments indicate that false negatives are rare, and the algorithm has excellent performance in practice. We explain this phenomenon in terms of the geometry of the triangulation problem.

Keywords

Singular Value Decomposition Camera Center Global Optimality Condition Epipolar Constraint Trifocal Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Chris Aholt
    • 1
  • Sameer Agarwal
    • 2
  • Rekha Thomas
    • 1
  1. 1.University of WashingtonUSA
  2. 2.Google Inc.USA

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