A fast optimal algorithm for L2 triangulation

  • Authors:

  • Fangfang Lu;Richard Hartley

  • Affiliations:

  • Australian National University;Australian National University

  • Venue:
  • ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
  • Year:
  • 2007

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Abstract

This paper presents a practical method for obtaining the global minimum to the least-squares (L2) triangulation problem. Although optimal algorithms for the triangulation problem under L8-norm have been given, finding an optimal solution to the L2 triangulation problem is difficult. This is because the cost function under L2-norm is not convex. Since there are no ideal techniques for initialization, traditional iterative methods that are sensitive to initialization may be trapped in local minima. A branch-and-bound algorithm was introduced in [1] for finding the optimal solution and it theoretically guarantees the global optimality within a chosen tolerance. However, this algorithm is complicated and too slow for large-scale use. In this paper, we propose a simpler branch-and-bound algorithm to approach the global estimate. Linear programming algorithms plus iterative techniques are all we need in implementing our method. Experiments on a large data set of 277,887 points show that it only takes on average 0.02s for each triangulation problem.