Triangulation of Points, Lines and Conics

  • Klas Josephson
  • Fredrik Kahl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4522)


The problem of reconstructing 3D scene features from multiple views with known camera motion and given image correspondences is considered. This is a classical and one of the most basic geometric problems in computer vision and photogrammetry. Yet, previous methods fail to guarantee optimal reconstructions - they are either plagued by local minima or rely on a non-optimal cost-function.

A common framework for the triangulation problem of points, lines and conics is presented. We define what is meant by an optimal triangulation based on statistical principles and then derive an algorithm for computing the globally optimal solution. The method for achieving the global minimum is based on convex and concave relaxations for both fractionals and monomials. The performance of the method is evaluated on real image data.


Fractional Programming Bundle Adjustment Convex Envelope Second Order Cone Program Point Case 
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 Berlin Heidelberg 2007

Authors and Affiliations

  • Klas Josephson
    • 1
  • Fredrik Kahl
    • 1
  1. 1.Centre for Mathematical Sciences, Lund University, LundSweden

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