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Triangulation of Points, Lines and Conics

På svenska

Author

  • Klas Josephson
  • Fredrik Kahl

Editor

  • Bjarne Ersbøll
  • Kim Pedersen

Summary, in English

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.

Department/s

Publishing year

2007

Language

English

Pages

162-172

Publication/Series

Image Analysis (Lecture Notes in Computer Science)

Volume

4522

Document type

Conference paper

Publisher

Springer

Topic

  • Computer Vision and Robotics (Autonomous Systems)
  • Mathematics

Conference name

15th Scandinavian Conference on Image Analysis

Conference date

2007-06-11 - 2007-06-13

Conference place

Aalborg, Denmark

Status

Published

Research group

  • Mathematical Imaging Group

ISBN/ISSN/Other

  • ISSN: 0302-9743
  • ISSN: 1611-3349
  • ISBN: 978-3-540-73039-2