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Fast Optimal Three View Triangulation

På svenska

Author

Editor

  • Yasushi Yagi
  • In So Kweon
  • Sing Bing Kang
  • Hongbin Zha

Summary, in English

We consider the problem of $L_2$-optimal triangulation from three separate views. Triangulation is an important part of numerous computer vision systems. Under gaussian noise, minimizing the $L_2$ norm of the reprojection error gives a statistically optimal estimate. This has been solved for two views. However, for three or more views, it is not clear how this should be done. A previously proposed, but computationally impractical, method draws on Gr{"o}bner basis techniques to solve for the complete set of stationary points of the cost function. We show how this method can be modified to become significantly more stable and hence given a fast implementation in standard IEEE double precision. We evaluate the precision and speed of the new method on both synthetic and real data. The algorithm has been implemented in a freely available software package which can be downloaded from the Internet.

Department/s

Publishing year

2007

Language

English

Pages

549-559

Publication/Series

Lecture Notes in Computer Science

Volume

4844

Document type

Conference paper

Publisher

Springer

Topic

  • Computer Vision and Robotics (Autonomous Systems)
  • Mathematics

Keywords

  • Triangulation
  • Gröbner Basis
  • Optimal

Conference name

Asian Conference on Computer Vision (ACCV 2007), 2007

Conference date

2007-11-18 - 2007-11-22

Conference place

Tokyo, Japan

Status

Published

Research group

  • Mathematical Imaging Group

ISBN/ISSN/Other

  • ISBN: 978-3-540-76389-5