Evaluation of epipole estimation methods with/without rank-2 constraint across algebraic/geometric error functions

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Citations (Scopus)

Abstract

The best method for estimating the fundamental matrix and/or the epipole over a given set of point correspondences between two images is a nonlinear minimization, which searches a rank-2 fundamental matrix that minimizes the geometric error cost function. When convenience is preferred to accuracy, we often use a linear approximation method, which searches a rank-3 matrix that minimizes the algebraic error. Although it has been reported that the algebraic error causes very poor results, it is currently thought that the relatively inaccurate results of a linear estimation method are a consequence of neglecting the rank-2 constraint, and not a result of exploiting the algebraic error. However, the reason has not been analyzed fully. In the present paper, we analyze the effects of the cost function selection and the rank-2 constraint based on covariance matrix analyses and show theoretically and experimentally that it is more important to enforce the rank-2 constraint than to minimize the geometric cost function.

Original languageEnglish
Title of host publication2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR'07
DOIs
Publication statusPublished - Oct 11 2007
Event2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR'07 - Minneapolis, MN, United States
Duration: Jun 17 2007Jun 22 2007

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
ISSN (Print)1063-6919

Other

Other2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR'07
CountryUnited States
CityMinneapolis, MN
Period6/17/076/22/07

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

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    Migita, T., & Shakunaga, T. (2007). Evaluation of epipole estimation methods with/without rank-2 constraint across algebraic/geometric error functions. In 2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR'07 [4270141] (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). https://doi.org/10.1109/CVPR.2007.383116