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 publicationProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
DOIs
Publication statusPublished - 2007
Event2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR'07 - Minneapolis, MN, United States
Duration: Jun 17 2007Jun 22 2007

Other

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

Fingerprint

Cost functions
Covariance matrix

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Vision and Pattern Recognition
  • Software
  • Control and Systems Engineering

Cite this

Evaluation of epipole estimation methods with/without rank-2 constraint across algebraic/geometric error functions. / Migita, Tsuyoshi; Shakunaga, Takeshi.

Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2007. 4270141.

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

Migita, T & Shakunaga, T 2007, Evaluation of epipole estimation methods with/without rank-2 constraint across algebraic/geometric error functions. in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition., 4270141, 2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR'07, Minneapolis, MN, United States, 6/17/07. https://doi.org/10.1109/CVPR.2007.383116
Migita T, Shakunaga T. Evaluation of epipole estimation methods with/without rank-2 constraint across algebraic/geometric error functions. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2007. 4270141 https://doi.org/10.1109/CVPR.2007.383116
Migita, Tsuyoshi ; Shakunaga, Takeshi. / Evaluation of epipole estimation methods with/without rank-2 constraint across algebraic/geometric error functions. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2007.
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