Epipolar geometry between photogrammetry and computer vision: a computational guide

B. Alsadik*, Nagham Amer Abdulateef

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)
335 Downloads (Pure)


Stereo image orientation is one of the major topics in computer vision, photogrammetry, and robotics. The stereo vision problem solution represents the basic element of the multi-view Structure from Motion SfM in computer vision and photogrammetry.
A successfully reconstructed stereo image geometry is based on solving the epipolar constraint using the fundamental matrix which is based on the projective geometry in computer vision. However, in photogrammetry, the problem is well known as relative orientation and there is a different solution that is based on the euclidean geometry using collinearity or coplanarity equations.
A lot of literature and discussions were found in the last decades to solve the epipolar geometry problem. However, there is still no clear description to compare between solutions introduced using both projective and euclidean solutions and which method of the relative image orientation is mostly preferred.
To the best of our knowledge, computing and plotting the epipolar lines using photogrammetric collinearity and coplanarity equations is not shown before in the educational litrature. In this paper, a detailed mathematical solution of the epipolar geometry will be shown using both photogrammetric and computer vision techniques. This is aimed to remove any confusion for new learners in using the current methods in both scientific fields and show that using any technique should lead to comparable results with advantages and disadvantages.
Original languageEnglish
Title of host publicationXXIV ISPRS Congress 2022
EditorsA.S. Kumar, P.L.N. Ranju, S.R. Reyes
PublisherInternational Society for Photogrammetry and Remote Sensing (ISPRS)
Number of pages8
Publication statusPublished - 18 May 2022
EventXXIV ISPRS Congress 2022: Congress “Imaging today, foreseeing tomorrow” - Nice, France
Duration: 6 Jun 202211 Jun 2022

Publication series

NameISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences


ConferenceXXIV ISPRS Congress 2022
Abbreviated titleISPRS 2022
Internet address


  • Coplanarity
  • Photogrammetry
  • Relative orientation
  • Essential matrix
  • Fundamental matrix
  • Collinearity


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