On the Existence of Epipolar Matrices

This paper considers the foundational question of the existence of a fundamental (resp. essential) matrix given m point correspondences in two views. We present a complete answer for the existence of fundamental matrices for any value of m. We disprove the widely held beliefs that fundamental matrices always exist whenever $$m \le 7$$m≤7. At the same time, we prove that they exist unconditionally when $$m \le 5$$m≤5. Under a mild genericity condition, we show that an essential matrix always exists when $$m \le 4$$m≤4. We also characterize the six and seven point configurations in two views for which all matrices satisfying the epipolar constraint have rank at most one.

• Publication year

  2015

• Venue

  International Journal of Computer Vision

• Publication date

  2015-10-06

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1007/s11263-016-0949-7arXiv 1510.01401
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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