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On the Existence of Epipolar Matrices

Authors
  • Agarwal, Sameer
  • Lee, Hon-Leung
  • Sturmfels, Bernd
  • Thomas, Rekha R.
Type
Preprint
Publication Date
Oct 05, 2015
Submission Date
Oct 05, 2015
Identifiers
arXiv ID: 1510.01401
Source
arXiv
License
Yellow
External links

Abstract

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 $m$. Using examples we disprove the widely held beliefs that fundamental matrices always exist whenever $m \leq 7$. At the same time, we prove that they exist unconditionally when $m \leq 5$. Under a mild genericity condition, we show that an essential matrix always exists when $m \leq 4$. 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.

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