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arXiv · 1510.01401

On the Existence of Epipolar Matrices

Sameer Agarwal·Hon-Leung Lee·Bernd Sturmfels·Rekha R. Thomas
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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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Sameer Agarwal, Hon-Leung Lee, Bernd Sturmfels, Rekha R. Thomas. 2015-10-06. On the Existence of Epipolar Matrices. https://arxiv.org/abs/1510.01401

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