On the Existence of Epipolar Matrices
It solves a foundational problem in computer vision for researchers, providing precise existence conditions for epipolar matrices.
This paper addresses the existence of fundamental and essential matrices for point correspondences in two-view geometry, disproving the belief that fundamental matrices always exist for m ≤ 7 and proving unconditional existence for m ≤ 5, with essential matrices existing under mild conditions for m ≤ 4.
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.