On The Existence of Epipolar Matrices
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.
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.
Research Areas
