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 $m\le 7$. At the same time, we prove that they exist unconditionally when $m\le 5$. Under a mild genericity condition, we show that an essential matrix always exists when $m\le 4$. 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.

19 pages, 2 figures; This paper is related to our previous paper arXiv:1407.5367. However, the two papers differ enough in their focus and results that they merit being archived separately

References in corpus (1)

• Certifying the Existence of Epipolar Matrices

Cited by in corpus (1)

• The Quadrifocal Variety