On the Existence of Epipolar Matrices
| Autor: | Agarwal, Sameer, Lee, Hon-Leung, Sturmfels, Bernd, Thomas, Rekha R. |
|---|---|
| Rok vydání: | 2015 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 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 |
| Databáze: | arXiv |
| Externí odkaz: |
|