2015/10/06 by Sameer Agarwal, Agarwal, Sameer, Hon-Leung Lee +5 · 1 citation
Computer Science · Engineering · Mathematics · #Algebraic Geometry (math.AG) #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Mathematics and Applications #Matrix Theory and Algorithms #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1510.01401
openalex publication_date 2015/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ≤ 7. At the same time, we prove that they exist unconditionally when m ≤ 5. Under a mild genericity condition, we show that an essential matrix always exists when m ≤ 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.