2014/07/21 by Sameer Agarwal, Agarwal, Sameer, Hon-Leung Lee +5
Computer Science · Engineering · #Algebraic Geometry (math.AG) #Computer Vision and Pattern Recognition (cs.CV) #Control and Dynamics of Mobile Robots #Digital Image Processing Techniques #FOS: Computer and information sciences #FOS: Mathematics #Robotic Mechanisms and Dynamics
paper · pdf · doi:10.48550/arxiv.1407.5367
openalex publication_date 2014/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a set of point correspondences in two images, the existence of a fundamental matrix is a necessary condition for the points to be the images of a 3-dimensional scene imaged with two pinhole cameras. If the camera calibration is known then one requires the existence of an essential matrix. We present an efficient algorithm, using exact linear algebra, for testing the existence of a fundamental matrix. The input is any number of point correspondences. For essential matrices, we characterize the solvability of the Demazure polynomials. In both scenarios, we determine which linear subspaces intersect a fixed set defined by non-linear polynomials. The conditions we derive are polynomials stated purely in terms of image coordinates. They represent a new class of two-view invariants, free of fundamental (resp.~essential)~matrices.