caa a22 4500 467914559 CHVBK 20180406152858.0 cr unu---uuuuu 170328e20060401xx s 000 0 eng 10.1007/s11263-005-4265-x doi (NATIONALLICENCE)springer-10.1007/s11263-005-4265-x Four Points in Two or Three Calibrated Views: Theory and Practice [Elektronische Daten] [David Nistér, Frederik Schaffalitzky] Suppose two perspective views of four world points are given and that the intrinsic parameters are known but the camera poses and the world point positions are not. We prove that the epipole in each view is then constrained to lie on a curve of degree ten. We derive the equation for the curve and establish many of the curve's properties. For example, we show that the curve has four branches through each of the image points and that it has four additional points on each conic of the pencil of conics through the four image points. We show how to compute the four curve points on each conic in closed form. We show that orientation constraints allow only parts of the curve and find that there are impossible configurations of four corresponding point pairs. We give a novel algorithm that solves for the essential matrix given three corresponding points and one of the epipoles. We then use the theory to create the most efficient solution yet to the notoriously difficult problem of solving for the pose of three views given four corresponding points. The solution is a search over a one-dimensional parameter domain, where each point in the search can be evaluated in closed form. The intended use for the solution is in a hypothesise-and-test architecture to solve for structure and motion. Springer Science + Business Media, Inc., 2006 structure-from-motion nationallicence multi-view geometry nationallicence minimal methods nationallicence RANSAC nationallicence Kruppa constraint nationallicence algebraic curves nationallicence Nistér David Sarnoff Corporation, CN5300, 08530, Princeton, NJ, USA aut Schaffalitzky Frederik Robotics Research Group, University of Oxford, UK aut International Journal of Computer Vision Kluwer Academic Publishers 67/2(2006-04-01), 211-231 0920-5691 67:2<211 2006 67 11263 https://doi.org/10.1007/s11263-005-4265-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11263-005-4265-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Nistér David Sarnoff Corporation, CN5300, 08530, Princeton, NJ, USA aut NATIONALLICENCE 700 1- Schaffalitzky Frederik Robotics Research Group, University of Oxford, UK aut NATIONALLICENCE 773 0- International Journal of Computer Vision Kluwer Academic Publishers 67/2(2006-04-01), 211-231 0920-5691 67:2<211 2006 67 11263 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer