@article{7407f10f511e41ed90fd9d433abacd70,
title = "Projective reconstruction in algebraic vision",
abstract = "We discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In particular, we give an algebro-geometric variant of the projective reconstruction theorem by Hartley and Scha{\`o}alitzky.",
keywords = "Algebraic vision, Computer vision, Hilbert scheme, Multiview geometry, Projective reconstruction",
author = "Atsushi Ito and Makoto Miura and Kazushi Ueda",
note = "Funding Information: Received by the editors March 8, 2019; revised October 14, 2019. Published online on Cambridge Core November 13, 2019. A. I. was supported by Grant-in-Aid for Scientific Research (14J01881, 17K14162). M. M. was supported by Korea Institute for Advanced Study. K. U. was partially supported by Grant-in-Aid for Scientific Research (15KT0105, 16K13743, 16H03930). AMS subject classification: 14E05, 68T45. Keywords: computer vision, algebraic vision, multiview geometry, projective reconstruction, Hilbert scheme. 1his condition on the field k allows us to use standard tools in complex algebraic geometry, such as the theorem of Bertini. From the viewpoint of application to computer vision, where the motivation for this paper comes from, the case k = R is of particular interest. As we mention later in this section, the reconstruction theorem for k = R follows from the reconstruction theorem for k = C. Publisher Copyright: {\textcopyright} 2020 Cambridge University Press. All rights reserved.",
year = "2020",
month = sep,
day = "1",
doi = "10.4153/S0008439519000687",
language = "English",
volume = "63",
pages = "592--609",
journal = "Canadian Mathematical Bulletin",
issn = "0008-4395",
publisher = "Canadian Mathematical Society",
number = "3",
}