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Projective Reconstruction in Algebraic Vision

Part of: Artificial intelligence (68Txx) Birational geometry

Published online by Cambridge University Press:  13 November 2019

Atsushi Ito ,
Makoto Miura  and
Kazushi Ueda
Atsushi Ito
Affiliation:
Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, 464-8602, Japan Email: atsushi.ito@math.nagoya-u.ac.jp
Makoto Miura
Affiliation:
Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul, 130-722, Republic of Korea Email: miura@kias.re.kr
Kazushi Ueda
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan Email: kazushi@ms.u-tokyo.ac.jp
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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 Schaffalitzky.

Keywords

computer visionalgebraic visionmultiview geometryprojective reconstructionHilbert scheme

MSC classification

Primary: 14E05: Rational and birational maps
Secondary: 68T45: Machine vision and scene understanding
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 3 , September 2020 , pp. 592 - 609
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Copyright
© Canadian Mathematical Society 2019

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Footnotes

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).

References

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