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TitleA Hilbert scheme in computer vision.
Author(s) Chris Aholt, Bernd Sturmfels, Rekha R. Thomas
TypeArticle in Journal
AbstractMultiview geometry is the study of two-dimensional images of three-dimensional scenes, a foundational subject in computer vision. We determine a universal Gröbner basis for the multiview ideal of n generic cameras. As the cameras move, the multiview varieties vary in a family of dimension 11n−15. This family is the distinguished component of a multigraded Hilbert scheme with a unique Borel-fixed point. We present a combinatorial study of ideals lying on that Hilbert scheme.
Keywords multigraded Hilbert Scheme, computer vision, monomial ideal, Groebner basis, generic initial ideal
ISSN0008-414X; 1496-4279/e
File
URL http://cms.math.ca/10.4153/CJM-2012-023-2
LanguageEnglish
JournalCan. J. Math.
Volume65
Number5
Pages961--988
PublisherUniversity of Toronto Press, Toronto
Year2013
Edition0
Translation No
Refereed No
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