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arXiv:1107.2875math.AG

A Hilbert Scheme in Computer Vision

Chris Aholt, Bernd Sturmfels, Rekha Thomas

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Abstract

Multiview geometry is the study of two-dimensional images of three-dimensional scenes, a foundational subject in computer vision. We determine a universal Groebner 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.

arXiv comments
26 pages
Journal reference
Can. J. Math.-J. Can. Math. 65 (2013) 961-988
DOI
doi:10.4153/CJM-2012-023-2
Subjects
math.AGAlgebraic Geometry cs.CVComputer Vision and Pattern Recognition

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  1. Why the world of scientific research needs to be disrupted 1 comment

    • Here's a paper I read yesterday. Kindly review it for me: http://arxiv.org/pdf/1107.2875.pdf The scheme you are advocating might have succeeded 200 years ago, when science was happening at a much for fundamental level than it is now. These days, things are so specialized that…

      hyperbovineView on HNParent context

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