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A Hilbert Scheme in Computer Vision |
26 pages
Published:2012-07-19
- Chris Aholt,
- Bernd Sturmfels,
- Rekha Thomas,
Abstract
Multiview 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 |
| MSC Classifications: |
14N - unknown classification 14N 14Q - unknown classification 14Q 68 - unknown classification 68 |