A Hilbert Scheme in Computer Vision
Printed: Oct 2013
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.
multigraded Hilbert Scheme, computer vision, monomial ideal, Groebner basis, generic initial ideal
14N - unknown classification 14N
14Q - unknown classification 14Q
68 - unknown classification 68