A Hilbert Scheme in Computer Vision
Algebraic Geometry
2019-08-15 v1 Computer Vision and Pattern Recognition
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.
Keywords
Cite
@article{arxiv.1107.2875,
title = {A Hilbert Scheme in Computer Vision},
author = {Chris Aholt and Bernd Sturmfels and Rekha Thomas},
journal= {arXiv preprint arXiv:1107.2875},
year = {2019}
}
Comments
26 pages