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A Hilbert Scheme in Computer Vision

  • Chris Aholt (a1), Bernd Sturmfels (a2) and Rekha Thomas (a1)
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 ngeneric 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.

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References
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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