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A study of nonlinear multiview varieties

Yairon Cid Ruiz (UGent) , Oliver Clarke (UGent) and Fatemeh Mohammadi (UGent)
(2021) ArXiv.
Author
Organization
Abstract
We study the nonlinear generalization of the classical multiview variety, which is a fundamental concept in computer vision. In this paper, we take the first comprehensive step to develop the nonlinear analogue of multiview varieties. To this end, we introduce a multigraded version of the saturated special fiber ring. By applying this tool, we are able to compute the multidegrees of several families of nonlinear multiview varieties.
Keywords
nonlinear multiview varieties, rational maps, multidegrees, mixed multiplicities, saturated special fiber ring, syzygies, blow-up algebras

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MLA
Cid Ruiz, Yairon, et al. “A Study of Nonlinear Multiview Varieties.” ArXiv, 2021.
APA
Cid Ruiz, Y., Clarke, O., & Mohammadi, F. (2021). A study of nonlinear multiview varieties.
Chicago author-date
Cid Ruiz, Yairon, Oliver Clarke, and Fatemeh Mohammadi. 2021. “A Study of Nonlinear Multiview Varieties.” ArXiv.
Chicago author-date (all authors)
Cid Ruiz, Yairon, Oliver Clarke, and Fatemeh Mohammadi. 2021. “A Study of Nonlinear Multiview Varieties.” ArXiv.
Vancouver
1.
Cid Ruiz Y, Clarke O, Mohammadi F. A study of nonlinear multiview varieties. ArXiv. 2021.
IEEE
[1]
Y. Cid Ruiz, O. Clarke, and F. Mohammadi, “A study of nonlinear multiview varieties,” ArXiv. 2021.
@misc{8730908,
  abstract     = {{We study the nonlinear generalization of the classical multiview variety, which is a fundamental concept in computer vision. In this paper, we take the first comprehensive step to develop the nonlinear analogue of multiview varieties. To this end, we introduce a multigraded version of the saturated special fiber ring. By applying this tool, we are able to compute the multidegrees of several families of nonlinear multiview varieties.}},
  author       = {{Cid Ruiz, Yairon and Clarke, Oliver and Mohammadi, Fatemeh}},
  keywords     = {{nonlinear multiview varieties,rational maps,multidegrees,mixed multiplicities,saturated special fiber ring,syzygies,blow-up algebras}},
  language     = {{eng}},
  pages        = {{23}},
  series       = {{ArXiv}},
  title        = {{A study of nonlinear multiview varieties}},
  year         = {{2021}},
}