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Consistent Sets of Lines with no Colorful Incidence

Authors Boris Bukh, Xavier Goaoc, Alfredo Hubard, Matthew Trager

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Boris Bukh
Xavier Goaoc
Alfredo Hubard
Matthew Trager

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Boris Bukh, Xavier Goaoc, Alfredo Hubard, and Matthew Trager. Consistent Sets of Lines with no Colorful Incidence. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 17:1-17:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.SoCG.2018.17

Abstract

We consider incidences among colored sets of lines in {R}^d and examine whether the existence of certain concurrences between lines of k colors force the existence of at least one concurrence between lines of k+1 colors. This question is relevant for problems in 3D reconstruction in computer vision.

Subject Classification

Keywords
  • Incidence geometry
  • image consistency
  • probabilistic construction
  • algebraic construction
  • projective configuration

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References

  1. Kalle Åström, Roberto Cipolla, and Peter J Giblin. Generalised epipolar constraints. In European Conference on Computer Vision, pages 95-108. Springer, 1996. Google Scholar
  2. Guillaume Batog, Xavier Goaoc, and Jean Ponce. Admissible linear map models of linear cameras. In Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference on, pages 1578-1585. IEEE, 2010. Google Scholar
  3. Edmond Boyer. On using silhouettes for camera calibration. Computer Vision-ACCV 2006, pages 1-10, 2006. Google Scholar
  4. Boris Bukh, Xavier Goaoc, Alfredo Hubard, and Matthew Trager. Consistent sets of lines with no colorful incidence. Preprint arXiv:1803.06267, 2018. Google Scholar
  5. Paul Erdős and George Purdy. Some extremal problems in geometry. Discrete Math, pages 305-315, 1974. Google Scholar
  6. Olivier Faugeras and Bernard Mourrain. On the geometry and algebra of the point and line correspondences between n images. In Computer Vision, 1995. Proceedings., Fifth International Conference on, pages 951-956. IEEE, 1995. Google Scholar
  7. Jacob Fox, János Pach, Adam Sheffer, Andrew Suk, and Joshua Zahl. A semi-algebraic version of Zarankiewicz’s problem. Journal of the European Mathematical Society, 19:1785-1810, 2017. Google Scholar
  8. Ben Green and Terence Tao. On sets defining few ordinary lines. Discrete &Computational Geometry, 50(2):409-468, 2013. Google Scholar
  9. Harald Gropp. Configurations and their realization. Discrete Mathematics, 174(1-3):137-151, 1997. Google Scholar
  10. Larry Guth. Ruled surface theory and incidence geometry. In A Journey Through Discrete Mathematics, pages 449-466. Springer, 2017. Google Scholar
  11. Larry Guth and Nets Hawk Katz. Algebraic methods in discrete analogs of the Kakeya problem. Advances in Mathematics, 225(5):2828-2839, 2010. Google Scholar
  12. Richard Hartley and Andrew Zisserman. Multiple view geometry in computer vision. Cambridge university press, 2003. Google Scholar
  13. Carlos Hernández, Francis Schmitt, and Roberto Cipolla. Silhouette coherence for camera calibration under circular motion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(2), 2007. Google Scholar
  14. Onur Özyeşil, Vladislav Voroninski, Ronen Basri, and Amit Singer. A survey of structure from motion. Acta Numerica, 26:305-364, 2017. Google Scholar
  15. József Solymosi and Miloš Stojaković. Many collinear k-tuples with no k+1 collinear points. Discrete &Computational Geometry, 50(3):811-820, 2013. Google Scholar
  16. Matthew Trager, Martial Hebert, and Jean Ponce. Consistency of silhouettes and their duals. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3346-3354, 2016. Google Scholar
  17. Matthew Trager, Bernd Sturmfels, John Canny, Martial Hebert, and Jean Ponce. General models for rational cameras and the case of two-slit projections. In CVPR 2017 - IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, United States, 2017. URL: https://hal.archives-ouvertes.fr/hal-01506996.
  18. Oswald Veblen and John Wesley Young. Projective geometry, volume 1. Ginn, 1918. Google Scholar
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