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Research Article

Line multiview ideals

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Pages 4204-4225 | Received 31 Mar 2023, Accepted 08 Apr 2024, Published online: 30 Apr 2024

References

  • Agarwal, S., Duff, T., Lieblich, M., Thomas, R. (2022). An atlas for the pinhole camera. Found. Comput. Math. 24:227–277. DOI: 10.1007/s10208-022-09592-6.
  • Agarwal, S., Pryhuber, A., Thomas, R. R. (2019). Ideals of the multiview variety. IEEE Trans. Pattern Anal. Mach. Intell. 43(4):1279–1292. DOI: 10.1109/TPAMI.2019.2950631.
  • Aholt, C., Sturmfels, B., Thomas, R. (2013). A Hilbert scheme in computer vision. Can. J. Math. 65(5):961–988. DOI: 10.4153/CJM-2012-023-2.
  • Borovik, V., Duff, T., Shehu, E. SagbiGbDetection: A Macaulay2 package. Version 0.1. A Macaulay2 package available at: https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages.
  • Breiding, P., Rydell, F., Shehu, E., Torres, A. (2023). Line multiview varieties. SIAM J. Appl. Algebra Geom. (to appear in 2023).
  • Cox, D. A., Little, J., O’Shea, D. (2015). Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 4th ed. Undergraduate Texts in Mathematics. Cham: Springer.
  • Decker, W., Lossen, C. (2006). Computing in Algebraic Geometry. Berlin, Heidelberg: Springer.
  • Eisenbud, D. (1995). Commutative Algebra. New York: Springer.
  • Faugeras, O. D., Mourrain, B. (1995). On the Geometry and Algebra of the Point and Line Correspondences Between N Images. In: Proceedings of the Fifth International Conference on Computer Vision (ICCV 95), Massachusetts Institute of Technology, Cambridge, Massachusetts, USA, June 20-23, 1995, IEEE Computer Society, pp. 951–956.
  • Gathmann, A. (2013/2014). Commutative Algebra, 2013/2014. Class Notes TU Kaiserslautern. Available at: https://www.mathematik.uni-kl.de/∼gathmann/class/commalg-2013/commalg-2013.pdf.
  • Grayson, D. R., Stillman, M. E. (2020). Macaulay2, a software system for research in algebraic geometry. Available at: http://www.math.uiuc.edu/Macaulay2/.
  • Gritzmann, P., Sturmfels, B. (1993). Minkowski addition of polytopes: computational complexity and applications to Gröbner bases. SIAM J. Discrete Math. 6(2):246–269. DOI: 10.1137/0406019.
  • Hartley, R., Zisserman, A. (2004). Multiple View Geometry in Computer Vision. Cambridge: Cambridge University Press.
  • Heyden, A., Åström, K. (1997). Algebraic properties of multilinear constraints. Math. Methods Appl. Sci. 20(13):1135–1162. DOI: 10.1002/(SICI)1099-1476(19970910)20:13<1135::AID-MMA908>3.0.CO;2-9.
  • Michałek, M., Sturmfels, B. (2021). Invitation to Nonlinear Algebra, Vol. 211. Providence, RI: AmericanMathematical Society.
  • Sturmfels, B. (1996). Gröbner bases and Convex Polytopes. University Lecture Series, Vol. 8. Providence, RI: American Mathematical Society.
  • Trager, M., Hebert, M., Ponce, J. (2015). The joint image handbook. In: 2015 IEEE International Conference on Computer Vision, ICCV 2015, Santiago, Chile, December 7–13, 2015, IEEE Computer Society, pp. 909–917.
  • Triggs, B. (1995). Matching Constraints and the Joint Image. In: Proceedings of the Fifth International Conference on Computer Vision (ICCV 95), Massachusetts Institute of Technology, Cambridge, Massachusetts, USA, June 20–23, 1995, IEEE Computer Society, pp. 338–343.

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