Geodesic
Projective Reconstruction in Algebraic Vision
Canadian mathematical bulletin, Tome 63 (2020) no. 3, pp. 592-609

Voir la notice de l'article provenant de la source Cambridge University Press

We discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In particular, we give an algebro-geometric variant of the projective reconstruction theorem by Hartley and Schaffalitzky.
DOI : 10.4153/S0008439519000687
Mots-clés : computer vision, algebraic vision, multiview geometry, projective reconstruction, Hilbert scheme 
Ito, Atsushi; Miura, Makoto; Ueda, Kazushi. Projective Reconstruction in Algebraic Vision. Canadian mathematical bulletin, Tome 63 (2020) no. 3, pp. 592-609. doi: 10.4153/S0008439519000687
@article{10_4153_S0008439519000687,
     author = {Ito, Atsushi and Miura, Makoto and Ueda, Kazushi},
     title = {Projective {Reconstruction} in {Algebraic} {Vision}},
     journal = {Canadian mathematical bulletin},
     pages = {592--609},
     year = {2020},
     volume = {63},
     number = {3},
     doi = {10.4153/S0008439519000687},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000687/}
}
TY  - JOUR
AU  - Ito, Atsushi
AU  - Miura, Makoto
AU  - Ueda, Kazushi
TI  - Projective Reconstruction in Algebraic Vision
JO  - Canadian mathematical bulletin
PY  - 2020
SP  - 592
EP  - 609
VL  - 63
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000687/
DO  - 10.4153/S0008439519000687
ID  - 10_4153_S0008439519000687
ER  - 
%0 Journal Article
%A Ito, Atsushi
%A Miura, Makoto
%A Ueda, Kazushi
%T Projective Reconstruction in Algebraic Vision
%J Canadian mathematical bulletin
%D 2020
%P 592-609
%V 63
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000687/
%R 10.4153/S0008439519000687
%F 10_4153_S0008439519000687

[ACGH85] Arbarello, E., Cornalba, M., Griffiths, P. A., and Harris, J., Geometry of algebraic curves. Vol. I, Grundlehren der Mathematischen Wissenschaften, 267, Springer-Verlag, 1985. https://doi.org/10.1007/978-1-4757-5323-3 Google Scholar | DOI

[AST13] Aholt, C., Sturmfels, B., and Thomas, R., A Hilbert scheme in computer vision. Canad. J. Math. 65(2013), no. 5, 961–988. https://doi.org/10.4153/CJM-2012-023-2 Google Scholar | DOI

[GKZ08] Gelfand, I. M., Kapranov, M. M., and Zelevinsky, A. V., Discriminants, resultants and multidimensional determinants. Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2008. Google Scholar

[HS09] Hartley, R. I. and Schaffalitzky, F., Reconstruction from projections using Grassmann tensors. Int. J. Comput. Vis. 83(2009), no. 3, 274–293. https://doi.org/10.1007/s11263-009-0225-1 Google Scholar

[HV08] Hartley, R. and Vidal, R., Perspective nonrigid shape and motion recovery. Computer Vision – ECCV 2008, Lecture Notes in Computer Science, 5302, 2008, pp. 276–289. Google Scholar

[Li] Li, B., Images of rational maps of projective spaces. Int. Math. Res. Not. IMRN 2008 no. 13, 4190–4228. https://doi.org/10.1093/imrn/rnx003 Google Scholar

[LV] Lieblich, M. and Van Meter, L., Two Hilbert schemes in computer vision. Google Scholar

[Muk92] Mukai, S., Polarized K3 surfaces of genus 18 and 20. In: Complex projective geometry (Trieste, 1989/Bergen, 1989), London Math. Soc. Lecture Note Ser., 179, Cambridge Univ. Press, Cambridge, 1992, pp. 264–276. https://doi.org/10.1017/CBO9780511662652.019 Google Scholar | DOI

[NHT14] Nasihatkon, B., Hartley, R., and Trumpf, J., On projective reconstruction in arbitrary dimensions. 2014 IEEE Conference on Computer Vision and Pattern Recognition (June 2014, pp. 477–484).10.1109/CVPR.2014.68 Google Scholar

[Ott95] Ottaviani, G., Varietà proiettive di codimensione piccola. Aracne, 1995. Google Scholar

[WS02] Wolf, L. and Shashua, A., On projection matrices 𝓟k to 𝓟2, k = 3, …, 6, and their applications in computer vision. Int. J. Comput. Vis. 48(2002), no. 1, 53–67. https://doi.org/10.1023/A:1014855311993 Google Scholar | DOI

Cité par Sources :