Consistent Sets of Lines with no Colorful Incidence

Boris Bukh (1) , Xavier Goaoc (2) , Alfredo Hubard (2) , Matthew Trager (3, 4)

1 Carnegie Mellon - Department of Mathematical Sciences
2 LIGM - Laboratoire d'Informatique Gaspard-Monge
3 LIENS - Laboratoire d'informatique de l'école normale supérieure
4 WILLOW - Models of visual object recognition and scene understanding

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.

Mots clés: Projective configuration; Algebraic construction; Probabilistic construction; Image consistency; Incidence geometry

Domaines: Géométrie algorithmique [cs.CG]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Boris Bukh, Xavier Goaoc, Alfredo Hubard, Matthew Trager. Consistent Sets of Lines with no Colorful Incidence. SoCG 2018 - 34thInternational Symposium on Computational Geometry, Jun 2018, Budapest, Hungary. pp.1-20. ⟨hal-01744125⟩