Consistent sets of lines with no colorful incidence
This addresses a theoretical problem in computational geometry for computer vision applications, but appears incremental as it builds on existing questions about colored line incidences.
The paper investigates whether concurrences among lines of k colors in ℝ^d imply at least one concurrence among lines of k+1 colors, with relevance to 3D reconstruction in computer vision, but no concrete results or numbers are provided in the abstract.
We consider incidences among colored sets of lines in $\mathbb{R}^d$ 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.