Kim Lukas Kiehn: Point-Line Minimal Problems for 3D Reconstruction

Abstract.

In this talk, we provide a brief introduction to the algebro-geometric perspective on 3D reconstruction, and we classify all arrangements of points and lines which are generically always reconstructible from 2D pictures under the assumption of full visibility under uncalibrated pinhole cameras. We discover 8 infinite families and 285 further arrangements not belonging to one of the families, and estimate their complexity by computing their degrees. Finally, we discuss how stabiliser subgroups of sub-arrangements, allow developing a geometric and systematic way to factorise minimal problems into smaller problems, identify minimal problems in under-constrained problems, and formally prove non-minimality.