Line Multiview Varieties

Abstract

We present an algebraic study of line correspondences for pinhole cameras, in contrast to the thoroughly studied point correspondences. We define the line multiview variety as the Zariski closure of the image of the map projecting lines in 3-space to tuples of image lines in 2-space. We prove that in the case of generic camera matrices the line multiview variety is a determinantal variety, and we provide a complete set-theoretic description for any camera arrangement. We investigate basic properties of this variety, such as dimension, smoothness, and multidegree. Finally, we give experimental results for the Euclidean distance degree and robustness under noise for the triangulation of lines. © 2023 Society for Industrial and Applied Mathematics.