Work

Line multiview ideals

Year: 2024

Type: article

Abstract: We study the following problem in computer vision from the perspective of algebraic geometry: Using m pinhole cameras we take m pictures of a line in P3. This produces m lines in P2 and the question is which m-tuples of lines can arise that way. We are interested in polynomial equations and therefore study the complex Zariski closure of all such tuples of lines. The resulting algebraic variety is a subvariety of (P2)m and is called line multiview variety. In this article, we study its ideal. We show that for generic cameras the ideal is generated by 3×3-minors of a specific matrix. We also compute Gröbner bases and discuss to what extent our results carry over to the non-generic case.

Source: Communications in Algebra

DOI: 10.1080/00927872.2024.2343762

Authors: Paul Breiding, Timothy Duff, Lukas Gustafsson, Felix Rydell, Elima Shehu

Institutions: Osnabrück University, University of Washington, KTH Royal Institute of Technology, Max Planck Institute for Mathematics in the Sciences

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Deutsche Forschungsgemeinschaft, Knut och Alice Wallenbergs Stiftelse

Awards: PostDoctoral Research Fellowship, Numerische und probabilistische nichtlineare Algebra in den Anwendungen