Two Hilbert schemes in computer vision

TL;DR

This paper investigates the geometric properties of multiview moduli spaces in computer vision, demonstrating their smoothness, irreducibility, and embedding into Hilbert schemes, and extends classical concepts related to the essential variety.

Contribution

It proves that multiview moduli spaces are always smooth and irreducible, and shows they can be embedded into Hilbert schemes for more than two views, extending prior work.

Findings

Multiview moduli spaces are smooth and irreducible.

These spaces admit open immersions into Hilbert schemes for more than two views.

Extended the classical twisted pair covering of the essential variety.

Abstract

We study multiview moduli problems that arise in computer vision. We show that these moduli spaces are always smooth and irreducible, in both the calibrated and uncalibrated cases, for any number of views. We also show that these moduli spaces always admit open immersions into Hilbert schemes for more than two views, extending and refining work of Aholt-Sturmfels-Thomas. We use these moduli spaces to study and extend the classical twisted pair covering of the essential variety.