A Functorial Approach to Algebraic Vision

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 embed in suitable Hilbert schemes, and that these embeddings are open immersions for more than four views, extending and refining work of Aholt--Sturmfels--Thomas. We also give a new construction of the space of essential matrices from first principles. This construction enables us to re-prove the fundamental results of Demazure and to re-prove the recent description of the essential variety due to Kileel--Fløystad--Ottaviani as well as extend the classical twisted pair covering of the essential variety.