Two Hilbert schemes in computer vision

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. In follow-up work, we will use the techniques developed here to give a new description of the essential variety that simultaneously recovers seminal work of Demazure and recent results of Kileel-Fl{\o}ystad-Ottaviani.