Two Hilbert schemes in computer vision

We study the 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 (diagram) Hilbert schemes, and that these embeddings are open immersions for more than four views. Our approach also yields a natural smooth cover of the classical variety of essential matrices that seems not to have appeared in the literature to date.