Universal Gröbner Bases of (Universal) Multiview Ideals
This provides theoretical foundations for computer vision geometry, though it appears incremental as it builds on existing criteria.
The authors proved that a natural collection of polynomials forms a universal Gröbner basis for multiview ideals and their universal analogs, which model image formation in pinhole cameras, by applying symmetry reduction and induction to handle an infinite family of ideals.
Multiview ideals arise from the geometry of image formation in pinhole cameras, and universal multiview ideals are their analogs for unknown cameras. We prove that a natural collection of polynomials form a universal Gröbner basis for both types of ideals using a criterion introduced by Huang and Larson, and include a proof of their criterion in our setting. Symmetry reduction and induction enable the method to be deployed on an infinite family of ideals. We also give an explicit description of the matroids on which the methodology depends, in the context of multiview ideals.