Existence of Two View Chiral Reconstructions
This addresses a fundamental problem in computer vision for researchers in 3D reconstruction and multiview geometry, but it is incremental as it builds on existing chiral reconstruction theory.
The paper tackles the problem of determining when a set of point pairs can be reconstructed as a scene in front of two cameras, known as a chiral reconstruction, by providing a complete classification for k point pairs. It proves that chiral reconstructions always exist for up to three point pairs, while for five or more, the set without such reconstructions is Zariski-dense, and for five generic pairs, the chiral region is bounded by specific geometric structures.
A fundamental question in computer vision is whether a set of point pairs is the image of a scene that lies in front of two cameras. Such a scene and the cameras together are known as a chiral reconstruction of the point pairs. In this paper we provide a complete classification of k point pairs for which a chiral reconstruction exists. The existence of chiral reconstructions is equivalent to the non-emptiness of certain semialgebraic sets. For up to three point pairs, we prove that a chiral reconstruction always exists while the set of five or more point pairs that do not have a chiral reconstruction is Zariski-dense. We show that for five generic point pairs, the chiral region is bounded by line segments in a Schläfli double six on a cubic surface with 27 real lines. Four point pairs have a chiral reconstruction unless they belong to two non-generic combinatorial types, in which case they may or may not.