Existence of Two View Chiral Reconstructions
Abstract
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 nonemptiness 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 Zariskidense. 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 nongeneric combinatorial types, in which case they may or may not.
 Publication:

arXiv eprints
 Pub Date:
 November 2020
 DOI:
 10.48550/arXiv.2011.07197
 arXiv:
 arXiv:2011.07197
 Bibcode:
 2020arXiv201107197P
 Keywords:

 Computer Science  Computer Vision and Pattern Recognition;
 Mathematics  Algebraic Geometry