论文标题
存在两个视图手性重建
Existence of Two View Chiral Reconstructions
论文作者
论文摘要
计算机视觉中的一个基本问题是一组点对是否是两个相机前面的场景的图像。这样的场景和相机一起被称为对点对的手性重建。在本文中，我们提供了k点对的完整分类，并为其提供手性重建。手性重建的存在等效于某些半ge式集合的非空性。对于最多三分，我们证明始终存在手性重建，而没有手性重建的五个或更多点对的集合是Zariski浓密的。我们表明，对于五个通用点对，手性区域在schläflidouble 6中的线段界定在具有27个真实线的立方体表面上。除非它们属于两种非一般组合类型，否则四个点对具有手性重建，在这种情况下，它们可能或可能不会。
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.
