Extracting Projective Information from Single Views of 3D Point Sets

摘要

Projectively invariant indexing functions, given some structural assumptions, are constructed for three dimensional point sets. Projective invariants are derived for two classes of object: the first is for points that lie on the vertices of polyhedra, and the second for objects that are projectively equivalent to ones possessing a bilateral symmetry. The first approach extends to structures whose features can be embedded within conceptual polyhedra and is called caging. The recovery of the projective structure of polyhedra and the application to caging point sets are described. The recovery of projective structure for objects with bilateral symmetry is discussed. The motivations for computing such invariants are: they can be used for recognition; they can be used to compute projective structure. Examples of invariants computed from real images are given.