Extracting Projective Information from Single Views of 3D Point Sets

In this report we demonstrate the construction of projective invariants for structured three dimensional point sets. We show how to cage points within a polyhedral structure and then introduce indexing functions for polyhedra. The index measures are projective and so no knowledge of the intrinsic or extrinsic parameters of the camera are required. This also enables full use of the perspective imaging model to be used. The results of this report are preliminary, and only introduce the constructs for forming the invariants. The examples we give of the invariant measures are for synthetic projections of simple polyhedra. Future work will test the paradigm thoroughly on real objects and images. 1 Introduction In this paper we report on shape descriptors for three dimensional polyhedra and point sets which may be considered to form the vertices of polyhedra. An image of a polyhedron normally consists of a set of edges that correspond to polyhedral edges, and points that correspond to the p..