Using algebraic functions of views for indexing-based object recognition

Current indexing-based approaches build the hash table using either a large number of reference views or 3D models. In this paper, we propose building the hash table using algebraic functions of views. During preprocessing, we consider groups of model points and we represent all the views (i.e., images) that they can produce in a hash table. These views are computed using algebraic functions of a small number of reference views which contain the group. Fundamental to this procedure is a methodology based on singular value decomposition and interval arithmetic for estimating the ranges of values that the parameters of algebraic functions can assume. During recognition, scene groups are used to retrieve from the hash table the model groups that might have produced them. Using algebraic functions of views for indexing-based recognition offers a number of advantages. First of all, the hash table can be built easier without requiring 3D models or a large number of reference views. Second, recognition does not rely on the similarities between new and reference views. Third, verification becomes simpler. Finally, the approach is more general and extendible.