Indexing Based on Algebraic Functions of Views

In this paper, we propose the use of algebraic functions of views for indexing-based object recognition. During indexing, we consider groups of model points and we represent all the views (i.e., images) that they can produce in a hash table. The images that a group of model points can produce are computed by combining a small number of reference views which contain the group using algebraic functions of views. Fundamental to this procedure is a methodology, based on Singular Value Decomposition and Interval Arithmetic, for estimating the allowable ranges of values that the parameters of algebraic functions can assume. During recognition, scene groups are used to retrieve from the hash table the most feasible model groups that might have produced the scene groups. The use of algebraic functions of views for indexing-based recognition offers a number of ad vantages. First of all, the hash table can be built using a small number of reference views per object. This is in contrast to current approaches which build the hash table using either a large number of reference views or 3D models. Most importantly, recognition does not rely on the similarity between reference views and novel views; all that is required for the novel views is to contain common groups of points with a small number of reference views. Second, verification becomes simpler. This is because candidate models can now be back-projected onto the scene by applying a linear transformation on a small number of reference views of the candidate model. Finally, the proposed approach is more general and extendible. This is because algebraic functions of views have been shown to exist over a wide range of transformations and projections. The recognition performance of the proposed approach is demonstrated using both artificial and real data. © 1998 Academic Press