Book Description

An indexed-based object recognition system using geometric invariance techniques has been designed, and used to recognize buildings in an image of a military site and for recognizing curved planar objects including gasless. New invariants and indexing techniques for polyhedral and curved objects with repetition or bilateral symmetry and objects with the imaged outline of a surface of revolution have been developed. A method to distinguish projectively equivalent but Euclidean distinct objects in an uncalibrated view has been investigated. A group-theoretic framework for relating quasi-invariants to invariants has been formulated. Computing invariants can be formulated as an algebraic manipulation problem involving variable elimination and solving nonlinear polynomial equations. Based on Dixon's formulation of resultants, new methods for eliminating variables have been developed and implemented. These methods are much faster and superior than other elimination techniques. A branch and prune approach for numerically solving polynomial equations has been developed. A simple algorithm for separating invariant relations among object and image features to compute invariants of object features has been designed. These algorithms can serve as a basis for building an invariant work-bench that would enable researchers to experiment with geometric configurations and investigate their geometric invariants.