Efficient Invariant Representations

Abstract

Invariant representations are frequently used in computer vision algorithms to eliminate the effect of an unknown transformation of the data. These representations, however, depend on the order in which the features are considered in the computations. We introduce the class of projective/permutation p^2-invariants which are insensitive to the labeling of the feature set. A general method to compute the p^2-invariant of a point set (or of its dual) in the n-dimensional projective space is given. The one-to-one mapping between n + 3 points and the components of their p^2-invariant representation makes it possible to design correspondence algorithms with superior tolerance to positional errors. An algorithm for coplanar points in projective correspondence is described as an application, and its performance is investigated. The use of p^2-invariants as an indexing tool in object recognition systems may also be of interest.