Peter Meer(1), Reiner Lenz(2) and Sudhir Ramakrishna(1)
(1)Department of Electrical and Computer Engineering
Rutgers University, Piscataway, NJ 08855, USA
(2)Image Processing Laboratory
Department of Electrical Engineering
Linköping University, S-58183 Linköping, Sweden.
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
The use of p^2-invariants as an indexing tool in object recognition
systems may also be of interest.
International Journal of Computer Vision, 26, 137-152, 1998.