Efficient Invariant Representations

  • Authors:

  • Peter Meer;Reiner Lenz;Sudhir Ramakrishna

  • Affiliations:

  • Department of Electrical and Computer Engineering, Rutgers University, P.O. Box 909, Piscataway, NJ 08855-0909, USA;Image Processing Laboratory, Department of Electrical Engineering, Linköping University, S-58183 Linköping, Sweden;Department of Electrical and Computer Engineering, Rutgers University, P.O. Box 909, Piscataway, NJ 08855-0909, USA

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1998

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Abstract

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