Point configuration invariants under simultaneous projective and permutation transformations

Reiner Lenz, Peter Meer

Research output: Contribution to journalArticle

35 Scopus citations


The projective invariants used in computer vision today are permutation-sensitive since their value depends on the order in which the features were considered in the computation. We derive, using tools from representation theory, the projective and permutation (p2) invariants of the four collinear and the five coplanar points configurations. The p2-invariants are insensitive to both projective transformations and changes in the labeling of the points. When used as model database indexing functions in object recognition systems, the p2-invariants yield a significant speedup. Permutation invariants for affine transformations are also discussed.

Original languageEnglish (US)
Pages (from-to)1523-1532
Number of pages10
JournalPattern Recognition
Issue number11
StatePublished - Jan 1 1994

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


  • Feature indexing
  • Object recognition
  • Permutation invariants
  • Projective invariants

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