The symmetry groupoid and weighted signature of a geometric object

Peter J. Olver

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We refine the concept of the symmetry group of a geometric object through its symmetry groupoid, which incorporates both global and local symmetries in a common framework. The symmetry groupoid is related to the weighted differential invariant signature of a submanifold, that is introduced to capture its fine grain equivalence and symmetry properties. Applications to the recognition and symmetry properties of digital images are indicated.

Original languageEnglish (US)
Pages (from-to)235-267
Number of pages33
JournalJournal of Lie Theory
Issue number1
StatePublished - Jan 1 2016


  • Coarea formula
  • Differential invariant
  • Equivalence
  • Global symmetry
  • Groupoid
  • Index
  • Local symmetry
  • Moving frame
  • Piece
  • Signature
  • Submanifold
  • Syzygy
  • Weighted signature


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