Abstract
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 language | English (US) |
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Pages (from-to) | 235-267 |
Number of pages | 33 |
Journal | Journal of Lie Theory |
Volume | 26 |
Issue number | 1 |
State | Published - Jan 1 2016 |
Keywords
- Coarea formula
- Differential invariant
- Equivalence
- Global symmetry
- Groupoid
- Index
- Local symmetry
- Moving frame
- Piece
- Signature
- Submanifold
- Syzygy
- Weighted signature