Geodesic
The Symmetry Groupoid and Weighted Signature of a Geometric Object
Journal of Lie theory, Tome 26 (2016) no. 1, pp. 235-267
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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.
Classification : 18B40, 20L05, 22A22, 53A04, 53A05, 53A55
Mots-clés : Coarea formula, differential invariant, equivalence, global symmetry, groupoid, index, local symmetry, moving frame, piece, signature, submanifold, syzygy, weighted signature 
@article{JLT_2016_26_1_JLT_2016_26_1_a12,
     author = {P. J. Olver},
     title = {The {Symmetry} {Groupoid} and {Weighted} {Signature} of a {Geometric} {Object}},
     journal = {Journal of Lie theory},
     pages = {235--267},
     year = {2016},
     volume = {26},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2016_26_1_JLT_2016_26_1_a12/}
}
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P. J. Olver. The Symmetry Groupoid and Weighted Signature of a Geometric Object. Journal of Lie theory, Tome 26 (2016) no. 1, pp. 235-267. http://geodesic.mathdoc.fr/item/JLT_2016_26_1_JLT_2016_26_1_a12/