Geodesic
Differential Invariant Signatures for Planar Lie Group Transformations with Application to Images
Journal of Lie theory, Tome 32 (2022) no. 3, pp. 709-736
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The actions of various Lie groups underlie the change of appearance of objects in images as the viewpoint changes, e.g., through camera motion. Despite significant advances in object recognition using machine learning in recent years, the question of how to recognise an object in an image as its appearance varies through camera motion and similar effects remains open. We demonstrate how differential invariant signatures can be derived for each of the transformation groups, and how the underlying invariances reflect the group-subgroup structure of the relevant Lie groups.
Classification : 65D18, 53A55, 68U10
Mots-clés : Object recognition, planar transformation, planar Lie groups, invariants, differential invariant signature 
@article{JLT_2022_32_3_JLT_2022_32_3_a4,
     author = {R. Brown and S. Marsland and R. McLachlan},
     title = {Differential {Invariant} {Signatures} for {Planar} {Lie} {Group} {Transformations} with {Application} to {Images}},
     journal = {Journal of Lie theory},
     pages = {709--736},
     year = {2022},
     volume = {32},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2022_32_3_JLT_2022_32_3_a4/}
}
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R. Brown; S. Marsland; R. McLachlan. Differential Invariant Signatures for Planar Lie Group Transformations with Application to Images. Journal of Lie theory, Tome 32 (2022) no. 3, pp. 709-736. http://geodesic.mathdoc.fr/item/JLT_2022_32_3_JLT_2022_32_3_a4/