Invariants of projective actions and their application to recognition of fingerprints (Q281030)

In the paper [Int. J. Comput. Vis. 70, No. 1, 55--75 (2006; Zbl 1477.68492)] devoted to computer vision, \textit{D. Mumford} and \textit{E. Sharon} introduced and investigated fingerprints of shape of plane curves in terms of the homogeneous space \(\mathrm{Diff}(S^1)/\mathrm{PSL}_2(\mathbb R)\) (fingerprints, i.h. classes of a diffeomorphisms \(\psi\) in the \(\mathrm{Diff}(S^1)/\mathrm{PSL}_2(\mathbb R)\)). In this paper, the authors study differential invariants of fingerprints in three cases \(\mathrm{Diff}(S^1)/\mathrm{PSL}_2(\mathbb R)\), \(\mathrm{SO}_2(\mathbb R)\setminus\mathrm{Diff}(S^1)/\mathrm{PSL}_2(\mathbb R)\) and \(\mathrm{PSL}_2(\mathbb R)\setminus\mathrm{Diff}(S^1)/\mathrm{PSL}_2(\mathbb R)\) and then use them to study equivalence (recognition) of oriented closed curves under one of the above groups.