Möbius invariants in image recognition

Nadiia Konovenko; Valentin Lychagin

doi:10.3934/jgm.2017008

Article Contents

2017, Volume 9, Issue 2: 191-206. Doi: 10.3934/jgm.2017008

This issue Previous Article Local well-posedness of the EPDiff equation: A survey Next Article The group of diffeomorphisms of the circle: Reproducing kernels and analogs of spherical functions

Möbius invariants in image recognition

Nadiia Konovenko^1, and
Valentin Lychagin^2,3,

1.
Department of Mathematics, ONAFT, Odessa, Ukraine
2.
Department of Mathematics, University of Tromsø, Norway
3.
Institute of Control Sciences of RAS, Moscow, Russia

Received: February 2016

Revised: August 2016

Published: October 2017

Abstract / Introduction Full Text(HTML) Related Papers Cited by

Abstract

In this paper rational differential invariants are used to classify various plane shapes as well as plane domains equipped with an additional geometrical object.

Keywords:

Mathematics Subject Classification: Primary: 53A55.

Citation:

FullText(HTML)

Related Papers

Cited by

References

	P. Bibikov and V. Lychagin , Projective classification of binary and ternary forms, Journal of Geometry and Physics, 61 (2011) , 1914-1927. doi: 10.1016/j.geomphys.2011.05.001.
	M. Gordina and P. Lescot , Riemannian geometry of $\mathbf{Diff}(S^{1})$, Journal of Functional Analysis, 239 (2006) , 611-630. doi: 10.1016/j.jfa.2006.02.005.
	E. Kamke, Differentialgleichungen. Lösungsmethoden und Lösungen. Teil Ⅰ: Gewöhnliche Differentialgleichungen, Mathematik und ihre Anwendungen in Physik und Technik, Reihe A, , Bd. Leipzig: Akademische Verlagsgesellschaft, Geest and Portig K. -G., 18 (1959), xxvi+666 pp.
	A. A. Kirillov , Geometric approach to discrete series of unireps for Vir, J. Math. Pures Appl., 77 (1998) , 735-746. doi: 10.1016/S0021-7824(98)80007-X.
	N. Konovenko and V. Lychagin , Invariants of projective actions and their application to recognition of fingerprints, Anal. Math. Phys., 6 (2016) , 95-107. doi: 10.1007/s13324-015-0113-5.
	N. Konovenko and V. Lychagin , Lobachevskian geometry in image recognition, Lobachevskii Journal of Mathematics, 36 (2015) , 286-291. doi: 10.1134/S1995080215030075.
	N. Konovenko, Differential invariants and $\mathfrak{sl}_{2}$-geometries, Naukova Dumka, Kiev, (2013), 188pp. (in Russian).
	I. S. Krasilshchik, V. V. Lychagin and A. M. Vinogradov, Geometry of Jet Spaces and Nonlinear Partial Differential Equations, Advanced Studies in Contemporary Mathematics, 1. Gordon and Breach Science Publishers, New York, 1986.
	B. Kruglikov and V. Lychagin, Geometry of differential equations, Handbook of global analysis, Elsevier Sci. B. V., Amsterdam, 1214 (2008), 725-771. doi: 10.1016/B978-044452833-9.50015-2.
	B. Kruglikov and V. Lychagin , Global Lie-Tresse theorem, Selecta Math., 22 (2016) , 1357-1411. doi: 10.1007/s00029-015-0220-z.
	P. Malliavin , The canonic diffusion above the diffeomorphism group of the circle, C. R. Acad. Sci. Paris, 329 (1999) , 325-329. doi: 10.1016/S0764-4442(00)88575-4.
	P. W. Michor and D. Mumford , An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach, Appl. Comput. Harmon. Anal., 23 (2007) , 74-113. doi: 10.1016/j.acha.2006.07.004.
	M. Rosenlicht , A remark on quotient spaces, An. Acad. Brasil. Ci., 35 (1963) , 487-489.
	G. Segal , The Geometry of the KdV equation, Inter. J. of Modern Physics A, 6 (1991) , 2859-2869. doi: 10.1142/S0217751X91001416.
	E. Sharon and D. Mumford , 2D-Shape Analysis Using Conformal Mapping, International Journal of Computer Vision, 70 (2006) , 55-75. doi: 10.1109/CVPR.2004.1315185.
	E. Witten , Coadjoint Orbits of the Virasoro Group, Commun. Math. Phys., 114 (1988) , 1-53. doi: 10.1007/BF01218287.