Geodesic
Analysis of three-channel images based on the theory of three-webs
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 4, Tome 182 (2020), pp. 119-124.

Voir la notice de l'article provenant de la source Math-Net.Ru

Currently, one of the most urgent problems of digital image processing is the search for new mathematical approaches to the analysis and processing of multichannel images. The relevance of these studies is due to the need of optimization of available methods of digital image processing and increase the quality of the results obtained. In this paper, a new approach to processing of digital RGB-images based on the Blaschke theory of three-webs is proposed. Invariants of three-channel images with respect to the widest “topological” transformation group are determined.
Keywords: multichannel image, three-web
Mots-clés : invariant. 
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O. V. Samarina; S. P. Semenov; V. V. Slavskii. Analysis of three-channel images based on the theory of three-webs. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 4, Tome 182 (2020), pp. 119-124. http://geodesic.mathdoc.fr/item/INTO_2020_182_a14/

[1] Bazylev V. T., “O mnogomernykh setyakh i ikh preobrazovaniyakh”, Itogi nauki. Geometriya. 1963., VINITI AN SSSR, M., 1965, 138–164

[2] Blyashke V., Vvedenie v geometriyu tkanei, M., 1959 | MR

[3] Lazareva V. B., “Klassifikatsiya regulyarnykh krugovykh tri-tkanei s tochnostyu do krugovykh preobrazovanii”, Fundam. prikl. mat., 16:1 (2010), 95–-107

[4] Poston T., Styuart I., Teoriya katastrof i ee prilozheniya, Mir, M., 1980

[5] Shelekhov A. M., Lazareva V. B., Utkin A. A., Krivolineinye tri-tkani, Tver, 2013

[6] Samarina O. V., Group Images Invariants, Lambert Academic Publishing, 2010

[7] Samarina O. V., Slavsky V. V., “W. Blaschke's theory application in digital image processing”, J. Math. Sci. Appl., 1:2 (2013), 17–23

[8] Xia G. S., Delon J., Gousseau Y., “Locally invariant texture analysis from the topographic map”, Proc. 19th Int. Conf. on Pattern Recognition (Tampa, Florida, USA, December 8–11, 2008), Paris, France, 2009, 1–4