Geodesic
Geometrical coding of colored images
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2018), pp. 3-11 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Formal analysis and computer recognition of 2D color images is an important branch of modern computer geometry. However, existing algorithms, although they are highly developed, are not quite satisfactory and seem to be much worse than (unknown) algorithms, which our brain uses to analyze eye information. Almost all existing algorithms omit colors and deal with grayscale transformations only. But in many cases color information is important. In this paper a fundamentally new method of coding and analyzing color digital images is proposed. The main point of this method is that a full-color digital image is represented without dropping colors by a special 2D surface in 3D space, after which it is analyzed by methods of differential geometry rather than traditional gradient-based or Hessian-based methods (like SIFT, GLOH, SURF, Canny operator, and many other algorithms). 
@article{VMUMM_2018_1_a0,
     author = {G. V. Nosovskii},
     title = {Geometrical coding of colored images},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {3--11},
     year = {2018},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2018_1_a0/}
}
TY  - JOUR
AU  - G. V. Nosovskii
TI  - Geometrical coding of colored images
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2018
SP  - 3
EP  - 11
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2018_1_a0/
LA  - ru
ID  - VMUMM_2018_1_a0
ER  - 
%0 Journal Article
%A G. V. Nosovskii
%T Geometrical coding of colored images
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2018
%P 3-11
%N 1
%U http://geodesic.mathdoc.fr/item/VMUMM_2018_1_a0/
%G ru
%F VMUMM_2018_1_a0
G. V. Nosovskii. Geometrical coding of colored images. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2018), pp. 3-11. http://geodesic.mathdoc.fr/item/VMUMM_2018_1_a0/

[1] Bay H., Ess A., Tuytelaars T., Gool L.V., “SURF: Speeded Up Robust Features”, Comput. Vision and Image Understanding (CVIU), 110:3 (2008), 346–359 | DOI

[2] Canny J., “A computational approach for edge detection”, IEEE Trans. Pattern Anal. and Machine Intell., 8:6 (1986), 679–698 | DOI

[3] Lowe D.G., “Object recognition from local scale-invariant features”, Proc. Inter. Conf. on Computer Vision (Corfu, 1999), 1150–1157

[4] Beis J., Lowe D.G., “Shape indexing using approximate nearest-neighbor search in high-dimensional spaces”, Conf. Computer Vision and Pattern Recognition (Puerto Rico, 1997), 1000–1006

[5] Mikolajczyk K., Schmid C., “A performance evaluation of local descriptors”, IEEE Trans. Pattern Anal. and Machine Intell., 10:27 (2005), 1615–1630 | DOI

[6] Bay H., Tuytelaars T., Gool L.V., “SURF: Speeded Up Robust Features”, Proc. Nineth Europ. Conf. on Computer Vision (Graz, Austria, May 2006)

[7] Lindeberg T., “Image matching using generalized scale-space interest points”, J. Math. Imaging and Vision, 52:1 (2015), 3–36 | DOI | MR | Zbl

[8] Ives R.-O., Delbracio M., “Anatomy of the SIFT method”, Image Processing On Line, 2014, 2014–12–22 | Zbl

[9] Nosovskiy G.V., “Computer gluing of 2D projective images”, Proc. Workshop “Contemporary Geometry and Related Topics” (Belgrade, Yougoslavia, 15–21 May 2002), World Scientific, New Jersey–London–Singapore, 2004, 319–334 | DOI | MR

[10] Hartley R., Zisserman A., Multiple View Geometry in Computer Vision, Cambridge Univ. Press, Cambridge, 2000 | MR | Zbl

[11] Hosaka M., Modelling of Curves and Surfaces in CAD/CAM, Springer-Verlag, Berlin–Heidelberg, 1992

[12] Golovanov N.N., Ilyutko D.P., Nosovskii G.V., Fomenko A.T., Kompyuternaya geometriya, Akademiya, M., 2006

[13] Nosovskiy G.V., Skripka E.S., “Error estimation for the direct algorithm of projective mapping calculation in multiple view geometry”, Proc. Workshop “Contemporary Geometry and Related Topics” (Belgrade, Serbia and Montenegro, June 26–July 2, 2005), University of Belgrade, Faculty of Mathematics, Belgrade, 2006, 399–408 | MR