Geodesic
Image filtering with the use of anisotropic diffusion
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 3, pp. 396-403 
L. E. Rossovskii. Image filtering with the use of anisotropic diffusion. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 3, pp. 396-403. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_3_a3/
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     title = {Image filtering with the use of anisotropic diffusion},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {396--403},
     year = {2017},
     volume = {57},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_3_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A system of nonlinear parabolic equations describing the evolution of a color image is considered. The existence and uniqueness of a global solution to the mixed problem for this system is proved.

[1] Perona P., Malik J., “Scale space and edge detection using anisotropic diffusion”, Proc. IEEE Comp. Soc. Workshop on Computer Vision Washington, IEEE Computer Society Press, 1987, 16–22

[2] Catté F., Lions P.-L., Morel J.-M., Coll T., “Image selective smoothing and edge detection by nonlinear diffusion”, SIAM J. Numer. Anal., 1992, 182–193 | DOI | MR | Zbl

[3] Weickert J., Anisotropic diffusion in image processing, Teubner, Stuttgart, 1998 | MR | Zbl

[4] Weickert J., “Coherence-enhancing diffusion of colour images”, Image and Vision Computing, 17:3–4 (1999), 201–212 | DOI

[5] Zeidler E., Nonlinear functional analysis and its applications II/B: nonlinear monotone operators, Springer-Verlag, New York, 1990 | MR | Zbl