Geodesic
Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing
Kybernetika, Tome 43 (2007) no. 6, pp. 777-788

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

This paper concerns with the finite volume scheme for nonlinear tensor diffusion in image processing. First we provide some basic information on this type of diffusion including a construction of its diffusion tensor. Then we derive a semi-implicit scheme with the help of so-called diamond-cell method (see [Coirier1] and [Coirier2]). Further, we prove existence and uniqueness of a discrete solution given by our scheme. The proof is based on a gradient bound in the tangential direction by a gradient in normal direction. Moreover, the proofs of $L^2(\Omega )$ – a priori estimates for our discrete solution are given. Finally we present our computational results.
Classification : 35B45, 35K57, 35K60, 65M60, 68U10, 74S10, 94A08
Keywords: finite volume method; diamond-cell method; image processing; nonlinear parabolic equation; tensor diffusion 
@article{KYB_2007__43_6_a2,
     author = {Drbl{\'\i}kov\'a, Olga},
     title = {Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing},
     journal = {Kybernetika},
     pages = {777--788},
     publisher = {mathdoc},
     volume = {43},
     number = {6},
     year = {2007},
     mrnumber = {2388392},
     zbl = {1140.35362},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007__43_6_a2/}
}
TY  - JOUR
AU  - Drblíková, Olga
TI  - Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing
JO  - Kybernetika
PY  - 2007
SP  - 777
EP  - 788
VL  - 43
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2007__43_6_a2/
LA  - en
ID  - KYB_2007__43_6_a2
ER  - 
%0 Journal Article
%A Drblíková, Olga
%T Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing
%J Kybernetika
%D 2007
%P 777-788
%V 43
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2007__43_6_a2/
%G en
%F KYB_2007__43_6_a2
Drblíková, Olga. Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing. Kybernetika, Tome 43 (2007) no. 6, pp. 777-788. http://geodesic.mathdoc.fr/item/KYB_2007__43_6_a2/