1. Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing
- Creator:
- Drblíková, Olga
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- funite volume method, diamond-cell method, image processing, nonlinear parabolic equation, and tensor diffusion
- Language:
- English
- Description:
- 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 \cite{Coirier1} and \cite{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 L2(Ω) - a priori estimates for our discrete solution are given. Finally we present our computational results.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public