Kybernetika 43 no. 6, 777-788, 2007

Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing

Olga Drblíková


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 $L^2(\Omega)$ - a priori estimates for our discrete solution are given. Finally we present our computational results.