# Nonlinear Tensor Diffusion in Image Processing

## Main Article Content

## Abstract

The paper deals with the nonlinear tensor diffusion which enhances image structure coherence. First we briefly describe the diffusion model and provide its basic properties. Further we build a semi-implicit finite volume scheme for the above mentioned model with the help of a co-volume mesh. This method is well-known as diamond-cell method owing to the choice of co-volume as a diamond-shaped polygon. The scheme design is shown for $2$D as well as $3$D case, cf. [3,4]. Then the convergence and error estimate analysis for $2$D scheme is presented, cf. [3,2]. The convergence proof is based on Kolmogorov's compactness theorem and a bounding of a gradient in tangential direction by means a gradient in normal direction. We proved that the error of the numerical solution in $L^2$-norm is of order $h$, where $h$ is a spatial step under the natural relation $k \approx h^2$ with a time step $k$. Last part is devoted to results of computational experiments. They confirm the usefulness this diffusion type especially as pre-processed algorithm. Let us note that this numerical technique was successfully applied within the framework of EU projects in such a way for the structure segmentation in zebrafish embryogenesis, cf [5].

## Article Details

How to Cite

Stašová, O., Handlovičová, A., Mikula, K., & Peyriéras, N.
(2017).
Nonlinear Tensor Diffusion in Image Processing.

*Proceedings Of Equadiff 2017 Conference,*, 377-386. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/equadiff/article/view/806/589
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