Nonlinear Tensor Diffusion in Image Processing

summary:This paper presents and summarize our results concerning the nonlinear tensor diffusion which enhances image structure coherence. The core of the paper comes from [3, 2, 4, 5]. 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 strategy is well-known as diamond-cell method owing to the choice of co-volume as a diamondshaped polygon, see [1]. We present here 2D as well as 3D case of a numerical scheme, see [3, 4]. Then the convergence and error estimate analysis for 2D scheme is presented, see [3, 2]. Last part is devoted to results of computational experiments. They confirm the usefulness this diffusion type not just for an image improvement but also as a pre-processed algorithm. Numerical techniques which require a good coherence of image structures (like edge detection and segmentation) achieve much better results when we use images pre-processed by such a filtration. Let us note that this diffusion technique was successfully applied within the framework of EU projects. It was used to pre-process images for the structure segmentation in zebrafish embryogenesis, see [5]