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Image processing, nonlinear tensor diffusion, coherence enhancing diffusion, numerical solution, semi-implicit scheme, diamond-cell finite volume method, convergence, error estimate, structure segmentation
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].
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