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000844935 1001_ $$0P:(DE-Juel1)169421$$aKleefeld, Andreas$$b0$$eCorresponding author
000844935 245__ $$aAnomalous diffusion, dilation, and erosion in image processing
000844935 260__ $$aLondon [u.a.]$$bTaylor and Francis$$c2018
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000844935 520__ $$aIn this paper, anomalous sub- and super-diffusion arising in image processing is considered and is modelled by a diffusion equation with fractional time derivative. It might serve as a building block for the construction of various filters. The resulting partial differential equation is discretized in space with centred differences and in time with the explicit or implicit Euler method, respectively. A numerical investigation is performed to illustrate new and interesting results. Additionally, the time derivative of the partial differential equation describing dilation and erosion is replaced by a fractional time derivative and then solved numerically. Interesting new questions arise from the presented numerical results. A short summary and outlook conclude this article.
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000844935 7001_ $$0P:(DE-Juel1)159531$$aVorderwülbecke, Sophia$$b1$$ufzj
000844935 7001_ $$0P:(DE-HGF)0$$aBurgeth, Bernhard$$b2
000844935 770__ $$aAdvances on Computational Fractional Partial Differential Equations
000844935 773__ $$0PERI:(DE-600)2028443-3$$a10.1080/00207160.2017.1423292$$gVol. 95, no. 6-7, p. 1375 - 1393$$n6-7$$p1375 - 1393$$tInternational journal of computer mathematics$$v95$$x1029-0265$$y2018
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