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High-order discretization of backward anisotropic diffusion and application to image processing

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Abstract

Anisotropic diffusion is a well recognized tool in digital image processing, including edge detection and focusing. We present here a particular nonlinear time-dependent operator together with an appropriate high-order discretization for the space variable. In just a single step, the procedure emphasizes the contour lines encircling the objects, paving the way to accurate reconstructions at a very low cost. One of the main features of such an approach is the possibility of relying on a rather large set of invariant discontinuous images, whose edges can be determined without introducing any approximation.

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Acknowledgements

Both authors are members of GNCS-INDAM (Gruppo Nazionale Calcolo Scientifico - Istituto Nazionale di Alta Matematica), Rome.

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  1. D. Funaro: The authors contributed equally to this work.

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Camerino, Via Madonna delle Carceri 9, Camerino, 62032, Italy

    Lorella Fatone

  2. Dipartimento di Scienze Chimiche e Geologiche, Università di Modena e Reggio Emilia, Via Campi 103, Modena, 41125, Italy

    Daniele Funaro

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  1. Lorella Fatone
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  2. Daniele Funaro
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Correspondence to Lorella Fatone.

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Fatone, L., Funaro, D. High-order discretization of backward anisotropic diffusion and application to image processing. Ann Univ Ferrara 68, 295–310 (2022). https://doi.org/10.1007/s11565-022-00419-4

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