Abstract
While shock filters are popular morphological image enhancement methods, no well-posedness theory is available for their corresponding partial differential equations (PDEs). By analysing the dynamical system of ordinary differential equations that results from a space discretisation of a PDE for 1-D shock filtering, we derive an analytical solution and prove well-posedness. Finally we show that the results carry over to the fully discrete case when an explicit time discretisation is applied.
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Welk, M., Weickert, J. (2005). Semidiscrete and Discrete Well-Posedness of Shock Filtering. In: Ronse, C., Najman, L., Decencière, E. (eds) Mathematical Morphology: 40 Years On. Computational Imaging and Vision, vol 30. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3443-1_28
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DOI: https://doi.org/10.1007/1-4020-3443-1_28
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