A fractional inpainting model based on the vector-valued Cahn-Hilliard equation / Jessica Bosch, Martin Stoll
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870915657
URN
urn:nbn:de:gbv:3:2-64705
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Autorin / Autor
Beiträger
Erschienen
Magdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, March 26, 2015
Umfang
1 Online-Ressource (29 Seiten = 2,44 MB) : Illustrationen, Diagramme
Ausgabevermerk
Sprache
eng
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Inhaltliche Zusammenfassung
Abstract: The Cahn--Hilliard equation provides a simple and fast tool for binary image inpainting. By now, two generalizations to gray value images exist: Bitwise binary inpainting and TV-H$^{-1}$ inpainting. This paper outlines a model based on the vector-valued Cahn--Hilliard equation. Additionally, we generalize our approach to a fractional-in-space version. Fourier spectral methods provide efficient solvers since they yield a fully diagonal scheme. Furthermore, their application to three spatial dimensions is straightforward. Numerical examples show the superiority of the fractional approach over the classical one. It improves the peak signal-to-noise ratio and structural similarity index. Likewise, the experiments confirm that the proposed model competes with previous inpainting methods, such as the total variation inpainting approach and its fourth-order variant.
Schriftenreihe
Max Planck Institute Magdeburg Preprints ; 15-04 ppn:870173030