Cahn--Hilliard inpainting with the double obstacle potential

Harald Garcke; Kei Fong Lam; Vanessa Styles

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Cahn--Hilliard inpainting with the double obstacle potential

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arxiv 1801.05527 v2 pith:OVKAXHEP submitted 2018-01-17 math.AP cs.CV

Cahn--Hilliard inpainting with the double obstacle potential

Harald Garcke , Kei Fong Lam , Vanessa Styles This is my paper

classification math.AP cs.CV

keywords inpaintingcahn--hilliarddoubleobstaclepotentialproblemresultsapproach

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The inpainting of damaged images has a wide range of applications, and many different mathematical methods have been proposed to solve this problem. Inpainting with the help of Cahn--Hilliard models has been particularly successful, and it turns out that Cahn--Hilliard inpainting with the double obstacle potential can lead to better results compared to inpainting with a smooth double well potential. However, a mathematical analysis of this approach is missing so far. In this paper we give first analytical results for a Cahn--Hilliard double obstacle inpainting model regarding existence of global solutions to the time-dependent problem and stationary solutions to the time-independent problem without constraints on the parameters involved. With the help of numerical results we show the effectiveness of the approach for binary and grayscale images.

Cahn--Hilliard inpainting with the double obstacle potential

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