International Journal of Scientific Engineering and Technology

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A Variational Approach to Image Inpainting and Text Removal


Affiliations
1 Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, P.O. Box 3900 Kigali, Rwanda
2 Division of Computational Mathematics, Department of Mathematics, Linkoping University, SE–581 83 Linkoping, Sweden
3 Campus Norrkoping, Linkoping University, S-581 83, Norrkoping, Sweden
 

A commonly occurring problem in image processing is the reconstruction of missing data, generally referred to as image inpainting and can be viewed as a 2D interpolation problem. In this paper we present an approach based on variational model to solve the inpainting problem. Previously the total variation model has been successfully used to solve inpainting problems. We introduce a variant of total variation model that includes a parameter q that controls the degree of smoothness of the reconstruction. The corresponding Euler-Lagrange equation is derived and the corresponding boundary value problem solved. Test examples show that the method works well.

Keywords

Inpainting, Total Variation, Minimization, Text Removal.
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  • A Variational Approach to Image Inpainting and Text Removal

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Authors

Japhet Niyobuhungiro
Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, P.O. Box 3900 Kigali, Rwanda
Froduald Minani
Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, P.O. Box 3900 Kigali, Rwanda
Fredrik Berntsson
Division of Computational Mathematics, Department of Mathematics, Linkoping University, SE–581 83 Linkoping, Sweden
George Baravdish
Campus Norrkoping, Linkoping University, S-581 83, Norrkoping, Sweden

Abstract


A commonly occurring problem in image processing is the reconstruction of missing data, generally referred to as image inpainting and can be viewed as a 2D interpolation problem. In this paper we present an approach based on variational model to solve the inpainting problem. Previously the total variation model has been successfully used to solve inpainting problems. We introduce a variant of total variation model that includes a parameter q that controls the degree of smoothness of the reconstruction. The corresponding Euler-Lagrange equation is derived and the corresponding boundary value problem solved. Test examples show that the method works well.

Keywords


Inpainting, Total Variation, Minimization, Text Removal.