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International Journal of Mathematics and Mathematical Sciences
Volume 2018, Article ID 3950312, 8 pages
Research Article

On Surface Completion and Image Inpainting by Biharmonic Functions: Numerical Aspects

1Mathematical Reviews, The American Mathematical Society, 416 Fourth Street, Ann Arbor, MI 48104, USA
2Department of Mathematics, University of Oklahoma, Norman, OK 73019-3103, USA

Correspondence should be addressed to S. B. Damelin; ude.hcimu@nilemad

Received 22 July 2017; Accepted 11 January 2018; Published 27 February 2018

Academic Editor: Irena Lasiecka

Copyright © 2018 S. B. Damelin and N. S. Hoang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Numerical experiments with smooth surface extension and image inpainting using harmonic and biharmonic functions are carried out. The boundary data used for constructing biharmonic functions are the values of the Laplacian and normal derivatives of the functions on the boundary. Finite difference schemes for solving these harmonic functions are discussed in detail.