Error Analysis for Image Inpainting |
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Authors: | Tony F Chan Sung Ha Kang |
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Affiliation: | (1) Department of Mathematics, UCLA, Los Angeles, CA 90095-1555, USA;(2) Department of Mathematics, University of Kentucky, Lexington, KY 40515, USA |
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Abstract: | Image inpainting refers to restoring a damaged image with missing information. In recent years, there have been many developments
on computational approaches to image inpainting problem 2, 4, 6, 9, 11–13, 27, 28]. While there are many effective algorithms
available, there is still a lack of theoretical understanding on under what conditions these algorithms work well. In this
paper, we take a step in this direction. We investigate an error bound for inpainting methods, by considering different image
spaces such as smooth images, piecewise constant images and a particular kind of piecewise continuous images. Numerical results
are presented to validate the theoretical error bounds.
Tony F. Chan received the B.S. degree in engineering and the M.S. degree in aerospace engineering in 1973, from the California Institute
of Technology, and the Ph.D. degree in computer science from Stanford University in 1978.
He is Professor of Mathematics and currently also Dean of the division of Physical science at University of California, Los
Angeles, where he has been a Professor since 1986. His research interests include mathematical and computational methods in
image processing, multigrid, domain decomposition algorithms, iterative methods, Krylov subspace methods, and parallel algorithms.
Sung Ha Kang received the Ph.D. degree in mathematics in 2002, from University of California, Los Angeles, and currently is Assistant
Professor of Mathematics at University of Kentucky since 2002. Her research interests include mathematical and computational
methods in image processing and computer vision. |
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Keywords: | inpainting total variation minimization error analysis inpainting domain image restoration |
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