Inpainting in Discrete Sobolev Spaces: Structural Information for Uncertainty Reduction

Author:

Seracini Marco1ORCID,Brown Stephen R.23ORCID

Affiliation:

1. Department of Physics and Astronomy “Augusto Righi”, University of Bologna, 6/2, Viale Carlo Berti Pichat, 40127 Bologna, Italy

2. Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA

3. Aprovechar Lab L3C, Montpelier, VT 05602, USA

Abstract

In this article, we introduce a new mathematical functional whose minimization determines the quality of the solution for the exemplar-based inpainting-by-patch problem. The new functional expression includes finite difference terms in a similar fashion to what happens in the theoretical Sobolev spaces: its use reduces the uncertainty in the choice of the most suitable values for each point to inpaint. Moreover, we introduce a probabilistic model by which we prove that the usual principal directions, generally employed for continuous problems, are not enough to achieve consistent reconstructions in the discrete inpainting asset. Finally, we formalize a new priority index and new rules for its dynamic update. The quality of the reconstructions, achieved using a reduced neighborhood size of more than 95% with respect to the current state-of-the-art algorithms based on the same inpainting approach, further provides the experimental validation of the method.

Publisher

MDPI AG

Subject

Fluid Flow and Transfer Processes,Computer Science Applications,Process Chemistry and Technology,General Engineering,Instrumentation,General Materials Science

Reference50 articles.

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3. Bertalmio, M., Sapiro, G., Caselles, V., and Ballester, C. (2000, January 23–28). Image Inpainting. Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’00, New Orleans, LA, USA.

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