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Total variation with nonlocal FT-Laplacian for patch-based inpainting

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Abstract

We consider the problem of inpainting for relatively large damaged areas where the best-known results are achieved using patches. We stem from the ROF-type model. We propose a new ROF model with nonlocal operators and modify it with the F-transform-based operators. As a result, the minimization is considered over a searching space restricted to a finite set of possible reconstructions; each of them is a result of a patch-based inpainting. The fidelity term in the proposed ROF model is estimated by the norm in a Sobolev-like space, which increases the overall quality of reconstruction.

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Notes

  1. The condition \(0<h<2H\) guarantees that every point from \(\mathbb {R}\) is covered by a certain partition element \(A_{k}\).

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Acknowledgements

This work was partially supported by the Project LQ1602 IT4 Innovations excellence in science. The implementation of the F-transform technique is available as a part of the OpenCV framework (Module fuzzy, which is included in opencv_contrib and available at https://github.com/itseez/opencv_contrib).

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  1. Both authors contributed equally to this work.

Authors and Affiliations

  1. University of Ostrava, Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, Ostrava, Czech Republic

    Irina Perfilieva & Pavel Vlašánek

Authors
  1. Irina Perfilieva
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  2. Pavel Vlašánek
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Correspondence to Irina Perfilieva.

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Authors Irina Perfilieva and Pavel Vlašánek declare that they have no conflict of interest.

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Communicated by I. Perfilieva.

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Perfilieva, I., Vlašánek, P. Total variation with nonlocal FT-Laplacian for patch-based inpainting. Soft Comput 23, 1833–1841 (2019). https://doi.org/10.1007/s00500-018-3589-8

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